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The Astrophysical Journal Supplement Series, 81:163-220, 1992 July © 1992. The American Astronomical Society. All rights reserved. Printed in U.S.A.

OXYGEN-ENHANCED MODELS FOR GLOBULAR CLUSTER STARS. II. ISOCHRONES AND LUMINOSITY FUNCTIONS

Peter A. Bergbusch Department of Physics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2

AND Don A. VandenBerg

Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, B.C., Canada V8W 3P6 Received 1991 August 8; accepted 1991 December 16

ABSTRACT

Isochrones and luminosity functions (LFs) on the 2? F photometric system have been constructed for ages from lOto ISGyrforeach ofthe seven values of [Fe/H] = -2.26, -2.03, -1.78, -1.66, -1.48, -1.26, and-1.03,and for ages from 5 to 18 Gyr for [Fe/H] = -0.78, -0.65, and -0.47. The loci for ages of 10 Gyr or more have been provided mainly for application to photometry of the Galactic globular clusters (GCs); the rest should be useful for interpreting data for old, metal-poor open clusters. Oxygen-to-iron ratios have been assumed that closely follow the relation [O/Fe] = —0.5[Fe/H], for [Fe/H] > -1.0, and [O/Fe] = -0.2[Fe/H] + 0.3, for lower iron abundances. The helium abundance was assumed to vary from Y = 0.2350 to 0.2454 over the adopted range in [Fe/H] while scaled-solar abundances were assumed for all other elements. A new interpolation code was used to generate the isochrones and LFs: as fully described herein, it is based on the technique first developed by Prather, but by using (among other refinements) an improved procedure to select the so-called “Equivalent Evolutionary Phase” points, nothing more sophisticated than linear interpolation is needed to produce exceedingly smooth and accurate results. Comparisons of the isochrones are made with the observed fiducial sequences for a few GCs (specifically M92, Ml3, and 47 Tue) and with a number of the Population II subdwarf standards that have accurate parallax-based distances, to demonstrate that they are consistent with these data within current uncertainties. Illustrative fits of the computed luminosity functions, which are provided for several power-law mass functions, to the observed LFs recently reported in the literature for M92, M13, and 47 Tue are also presented and discussed. The calculations are extensively tabulated: they should be particularly useful for determining the ages of the GCs, and for population synthesis analyses, given that they are predicted for the entire magnitude range

12.

Subject headings: globular clusters: general — luminosity function, mass function — stars: abundances — stars: evolution — stars: interiors

1. INTRODUCTION

Since the mid-1980’s, there have been dramatic improve- ments in the quality of the color-magnitude diagrams (CMDs) for many of the Galactic globular clusters (GCs)—due to the use of the CCD—as well as in the theoretical isochrones used tofitthem(seeHesseretal. 1987; McClure et al. 1987;Stetson & Harris 1988 for some of the best examples to date). How- ever, because the best estimates of cluster distance moduli, derived from the subdwarf and RR Lyrae standard candles, are still uncertain by ±0.2 mag, Renzini’s (1986) remark that “GC ages cannot be determined with an accuracy better than ~25%” is nearly as true today as when it was made more than 5 years ago. And, although it might be tempting to employ morphological arguments to infer the distances and ages of the globulars directly from overlays of synthetic CMDs onto those observed, uncertainties in opacities, convection theory, atmo- spheric boundary conditions, etc., are still too large for this approach to yield rehable results (see VandenBerg 1991 ).

Indeed, were it not for the fact that all of the presently available large grids of isochrones for metal-poor compositions (Hejlesen 1980; VandenBerg & Bell 1985; Green, Demarque, 6 King 1987; Chieffi & Straniero 1989; Straniero & Chieffi

163

1991 ) assume scaled-solar abundances of the heavy elements and, in the case of pre-1988 computations, what are now known to be inappropriate helium contents (Y = 0.2, 0.3), further such computations would really serve very little purpose.1 However, it has now become quite well-established that Y æ 0.24 in GC stars (e.g., see Buzzoni et al. 1983; Caputo, Martinez Roger, & Paez 1987; Dorman, VandenBerg, & Las- karides 1989 ) and that oxygen and other a-nuclei elements are overabundant—i.e., [O, a/Fe] > 0—in metal-poor stars (e.g., see Pilachowski, Sneden, & Wallerstein 1983; Brown, Waller- stein, & Oke 1990; and the reviews by Kraft 1985; Wheeler, Sneden, & Truran 1989). As a result, further sets of isochrones, for the abundances of the chemical elements that

1 The computed turnoff age-luminosity relations for a given chemical composition have not changed significantly as a result of the improve- ments in stellar physics that have occurred since 1970 (e.g., see Vanden- Berg 1983). And, although there are differences in the Tcff and color scales of the isochrones computed by different workers (see, for instance, Chieffi &Straniero 1989), they are well understood (VandenBerg 1991; Pedersen, VandenBerg, & Irwin 1990). Indeed, it has been demonstrated that different codes produce nearly identical results if the same physics is assumed and treated with care (Pedersen, VandenBerg, & Irwin 1991 ).

© American Astronomical Society • Provided by the NASA Astrophysics Data System

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are actually observed, are required in order to obtain the best possible estimates of GC ages (even though associated uncertainties of ^ ±3 Gyr will persist until distance estimates are refined).

It is the main purpose of the present series of papers to provide such models, though as discussed by VandenBerg ( 1992a, hereafter Paper I), it is not presently possible to treat enhancements in the «-nuclei elements Mg, Si, S, etc., correctly. But such elements will influence the stellar structure only through their contribution to the bound-bound and bound-free opacity, which is generally less important than the free-free opacity arising from H and He atoms, particularly for extremely metal-deficient stars. It is much more critical that accurate estimates of Y and [O/Fe] be employed in the calculations, since helium has a major influence on the evolution of a star through the mean molecular weight, while oxygen is a key element in the CNO-cycle and is an important opacity source only at relatively high temperatures (where its contribution to the opacity can be calculated using the Los Alamos Astrophy- sical Opacity Library by Huebner et al. 1977). Indeed, as shown in Paper I, the nucleosynthesis effect of enhanced oxygen is the dominant one for stars with low iron abundances. So, while further work will be required to assess the imphca- tions of high [a/Fe], it is anticipated that they will be less important than those arising from high [O/Fe].

Paper I presented the evolutionary tracks for the values of [Fe/H], [O/Fe], and Y that are listed in Table 1. Reference should be made to that study for a full discussion of the considerable uncertainty that exists in the [ O / Fe] versus [ Fe/ H ] relation that applies to real stars and the reasons why

Í—0.5[Fe/H] ([Fe/H] > —1 ) [O/Fe] = l (1)

[—0.2[Fe/H] + 0.3 ([Fe/H] < -1)

has been adopted. In addition, one of the main contributions of Paper I was the development of an improved set of color-reff

relations and bolometric corrections that satisfies a variety of observational constraints. These transformations are used here without further justification.

Using the new interpolation code that is described in § 2, isochrones and luminosity functions (LFs) have been computed from the tracks reported in Paper I. These are tabulated and discussed in § 3, and brief summarizing remarks are provided in § 4. Particular attention is paid to the properties of the

TABLE 1 Abundance Parameters

Z Zo [O/Fe] [Fe/H] Y

0.000323.... 0.00010 0.000497.... 0.00017 0.000816.... 0.00030 0.001030.... 0.00040 0.001460.... 0.00060 0.002227.... 0.00100 0.003470 .... 0.00170 0.005100.... 0.00300 0.006012.... 0.00400 0.008000 .... 0.00600

+0.75 -2.26 0.2350 +0.70 -2.03 0.2350 +0.66 -1.78 0.2351 +0.63 -1.66 0.2352 +0.60 -1.48 0.2354 +0.55 -1.26 0.2358 +0.50 -1.03 0.2368 +0.39 -0.78 0.2391 +0.30 -0.65 0.2413 +0.23 -0.47 0.2454

LFs in view of the likelihood that we are close to reaching the Unfit of what can be learned from CMD fits (at least for the foreseeable future). Since it is known from previous theoretical work (e.g., by Simoda & Iben 1970; Ratchff 1987) that the shape of the LF through the turnoff to the lower red giant branch depends on Y, [Fe/H], and age, luminosity functions might offer the means by which, for instance, the absolute ages of the globulars can be more tightly constrained. As Renzini & Fusi Pecci ( 1988) have reminded us in their excellent review, LFs give a direct measure of the relative evolutionary lifetimes of stars in different parts of the CMD and therefore provide a much deeper, more stringest test of stellar structure theory than the fitting of isochrones to photometric observations. And, surprising as it may seem, it has not yet been firmly estab- Ushed from LF work that canonical evolutionary theory even apphes to globular cluster stars. In fact, there are some indications to the contrary (e.g., Faulkner & Swenson 1991 ; Vanden- Berg & Stetson 1991).

So there is much to be gained from high-precision, accurate luminosity functions once they become available. Although a considerable effort over the past 25 years has already been made to obtain such data—generally by photographic means (see Ratchff’s [1987] fine summary of this work)—it has become clear (e.g., Bergbusch 1990) that much higher quality data are required in order to be able to draw meaningful conclusions from comparisons with theoretical predictions. Most recent CCD studies have concentrated on the faint main-sequence distributions of GC stars, where the shape of the LF depends essentially entirely on the mass function, and they have produced important new revelations (e.g., see Richer & Fahlman 1991, and references therein ). The power of luminosity functions to assist one’s understanding of stellar populations is nicely demonstrated in Mighell’s ( 1990) study of the Carina dwarf spheroidal galaxy. To further assist such studies and in anticipation of similar attention being given to the turnoff and more advanced phases in GCs in the near future, we provide detailed luminosity functions for about a 15 mag range between Mv ~ 12 and Mv 3 ( helium flash luminosities) for a wide variation in age and metaflicity.

2. NUMERICAL METHODS

2.1. Mathematical Formalism

Deep CCD studies have revealed that the CMDs of the Ga- lactic globular clusters tend to be exceedingly tight through the turnoff region, with a photometric scatter that is fully consistent with (small) observational uncertainties. This result provides very strong support for the basic assumptions that are made about the stars in most globular clusters; namely, that ( 1 ) they are coeval, and ( 2 ) the material out of which they were formed was chemically homogeneous. These assumptions, together with the Vogt-Russell Theorem, imply that at any given epoch, the number of stars, 0(L)rfL, in the luminosity interval (L, L + dL) is equal to the number of stars, N(J()dJ(, in the corresponding mass interval {Jí, JÍ + dJi). The quantity (/>(L) is called the luminosity function (LF), and the quantity N {.JÍ) is called the initial mass function (IMF).2 Formally,

2 What is observed, of course, is the present mass function (PMF ). How well this matches the IMF will depend on the various dynamical processes that have occurred during the cluster’s existence.


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the equality is expressed as

<!){L)dL = N(Jt)dJt, (2)

vihzTtL = L(J(,t),anAN(J() oc ^~<1+x) is the form usually adopted for the IMF. The LF may then be expressed as

<HL) = N(JÏ)^-, (3)

and it remains to find a suitable expression for the derivative dJi /dL which can be evaluated from the theoretical evolutionary tracks and isochrones.

For a set of evolutionary sequences that have been computed with a certain helium abundance and metallicity, the luminosity can be treated as a function of two variables— mass, Jt, and age, t. The functional relation L = L(M, t) then defines a surface in the L-Ji-t coordinate frame. As illustrated in Figure 1, the difference in luminosity, dL, between the points Px and P2 along the direction 0 in the Jf-t plane is given by

dL ds

dL{Jtx,tx) dJ(

sin 0 + dL^M^D

dt cos 0 , (4)

where ds = {dJi2 + dt2)1'2. (The direction 0 will be identified with the direction of interpolation between equivalent evolutionary phases [see § 2.2] in tracks of different mass.) Rearranging equation (4), we get

dL(J(x, tx) dJt

dL ds

esc 0 - dt

cot 0 M

L

Fig. 1.—The L-Ji-t coordinate frame showing the relation between dL, dM, dt, and the direction of differentiation 0.

dL ds dL{Jix,tx) ds dJi

dL{Jix, tx) dJi

dt dt

M brM

dL{Jix, tx) dt

dt

M djH • (5)

Taking this result back to equation (3), the LF may now be expressed as

<¡)(L) = N{M) (6)

where dL

may be evaluated at points along an isochrone via

dL and

dt equation (5). The quantities ^ „ „ ^

^ ^ dM dL

along the direction of interpolation, while — dt

are evaluated

is interpo-

lated to the isochrone point from its values obtained numeri- cally along the evolutionary tracks.

In practice, logarithmic quantities (i.e., log L/LG, log TeS, log t) are employed when describing stellar models and evolutionary sequences, but each sequence is identified by its mass. Thus, on the theoretical plane, equation (6) becomes

^[log (L/Lg)] = N(.Jl) d log L/L0

(7)

where the use of log J( has deliberately been avoided. One reason for doing this is that no interpolation advantage is gained by the use of log Jt because the stellar masses consid- ered range between 0.15-1.5eJf0; another justification is that the equations are simplified-using log Jt would have intro- duced Jt into the equations anyway.

The advantage of this approach to calculating model LFs, over direct integration of the mass-luminosity relation, is that the range in mass from the base to the tip of the giant branch is less than 0.01^0 for the metallicities and ages we are concerned with, which can lead to considerable numerical noise in the interpolated masses along the isochrone. However, by a suitable choice of equivalent evolutionary phases (see below), the interpolations between the tracks to the desired isochrones can be made very nearly linear, resulting in well determined

values for d log L

dM and

d log t dM

in equation (5). Moreover,

is a smoothly varying and well-determined function M

along the evolutionary tracks, and thus may easily be interpolated to the location of the isochrone.

To transform the model LFs from the theoretical plane [log (^(Mhoj) versus M^] to the observer’s plane [log 0(F) vs. V], where V is the V-magnitude, we use the bolometric correc- tion, BCV, defined by

dlogL d log t

Mxd = V + BCk . (8)

Differentiating equation (8) with respect to M along an


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dlogZ, d.Æ

1 / dV 2.5

dBCy àJi

(9)

isochrone gives

so that the model LF, transformed to the observer’s plane, can then be written

0(F) = V(.. -2.5 d log L

d.M (3BC,

(10)

In practice, we have not attempted to calculate the derivative dBC v . Instead, we have defined the bin limits of the differen-

tial luminosity function for the K-magnitude, and interpolated to the corresponding values.

2.2. Equivalent Evolutionary Phases

We wish to set up an interpolation scheme that will produce isochrones accurately from a set of evolutionary sequences for stars of different masses but with a common chemical composition. Equivalent evolutionary phases (EEPs) are locations on these sequences that share a common property, such as the same central hydrogen content—i.e., at the zero-age main-sequence ( ZAMS ) or core hydrogen exhaustion ( CHE ) points— or helium core mass ( Prather 1976). Such definitions of equiv- alence are somewhat arbitrary, but they do produce an essentially linear interpolation scheme, which has obvious ad- vantages with respect to interpolation accuracy.

The equivalent evolutionary phases defined here are based

on the behavior of the derivative along the evo- d(log t) ^

lutionary sequences,3 and these equivalent points reflect the nature of the EEPs as defined by Prather (i.e., similar hydrogen content) as well as the structural changes in the star ( essentially the response of the stellar atmosphere to the evolving core ). Furthermore, because this approach uses the mathematical properties of the curves defined by the evolutionary sequences in the log L-log Tplane, it has the advantage that only these quantities are needed to define the interpolation scheme. As will be shown in the following discussion, interpolation between corresponding primary EEPs on tracks of different masses is also very nearly linear, so by dividing the corresponding regions between the primary EEPs into equal numbers of secondary interpolation points, the essential linearity of the interpolations is preserved.

2.2.1. Zero-Age Main Sequence

The evolutionary sequences used to produce the isochrones and luminosity functions were contracted to their ZAMS points from fully convective, chemically homogeneous models high on the Hayashi track. But, because of the vastly different rates at which stars of different mass evolve, the definition of a ZAMS point is somewhat arbitrary. For the upper main-sequence grids, VandenBerg & Laskarides ( 1987) have shown

3 The derivative with respect to time of log L or of the “distance along a track,” measured in terms of the changes in log L and log refr, could also be used.

that a very smooth age-luminosity relation can be obtained if the ZAMS locus is defined by the points on the tracks which share a common central hydrogen content (Xc) and for which at least 99% of the luminosity is generated by nuclear reactions instead of by gravitational contraction. However, when this criterion is applied to the low-mass (^0.5.//©) evolutionary sequences, the first model retained already has an age of several gigayears (depending on the value of Xc selected), with monotonically higher ages for lower masses (>10 Gyr for masses < 0.35,//©). For our purposes, it is sufficient to consider only the models following the point of minimum luminosity on these low-mass tracks. At this point, the ages range from ^4 Gyr for the 0.15,#© sequences, depending on the metal abundance, to ^1.5 Gyr for those of 0.45,#©. (These are, of course, still much longer than the actual pre-main- sequence lifetimes of such stars.) The chief advantage of this approach is that we avoid the complicated morphology of the evolutionary sequences that occurs before the luminosity minimum.

It should be noted that these definitions for the ZAMS points are not based entirely on the morphology of the evolutionary loci in the log L-log TeS plane. Moreover, because the ZAMS can be divided into regions where fundamental changes in the structure and consequent evolution of a star occur (i.e., near 0.35,#© and just above 1.1«#©), these definitions do not produce linear interpolations over the entire mass range. Evo- lutionary sequences with masses of ~0.65,#© or smaller do not achieve core hydrogen exhaustion within times compara- ble to the estimated age of the universe, so the isochrone and LF points for the lower main-sequence were obtained from them by interpolating to the desired age along the tracks. The tabulated isochrone and LF points were then obtained from cubic sphnes that were constructed for each isochrone from these points.

2.2.2. Core Hydrogen Exhaustion

In the evolutionary sequences that have the convective hook-back feature following central hydrogen exhaustion, the CHE point corresponds to a local TeS minimum, while the sequences without it have the CHE point at a local reff maximum. There is an intermediate mass range over which a temperature maximum occurs before the CHE point (see Fig. 2b). We have opted to assign the CHE point to the location where

= 0 for the first time after the ZAMS point, M

unless a local temperature minimum is located before the end of the track, in which case the CHE point is identified with the second occurrence of the zero.4 As will be shown below, the

¿(log ^eff) ¿(log 0

4 By ignoring the temperature maximum that sometimes occurs before the CHE point, we are clearly glossing over the morphological differences of the sequences in the CMD. The main reason for doing so is to enforce the requirement—for simplification—that age be a monotonie function of mass in the interpolation scheme. This may not be correct. As Maeder & Meynet ( 1989; see their Fig. 17) have recently pointed out, there is a near discontinuity in the age versus turnoff luminosity relations between ^;1.2^0 and ;S1.1*#Q, in the sense that the age barely changes over this mass range (at least in canonical as opposed to overshooting stellar models). This seems to be a real physical effect brought on by the development of the convective core. We have carried out a further, although preliminary, investigation of the detailed development of the hook-back feature,


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interpolation relations for the CHE point are remarkably linear up to the models in which the blue hook appears.

2.2.3. The Blue Hook

The blue hook (BH) first appears in the evolutionary sequences for masses greater than ~1.L#0, and more noticeably in the more metal rich sequences. Temperature evolution first accelerates from the CHE point to a location near the middle of the hook, and then decelerates to the end. Thus at

the middle of the hook, has a maximum, while it d(log t) ^

is zero at the beginning (CHE point) and at the end. Because the hook does not occupy a large region of the CMD, only the endpoint of the hook was adopted as a primary EEP: this does not seem to have affected the accuracy of the interpolations to any significant extent.

The BH feature does not occur in the evolutionary tracks with masses typically less than ~ l.L#0, so that near l.L#0

the CHE becomes a branch point in the interpolation scheme —one branch connects all the CHE points in the grid, the other connects the lower mass CHE points to the BH points on the higher mass tracks. The tendency for the hook to develop becomes apparent as a “dimple” in the turnoff* region of the tracks for masses of less than ~ 1.15.#0 preceding its obvious appearance. To avoid having the BH points branch too sharply from the CHE points, thus introducing a severe nonlinearity into the interpolations, a primary EEP point is added at the end of the “dimple,” which seems to correspond with the end of the hook in the higher mass tracks. The location of this EEP was sometimes adjusted slightly in the lower mass track adja- cent to the first one with a BH in order to preserve a monotonie relationship between age and mass (see footnote 4).

2.2.4. Post-Main-Sequence EEPs

The remaining EEPs, except for the one at the tip of the giant

branch, are defined by the locations where d^yr has a d(log t) ^

local maximum or minimum. These local extrema occur at the middle of the Hertzsprung gap region (a minimum), at the base of the giant branch (a maximum), the beginning of the evolutionary pause on the giant branch (a minimum), the end of the pause (a maximum), and just below the tip of the giant branch (a minimum). Not all of these extrema are necessary for the construction of a good interpolation scheme, particularly where they are closely spaced (e.g., the evolutionary pause on the giant branch, or as mentioned in § 2.2.3, the BH feature), because the interpolated quantities do not undergo large variations in these regions. (On the other hand, were it necessary to follow very closely the evolution through the BH, for example, then the CHE point as well as both local extrema

over the narrow mass range where it first appears, and we find that intermediate masses («1.15Ji0) can have marginally greater ages at the CHE point than slightly higher or lower mass values. However, indications are that this “problem” will have no more than a small effect on the 5 Gyr isochrones in our grid ( it certainly has no effect whatsoever on our calculations for older ages). We intend to examine this interesting phenomenon further in the near future.

along the hook could be used.) Similarly, at the tip of the giant branch, only a few points on each evolutionary sequence follow the point at the temperature minimum, which signals the imminent development of the helium flash. To ensure that our interpolation scheme reaches to the extreme giant branch tip, we have adopted the last point in each evolutionary sequence as the final EEP.

In Figure 2a, the locations of the EEPs defined in this way

are identified on the - derivative, while in Figure ¿(log t) ^

2b, the locations of the primary EEPs are shown on a grid of evolutionary tracks. A schematic representation illustrating the essential Unearity of the interpolation method is shown in Figure 3.

2.3. Joining the Giant Branch to the Main-Sequence Track

As described in Paper I, the stellar structure equations in their usual Lagrangian form were solved to generate the evolutionary tracks for the pre-main-sequence, main-sequence, and subgiant phases; while the giant branches were constructed using Eggleton’s (1971) non-Lagrangian technique. We now comment on the two difficulties that arose in our initial at- tempts to sphee the two parts of a given track together.

The first problem was that the predicted reff’s from the La- grangian code became increasingly noisy as the track ap- proached the base of the red giant branch ( RGB ). This was not obvious in a plot of the track on the H-R diagram, where it appeared to be very smooth, but was clearly apparent in the

derivative . We found that an appreciable fraction ¿(log t)

of this noise could be eliminated by improving the time-step algorithm, because it was noticed that instability in the derivative was usually associated with erratic behavior in the size of the time step between models. We believe that the remaining noise is consistent with that expected from the modeling of a star with a finite number of mesh points, the discrete nature of the nucleosynthesis over a given time step, the errors associated with the various interpolations that are made in con- structing a stellar model, etc.

The second difficulty was (and is) associated with the relax- ation of the first few models that are obtained with the Eggle- ton code (using very short time steps). Again, the effect is not obvious in a CMD, but can clearly be seen in the derivative

• Typically, eight to 11 models along the track are ¿(log t) computed before the evolutionary behavior begins to follow that at the end of the tracks generated with the Lagrangian code. These initial models were deleted before joining the two parts of a given track together.

After dealing with these problems, there remain small systematic differences in log Teff and in log t between the portions of the tracks generated by the two different codes. The shifts are quite small (typically, Alog Teff « 5 X 10-4 at log Teff = 3.7, which implies Areff = 2.5 K) and are smaller than the uncertainties in the models themselves, but they cause noticeable spikes in the derivatives. Since the Eggleton code produces considerably smoother tracks because it is much more adept at following the evolution of a thin H-buming shell—which it was designed to do—we chose to adjust the ends of the Lagran-


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Fig. 2a

Fig. 2.—(a) The locations of the primary interpolation points (EEPs) are identified according to the behavior of the temperature derivative (solid curve). The EEPs shown are those for the ( 1 ) ZAMS, (2 ) CHE, ( 3) BH, (4) Hertzsprung gap, (5) base of the GB, (6) GB evolutionary pause, and (7) GB tip. The corresponding locations on the luminosity derivative (dashed curve) are also indicated. The independent quantity Z) is a measure of the distance along the track in the log L-log 7^ plane, (b) Evolu- tionary tracks for the indicated composition with the locations of the primary EEPs as defined in (¿z) given by the small crosses.

gian calculations so as to make a smooth join to the giant branches. The first step was to delete those Lagrangian models with ages greater than the age at the join. Then the effective temperatures of the last 20 remaining points on the post- main-sequence portion of these tracks were corrected so as to

À produce a smooth match in the log L-log TeS plane. (Re- cé member that these adjustments in log Teff amount to only a ^ few parts in 104.) Finally, the age along the giant branch was

adjusted by applying a constant A/ at each point, so that the , . . <9(log L) A d(log reff) . derivatives / and ' ° - were smooth across the

¿(log/) d(log t) join. These techniques have proven so successful that it is not generally possible to detect the location of the join in the log L-log Jeff plane (see Figure 2b, for example), nor are any discontinuities evident in the derivatives.

2.3.1. Idealized Upper Giant Branches

Above the location of the pause on the giant branch, the evolutionary sequences occasionally show evidence of a problem with the interpolation in the tables of photospheric pres- sures, from which the pressure boundary condition was de-

Fig. 3.—The interpolation scheme to produce isochrone points for the primary EEPs corresponding to the CHE, BH, Hertzsprung gap, and GB pause—as identified in Fig. 2—is illustrated. (The development of the BH in the higher mass models shows the largest deviation from linearity.) Given that an isochrone is a horizontal fine in the uppermost panel, the intersection of that line with each of the EEP curves in this panel will yield a number of mass values. From these, the corresponding luminosity and temperature information can be readily determined using the middle and lower panels.


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rived. Recall from Paper I that adjustments were made of the log P values originally obtained from published model atmospheres, particularly of those for low log g, in order to obtain predicted RGBs whose slopes on the (M^, log Teff)-plane agreed well with those inferred from infrared photometry for a number of GCs like M92 and 47 Tue. Although every effort was made to revise this table in a way which would not intro- duce any kinks in the model sequences, only partial success was possible. ( It can be appreciated that it is a nontrivial task to estimate how much of a change in the surface pressure is needed to shift a particular RGB model a certain amount in log Teff and to alter a three-dimensional table of numbers—in log g, log reff, and [Fe/H]—to achieve a smooth, systematic shift of an entire track.) One manifestation of the resultant

,, - , d(l0g T^ff) . , . problem is that d(iQg ¿ ) 18 on ^ Piece_wise continuous over

this region of the CMD, which is almost certainly due to changes from one interpolation regime to another in the pressure tables. Another manifestation of this problem is that some of the RGBs develop a reverse curvature near the tip. Because the model atmospheres are themselves uncertain for giant branch models, and because of the deviations from expected behavior just mentioned, we have chosen to idealize the upper portion of the giant branch in the following way:

1. The luminosity and effective temperature values of the last point on the RGB evolutionary sequence and of the point coinciding with the temperature derivative maximum at the evolutionary pause (the sixth primary EEP; see Fig. 2a) were adopted.

2. The slope of the giant branch at the end of ¿(log L)

the evolutionary pause was calculated. 3. A quadratic polynomial (log reff as a function of log L)

was derived from the two adopted points on the upper GB and the slope of the GB at the end of the evolutionary pause.

4. Idealized temperatures were computed from this quadratic, and then these were used to recompute values for log g, to enforce consistency in the output model parameters.

Differences between isochrones interpolated from the idealized giant branches and the raw tracks are illustrated in Figure 4 for one of the most offending cases. The adjustments that were made have negligible effects on the computed LFs: all that they really do is modify the shapes of the upper parts of the isochrones to make them look more like the fiducial sequences that are observed.

2.4. Tests of Interpolation Accuracy

Comparisons of the interpolation scheme among the evolutionary grids of different abundances indicate that the largest deviations from linearity in the interpolations occur in the metal-rich grids. The first test of the accuracy of the interpolation scheme is illustrated in Figure 5, for the metallicity [Fe/H] = —0.65 (the second highest metal abundance consid- ered). In this example, a set of isochrones, shown as dashed lines, has been interpolated between the 0.15Jto and 1.05ô

tracks. The maximum difference between the dashed and solid curves at the position of the turnoff amounts to less than 0.002 in log Tee, which corresponds to a temperature difference

Fig. 4.—The differences between 8 and 18 Gyr isochrones derived from idealized giant branches {dashedcurves), on the one hand, and from giant branches generated by the Eggleton code (solid curves), on the other. The deviations of the isochrones, which are most noticeable near log L/L© = 2.9, arise as a consequence of the interpolations that are made in the model atmosphere grids of the stellar models.

AT æ 25 K. However, it should be noted that the isochrones and luminosity functions presented in this paper, of which the solid curves are a small subset, have been interpolated from grids in which the evolutionary sequences are separated by only 0.1eô, whereas for this test, the spacing is 0.3ô. The differences between the two sets of isochrones imply that the upper limit to the interpolation error at the location of the turnoff, for the full grid, is ^0.0007 in log Teff, or AT ^ 10 K. As indicated in Figure 5, the errors will tend to be even smaller in other parts of the CMD.

The second test of the accuracy of the interpolations is illustrated in Figure 6, again for the metallicity [Fe/H] = -0.65. We first generated a set of isochrones with roughly the same spacing between them at the position of the turnoff on the log L-log T plane as between the evolutionary sequences. From this set of isochrones, the interpolation scheme was run in reverse to recover the original evolutionary tracks. Figure 6b clearly shows that the interpolation scheme is extremely reli- able, even in recovering the morphology of the BH for the 1.15ô track. The deviations appearing in the main-sequence segment of the 0.85ô track are due to the fact that when the interpolations are run in reverse, five isochrones are crossed, and linear interpolation can produce slight discontinuities at the boundaries of interpolation regimes. The small hook at the position of the turnoff in the 1.05JIo track is due to the “mem- ory” of the hook feature in the higher mass tracks, preserved by the placement of the primary EEPs in the interpolation scheme down to this track (see Fig. 2b). This is just what one would expect from linear interpolation between curves with different morphologies.

The major impheation of these tests is that a spacing of


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BERGBUSCH & VANDENBERG 170

Fig. 5.—A test of the linearity of the interpolation scheme with 6, 10, and 18 Gyr isochrones for the metallicity [Fe/H] = -0.65. The dotted curves represent the two tracks (for 0.75o and 1.05^o) that were used to generate the test isochrones {dashed curves). The solid curves are the isochrones for the same ages as interpolated from the full grid of stellar models, spaced at 0. \JiQ mass intervals.

O.l^o is fine enough to produce isochrones and luminosity functions to an accuracy commensurate with the uncertainties in the evolutionary sequences from which they were derived. However, there is potential for further improvement in the interpolation scheme by more careful consideration of the locations in the evolutionary grids where distinct morphological changes occur. In particular, it is desirable to have a much finer spacing of the evolutionary sequences in the vicinity of the transition mass dividing those stars which have a convective core throughout their main-sequence lifetimes and those which do not.

3. ISOCHRONES AND LUMINOSITY FUNCTIONS

Using the procedures just described, theoretical isochrones have been computed for ages from 8 to 18 Gyr (in 1.0 Gyr steps) for those grids of evolutionary sequences for which [Fe/H] < -1.03 (see Table 1). For each of the three sets of tracks at higher [Fe/H], time-constant loci were produced for a 5-18 Gyr range in age. Some of the youngest of the latter isochrones have already been used to interpret recent CCD photometry for the old, metal-poor open cluster NGC 2243 (Bergbusch, VandenBerg, & Infante 1991), and it is anticipated that they will be useful in future analyses of similar ob- jects. However, to reduce the length of the present paper, we have chosen to tabulate here only those isochrones for ages of 12, 14, and 16 Gyr, which seem (to us) to be of the greatest relevance for the Galactic GCs.5 They are listed in Tables 2-4, respectively.

5 All of the computed isochrones and the means to generate luminosity functions from them will be made available through the Astronomical Data Center. To obtain a magnetic tape containing the present computa-

Fig. 6b

Fig. 6.—(a) The grid of evolutionary sequences ([Fe/H] = -0.65) over the mass range 0.75-1.25^© is shown as dotted curves; isochrones interpolated from these sequences for the ages 2, 3,4,6, 9, 14, and 22 Gyr {solid curves) were used to reconstruct the evolutionary sequences shown in (£). {b) Evolutionary sequences for the indicated masses, reconstructed from the isochrones in (a) are shown as dashed curves. The sequences originally computed (from Paper I) are shown as dotted curves.

tions, as well as those by VandenBerg (1985a), VandenBerg & Bell (1985), Bell & VandenBerg (1987), VandenBerg & Laskarides ( 1987), and Proffitt & VandenBerg ( 1991 ), a request should be made to Gail L. Scheider, Astronomical Data Center, Code 633, NASA Goddard Space Flight Center, Greenbelt, MD 20771. D.A.V. may also be contacted for information on how to obtain these results via anonymous FTP from the University of Victoria.


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TABLE 2 Isochrones and Luminosity Functions for 12 Gyr

log</>

Mv B — V Mass Mbd logTeff log^r x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

[Fe/H] = -2.26 [O/Fe] = -1-0.75 Y = 0.2350

11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.800 4.600 4.501 4.400 4.300 4.200 4.101 4.000 3.901 3.800 3.700 3.600 3.496 3.400 3.290 3.200 3.092 3.000 2.909 2.800 2.706 2.600 2.400 2.200 2.000 1.800 1.600 1.400

1.491 1.449 1.408 1.369 1.333 1.303 1.276 1.251 1.227 1.203 1.178 1.154 1.129 1.101 1.069 1.035 0.999 0.959 0.915 0.870 0.827 0.785 0.740 0.693 0.647 0.604 0.564 0.528 0.497 0.470 0.445 0.422 0.401 0.382 0.364 0.357 0.349 0.342 0.335 0.328 0.322 0.318 0.314 0.312 0.313 0.317 0.326 0.344 0.365 0.404 0.444 0.481 0.516 0.533 0.548 0.566 0.580 0.592 0.602 0.611 0.620

0.1585 0.1670 0.1763 0.1865 0.1978 0.2108 0.2263 0.2442 0.2646 0.2874 0.3130 0.3419 0.3744 0.4056 0.4325 0.4567 0.4791 0.4997 0.5186 0.5365 0.5538 0.5707 0.5874 0.6043 0.6214 0.6386 0.6562 0.6743 0.6924 0.7104 0.7280 0.7442 0.7591 0.7727 0.7848 0.7904 0.7957 0.8009 0.8064 0.8116 0.8165 0.8209 0.8249 0.8286 0.8318 0.8347 0.8370 0.8393 0.8408 0.8424 0.8435 0.8446 0.8456 0.8462 0.8467 0.8475 0.8482 0.8487 0.8492 0.8497 0.8500

10.434 10.282 10.128 9.971 9.811 9.648 9.480 9.309 9.136 8.964 8.790 8.616 8.441 8.267 8.096 7.926 7.757 7.590 7.424 7.259 7.094 6.927 6.758 6.587 6.413 6.236 6.053 5.860 5.663 5.464 5.268 5.074 4.881 4.687 4.493 4.396 4.298 4.201 4.104 4.007 3.909 3.812 3.714 3.616 3.517 3.414 3.317 3.204 3.109 2.993 2.889 2.780 2.652 2.548 2.434 2.224 2.017 1.810 1.605 1.399 1.194

3.5826 3.5877 3.5927 3.5976 3.6023 3.6067 3.6107 3.6145 3.6182 3.6219 3.6257 3.6295 3.6332 3.6373 3.6422 3.6474 3.6530 3.6594 3.6668 3.6749 3.6837 3.6931 3.7030 3.7132 3.7235 3.7339 3.7443 3.7547 3.7648 3.7741 3.7828 3.7909 3.7983 3.8053 3.8119 3.8150 3.8179 3.8207 3.8235 3.8262 3.8285 3.8303 3.8315 3.8317 3.8308 3.8283 3.8239 3.8160 3.8071 3.7917 3.7749 3.7572 3.7439 3.7387 3.7349 3.7304 3.7272 3.7244 3.7218 3.7193 3.7167

5.200 5.183 5.164 5.145 5.126 5.106 5.086 5.066 5.046 5.028 5.011 4.995 4.979 4.961 4.939 4.916 4.892 4.869 4.848 4.829 4.812 4.796 4.780 4.765 4.749 4.731 4.712 4.688 4.661 4.630 4.597 4.561 4.522 4.480 4.436 4.413 4.388 4.363 4.338 4.313 4.286 4.257 4.224 4.188 4.146 4.097 4.041 3.966 3.893 3.786 3.678 3.564 3.460 3.398 3.338 3.236 3.140 3.047 2.954 2.862 2.770

2.9131 2.9262 2.9422 2.9627 2.9912 3.0288 3.0685 3.0983 3.1131 3.1263 3.1404 3.1574 3.1451 3.0561 2.9701 2.9104 2.8540 2.7991 2.7523 2.7162 2.6903 2.6715 2.6591 2.6511 2.6419 2.6359 2.6385 2.6326 2.6155 2.5910 2.5521 2.5191 2.4806 2.4356 2.3883

2.3428

2.3012

2.2371

2.1492

2.0485

1.9241

1.7695

1.6692

1.4378

1.2231 1.1332 1.0648 1.0000 0.9345 0.8677 0.8028

3.2775 3.2792 3.2835 3.2918 3.3074 3.3309 3.3555 3.3688 3.3662 3.3614 3.3570 3.3548 3.3233 3.2170 3.1169 3.0453 2.9784 2.9143 2.8594 2.8159 2.7831 2.7577 2.7390 2.7249 2.7096 2.6977 2.6944 2.6826 2.6598 2.6297 2.5855 2.5477 2.5049 2.4561 2.4053

2.3569

2.3123

2.2456

2.1555

2.0530

1.9271

1.7716

1.6705

3.6420 3.6323 3.6249 3.6209 3.6236 3.6332 3.6425 3.6393 3.6194 3.5966 3.5737 3.5523 3.5015 3.3779 3.2637 3.1801 3.1029 3.0296 2.9665 2.9156 2.8759 2.8440 2.8190 2.7987 2.7774 2.7595 2.7503 2.7327 2.7041 2.6683 2.6189 2.5763 2.5292 2.4765 2.4224

2.3709

2.3235

2.2541

2.1617

2.0574

1.9302

1.7737

1.6719

1.4386 1.4395

1.2237 1.1335 1.0649 1.0000 0.9344 0.8674 0.8025

1.2242 1.1338 1.0651 1.0000 0.9342 0.8672 0.8022

4.0066 3.9856 3.9664 3.9502 3.9399 3.9355 3.9297 3.9100 3.8727 3.8319 3.7905 3.7499 3.6798 3.5389 3.4105 3.3150 3.2273 3.1449 3.0737 3.0153 2.9688 2.9303 2.8990 2.8726 2.8451 2.8213 2.8062 2.7827 2.7483 2.7070 2.6523 2.6050 2.5535 2.4970 2.4394

2.3850

2.3346

2.2625

2.1679

2.0618

1.9333

1.7757

1.6732

1.4403

1.2247 1.1342 1.0652 1.0000 0.9341 0.8670 0.8018

4.3713 4.3389 4.3080 4.2795 4.2563 4.2380 4.2169 4.1807 4.1260 4.0673 4.0073 3.9475 3.8581 3.7000 3.5574 3.4500 3.3518 3.2602 3.1808 3.1150 3.0616 3.0166 2.9789 2.9464 2.9129 2.8832 2.8622 2.8327 2.7926 2.7458 2.6857 2.6336 2.5778 2.5174 2.4565

2.3990

2.3458

2.2710

2.1742

2.0663

1.9363

1.7778

1.6746

1.4412

1.2253 1.1345 1.0654 1.0000 0.9340 0.8667 0.8015

4.7360 4.6923 4.6496 4.6089 4.5727 4.5405 4.5042 4.4515 4.3794 4.3028 4.2243 4.1453 4.0366 3.8611 3.7043 3.5849 3.4763 3.3755 3.2880 3.2148 3.1545 3.1029 3.0589 3.0203 2.9807 2.9450 2.9181 2.8828 2.8370 2.7845 2.7191 2.6622 2.6021 2.5379 2.4736

2.4130

2.3569

2.2795

2.1804

2.0707

1.9394

1.7799

1.6759

1.4420

1.2258 1.1348 1.0655 1.0000 0.9339 0.8665 0.8012


TABLE 2—Continued

Mv B-V Mass Mhoi logTc// log^ a: = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

1.200 1.000 0.800 0.600 0.400 0.200 0.000

—0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.600 -2.723 -2.746

11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.800 4.600 4.500 4.400 4.300 4.200 4.101 4.000 3.901

0.630 0.642 0.654 0.668 0.684 0.701 0.721 0.742 0.765 0.790 0.818 0.849 0.884 0.921 0.962 1.008 1.060 1.118 1.187 1.266 1.321 1.332

1.537 1.499 1.460 1.423 1.387 1.353 1,323 1.297 1.273 1.249 1.225 1.202 1.179 1.153 1.123 1.091 1.056 1.019 0.978 0.933 0.887 0.842 0.798 0.753 0.707 0.661 0.617 0.576 0.540 0.510 0.483 0.458 0.434 0.413 0.394 0.376 0.368 0.361 0.354 0.347 0.341 0.335 0.331

0.8503 0.8506 0.8508 0.8510 0.8512 0.8514 0.8515 0.8516 0.8517 0.8519 0.8519 0.8520 0.8520 0.8521 0.8521 0.8522 0.8522 0.8522 0.8522 0.8523 0.8523 0.8523

0.1576 0.1657 0.1745 0.1842 0.1950 0.2072 0.2214 0.2380 0.2570 0.2783 0.3024 0.3301 0.3610 0.3919 0.4195 0.4440 0.4665 0.4872 0.5063 0.5242 0.5414 0.5580 0.5745 0.5909 0.6075 0.6242 0.6411 0.6583 0.6762 0.6941 0.7125 0.7301 0.7464 0.7614 0.7751 0.7873 0.7930 0.7983 0.8040 0.8096 0.8149 0.8197 0.8241

0.987 0.781 0.573 0.365 0.157

■ 0.053 - 0.264 0.475

-0.687 0.901 1.116

■ 1.334 1.554

- 1.775 2.000

■ 2.230 - 2.466 2.709 2.959 3.220 3.388 3.420

3.7139 3.7110 3.7080 3.7049 3.7017 3.6984 3.6949 3.6912 3.6875 3.6836 3.6796 3.6754 3.6711 3.6665 3.6618 3.6568 3.6514 3.6458 3.6398 3.6334 3.6291 3.6283

2.676 2.582 2.488 2.392 2.296 2.199 2.101 2.001 1.902 1.801 1.699 1.595 1.490 1.383 1.274 1.162 1.046 0.927 0.802 0.672 0.588 0.572

0.7364 0.6704 0.6041 0.5381 0.4727 0.4088 0.3524 0.3379 0.3637 0.2228 0.0886 0.0088

-0.0564 -0.1174 -0.1756 -0.2306 -0.2845 -0.3387 -0.3899 -0.4315 -0.3898

0.7360 0.6699 0.6035 0.5375 0.4721 0.4081 0.3517 0.3371 0.3630 0.2220 0.0878 0.0080

-0.0573 -0.1183 -0.1764 -0.2315 -0.2853 -0.3396 -0.3908 -0.4324 -0.3907

0.7356 0.6695 0.6030 0.5369 0.4715 0.4074 0.3509 0.3364 0.3622 0.2212 0.0869 0.0071

-0.0581 -0.1192 -0.1773 -0.2324 -0.2862 -0.3405 -0.3917 -0.4333 -0.3916

[Fe/H] = -2.03 [O/Fe] = +0.70 Y = 0.2350

10.520 10.374 10.225 10.073 9.917 9.758 9.595 9.428 9.259 9.088 8.917 8.744 8.570 8.399 8.229 8.061 7.893 7.727 7.564 7.401 7.239 7.077 6.912 6.745 6.576 6.404 6.229 6.048 5.859 5.664 5.467 5.272 5.078 4.883 4.689 4.494 4.397 4.299 4.202 4.104 4.008 3.909 3.812

3.5746 3.5796 3.5846 3.5895 3.5943 3.5988 3.6030 3.6069 3.6106 3.6144 3.6181 3.6217 3.6254 3.6295 3.6340 3.6389 3.6443 3.6502 3.6570 3.6647 3.6731 3.6822 3.6918 3.7019 3.7123 3.7227 3.7332 3.7436 3.7539 3.7637 3.7728 3.7813 3.7893 3.7966 3.8033 3.8095 3.8124 3.8153 3.8181 3.8207 3.8230 3.8249 3.8263

5.200 5.184 5.166 5.149 5.130 5.111 5.092 5.072 5.052 5.034 5.016 4.999 4.984 4.967 4.947 4.924 4.900 4.876 4.854 4.835 4.818 4.802 4.788 4.774 4.759 4.744 4.727 4.708 4.685 4.658 4.627 4.593 4.557 4.517 4.474 4.428 4.404 4.379 4.355 4.329 4.303 4.274 4.242

2.9047 2.9177 2.9352 2.9549 2.9815 3.0160 3.0524 3.0861 3.1043 3.1202 3.1432 3.1616 3.1516 3.0882 3.0021 2.9341 2.8771 2.8222 2.7734 2.7354 2.7050 2.6832 2.6674 2.6560 2.6494 2.6405 2.6343 2.6389 2.6347 2.6220 2.5990 2.5638 2.5310 2.4930 2.4478 2.4006

2.3592

2.3164

2.2407

3.2710 3.2732 3.2793 3.2873 3.3015 3.3226 3.3446 3.3626 3.3642 3.3628 3.3678 3.3673 3.3381 3.2571 3.1561 3.0757 3.0079 2.9435 2.8863 2.8408 2.8033 2.7749 2.7528 2.7353 2.7226 2.7078 2.6959 2.6947 2.6847 2.6663 2.6377 2.5971 2.5596 2.5172 2.4681 2.4175

3.6375 3.6287 3.6236 3.6197 3.6215 3.6293 3.6369 3.6393 3.6243 3.6056 3.5925 3.5730 3.5247 3.4260 3.3102 3.2173 3.1387 3.0649 2.9993 2.9461 2.9016 2.8667 2.8382 2.8145 2.7959 2.7752 2.7574 2.7505 2.7347 2.7106 2.6763 2.6305 2.5882 2.5415 2.4885 2.4345

0.7352 0.6690 0.6025 0.5363 0.4708 0.4067 0.3502 0.3357 0.3614 0.2204 0.0861 0.0063

-0.0589 -0.1200 -0.1782 -0.2332 -0.2871 -0.3414 -0.3926 -0.4342 -0.3925

4.0040 3.9844 3.9679 3.9523 3.9416 3.9361 3.9292 3.9160 3.8844 3.8484 3.8172 3.7788 3.7114 3.5951 3.4643

„3-3589 3.2695 3.1862 3.1122 3.0515 3.0000 2.9584 2.9236 2.8938 2.8691 2.8426 2.8190 2.8063 2.7847 2.7550 2.7150 2.6638 2.6167 2.5657 2.5088 2.4514

0.7347 0.6685 0.6019 0.5357 0.4702 0.4061 0.3495 0.3349 0.3607 0.2196 0.0853 0.0055

-0.0598 -0.1209 -0.1790 -0.2341 -0.2880 -0.3423 -0.3935 -0.4351 -0.3934

4.3707 4.3401 4.3123 4.2849 4.2618 4.2430 4.2217 4.1928 4.1446 4.0914 4.0421 3.9847 3.8982 3.7642 3.6185 3.5006 3.4004 3.3076 3.2252 3.1568 3.0984 3.0502 3.0090 2.9731 2.9424 2.9100 2.8806 2.8621 2.8347 2.7993 2.7537 2.6972 2.6453 2.5899 2.5292 2.4684

0.7343 0.6680 0.6014 0.5352 0.4695 0.4054 0.3488 0.3342 0.3599 0.2188 0.0845 0.0046

-0.0606 -0.1217 -0.1799 -0.2350 -0.2889 -0.3432 -0.3944 -0.4360 -0.3943

4.7374 4.6959 4.6568 4.6176 4.5820 4.5499 4.5142 4.4697 4.4049 4.3344 4.2670 4.1907 4.0850 3.9333 3.7726 3.6423 3.5313 3.4290 3.3382 3.2622 3.1967 3.1419 3.0945 3.0524 3.0157 2.9773 2.9422 2.9179 2.8847 2.8437 2.7923 2.7306 2.6739 2.6142 2.5496 2.4854

2.3731 2.3870 2.4009 2.4148 2.4287

2.3273 2.3382

2.2489 2.2571

2.3491

2.2653

2.3600

2.2735

2.3709

2.2818

172


PQ oo KO TABLE 2—Continued

00 My B — V Mass Mboi logTe/y log# x = 0.0 x = 0.5 a: = 1.0 x = 1.5 x = 2.0

3.800 3.699 3.600 3.495 3.400 3.288 3.200 3.096 3.000 2.922 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.598 -2.697

11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800

0.329 0.329 0.332 0.339 0.351 0.374 0.401 0.445 0.490 0.521 0.547 0.573 0.588 0.600 0.611 0.621 0.629 0.639 0.650 0.661 0.675 0.689 0.705 0.723 0.744 0.766 0.790 0.817 0.847 0.880 0.917 0.958 1.003 1.055 1.113 1.181 1.261 1.353 1.404

1.567 1.535 1.501 1.467 1.433 1.401 1.372 1.345 1.320 1.296 1.272 1.250 1.228 1.204 1.176 1.145 1.113 1.079 1.041 1.000 0.954 0.907 0.860 0.814 0.769 0.724

0.8281 0.8316 0.8347 0.8376 0.8398 0.8420 0.8434 0.8449 0.8463 0.8472 0.8481 0.8491 0.8498 0.8505 0.8511 0.8515 0.8520 0.8523 0.8526 0.8529 0.8531 0.8533 0.8535 0.8536 0.8538 0.8539 0.8540 0.8541 0.8542 0.8543 0.8543 0.8543 0.8544 0.8544 0.8545 0.8545 0.8545 0.8545 0.8545

0.1573 0.1651 0.1735 0.1826 0.1929 0.2046 0.2181 0.2338 0.2518 0.2719 0.2945 0.3205 0.3502 0.3812 0.4090 0.4332 0.4556 0.4769 0.4966 0.5145 0.5315 0.5479 0.5639 0.5800 0.5961 0.6124

3.714 3.615 3.516 3.410 3.314 3.198 3.105 2.991 2.875 2.780 2.643 2.429 2.220 2.013 1.807 1.601 1.396 1.190 0.983 0.776 0.568 0.360 0.150

-0.060 - 0.271 - 0.484 - 0.697 - 0.912 - 1.130 - 1.349 - 1.571 - 1.797 - 2.027 - 2.265 - 2.509 - 2.763 - 3.030 - 3.312 - 3.458

3.8269 3.8264 3.8246 3.8209 3.8156 3.8063 3.7958 3.7789 3.7590 3.7469 3.7389 3.7321 3.7283 3.7254 3.7228 3.7203 3.7178 3.7151 3.7123 3.7093 3.7063 3.7032 3.7000 3.6966 3.6928 3.6890 3.6851 3.6810 3.6767 3.6722 3.6674 3.6624 3.6570 3.6513 3.6452 3.6386 3.6314 3.6235 3.6193

4.207 4.168 4.123 4.067 4.008 3.926 3.848 3.735 3.610 3.524 3.437 3.325 3.227 3.133 3.040 2.948 2.856 2.763 2.669 2.575 2.480 2.384 2.288 2.190 2.090 1.990 1.889 1.787 1.683 1.577 1.469 1.359 1.245 1.127 1.005 0.877 0.742 0.597 0.522

2.1519 2.1579

2.0466

1.9154

1.7700

2.0509

1.9184

1.7720

2.1639

2.0551

1.9213

1.7740

2.1699

2.0594

1.9242

2.1759

2.0636

1.9272

1.7759 1.7779

1.6835 1.6848 1.6860 1.6873 1.6885

1.3563 1.2134 1.1339 1.0655 1.0000 0.9340 0.8690 0.8022 0.7360 0.6698 0.6031 0.5376 0.4731 0.4117 0.3696 0.3987 0.3504 0.1781 0.0775 0.0082

-0.0538 -0.1128 -0.1682 -0.2223 -0.2776 -0.3279 -0.3721 -0.3987

1.3571 1.2139 1.1342 1.0657 1.0000 0.9338 0.8688 0.8019 0.7356 0.6694 0.6026 0.5371 0.4725 0.4110 0.3689 0.3979 0.3496 0.1773 0.0767 0.0074

-0.0546 -0.1137 -0.1691 -0.2232 -0.2785 -0.3288 -0.3730 -0.3996

1.3579 1.2145 1.1345 1.0658 1.0000 0.9337 0.8685 0.8016 0.7352 0.6689 0.6021 0.5365 0.4718 0.4103 0.3682 0.3972 0.3489 0.1765 0.0759 0.0066

-0.0554 -0.1145 -0.1699 -0.2240 -0.2794 -0.3297 -0.3738 -0.4005

[Fe/H] = -1.78 [O/Fe] = +0.66 Y = 0.2351

10.592 10.452 10.309 10.162 10.012 9.857 9.698 9.534 9.368 9.201 9.033 8.862 8.690 8.519 8.351 8.187 8.021 7.855 7.692 7.533 7.374 7.215 7.055 6.893 6.729 6.562

3.5666 3.5716 3.5766 3.5815 3.5863 3.5908 3.5951 3.5990 3.6027 3.6064 3.6102 3.6138 3.6173 3.6210 3.6255 3.6304 3.6354 3.6408 3.6469 3.6540 3.6620 3.6708 3.6801 3.6900 3.7002 3.7106

5.196 5.181 5.165 5.149 5.131 5.113 5.094 5.075 5.055 5.037 5.019 5.002 4.985 4.969 4.950 4.929 4.905 4.880 4.857 4.837 4.819 4.804 4.790 4.777 4.764 4.750

2.9009 2.9125 2.9284 2.9488 2.9755 3.0102 3.0490 3.0823 3.1016 3.1150 3.1375 3.1639 3.1679 3.1171 3.0234 2.9519 2.9054 2.8567 2.8013 2.7520 2.7183 2.6937 2.6763 2.6658 2.6576 2.6532

3.2688 3.2699 3.2750 3.2841 3.2988 3.3207 3.3456 3.3638 3.3671 3.3639 3.3690 3.3770 3.3620 3.2932 3.1841 3.0999 3.0424 2.9838 2.9196 2.8625 2.8218 2.7906 2.7668 2.7502 2.7360 2.7258

3.6368 3.6274 3.6216 3.6194 3.6222 3.6314 3.6424 3.6455 3.6327 3.6128 3.6006 3.5902 3.5561 3.4693 3.3448 3.2480 3.1794 3.1109 3.0379 2.9730 2.9253 2.8874 2.8574 2.8347 2.8145 2.7984

1.3587 1.2150 1.1348 1.0660 1.0000 0.9336 0.8683 0.8012 0.7348 0.6684 0.6015 0.5359 0.4712 0.4097 0.3675 0.3965 0.3481 0.1757 0.0751 0.0058

-0.0563 -0.1154 -0.1708 -0.2249 -0.2802 -0.3305 -0.3747 -0.4013

4.0049 3.9850 3.9683 3.9548 3.9457 3.9421 3.9392 3.9272 3.8984 3.8618 3.8322 3.8035 3.7504 3.6455 3.5056 3.3961 3.3165 3.2380 3.1563 3.0836 3.0287 2.9843 2.9479 2.9192 2.8930 2.8710

1.3594 1.2155 1.1351 1.0661 1.0000 0.9335 0.8681 0.8009 0.7344 0.6680 0.6010 0.5353 0.4706 0.4090 0.3668 0.3958 0.3474 0.1749 0.0743 0.0049

-0.0571 -0.1162 -0.1716 -0.2257 -0.2811 -0.3314 -0.3756 -0.4022

4.3731 4.3426 4.3152 4.2903 4.2693 4.2528 4.2361 4.2090 4.1642 4.1109 4.0639 4.0169 3.9447 3.8218 3.6665 3.5442 3.4535 3.3652 3.2746 3.1941 3.1322 3.0812 3.0385 3.0036 2.9715 2.9437

173

x = 2.5

2.1820

2.0679

1.9301

1.7799

1.6898

1.3602 1.2160 1.1354 1.0663 1.0000 0.9333 0.8678 0.8006 0.7340 0.6675 0.6005 0.5348 0.4700 0.4084 0.3661 0.3950 0.3466 0.1742 0.0735 0.0041

-0.0579 -0.1170 -0.1725 -0.2266 -0.2820 -0.3323 -0.3765 -0.4031

4.7414 4.7004 4.6620 4.6259 4.5929 4.5637 4.5330 4.4908 4.4300 4.3601 4.2957 4.2303 4.1392 3.9981 3.8274 3.6924 3.5906 3.4923 3.3930 3.3047 3.2357 3.1780 3.1291 3.0881 3.0500 3.0163



S Mv B-V Mass Mboi logT^yy log^ X = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.800 4.700 4.600 4.500 4.400 4.301 4.200 4.101 4.000 3.900 3.800 3.698 3.600 3.492 3.400 3.286 3.200 3.136 3.080 3.000 2.908 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.555 -2.610

0.679 0.634 0.592 0.557 0.526 0.499 0.475 0.450 0.428 0.409 0.400 0.392 0.385 0.377 0.369 0.363 0.358 0.354 0.351 0.351 0.353 0.358 0.370 0.386 0.418 0.453 0.485 0.518 0.548 0.567 0.582 0.601 0.614 0.624 0.634 0.643 0.652 0.663 0.674 0.687 0.701 0.716 0.733 0.754 0.776 0.799 0.825 0.855 0.887 0.924 0.964 1.010 1.062 1.121 1.189 1.271 1.367 1.453 1.486

0.6290 0.6457 0.6628 0.6804 0.6982 0.7163 0.7339 0.7503 0.7655 0.7792 0.7856 0.7917 0.7974 0.8033 0.8093 0.8150 0.8202 0.8250 0.8294 0.8333 0.8368 0.8398 0.8427 0.8447 0.8468 0.8483 0.8494 0.8504 0.8513 0.8520 0.8526 0.8535 0.8543 0.8549 0.8555 0.8559 0.8563 0.8567 0.8570 0.8572 0.8575 0.8577 0.8578 0.8580 0.8581 0.8583 0.8584 0.8585 0.8585 0.8586 0.8586 0.8587 0.8587 0.8588 0.8588 0.8588 0.8588 0.8589 0.8589

6.392 6.219 6.042 5.856 5.665 5.471 5.275 5.081 4.886 4.691 4.593 4.495 4.397 4.300 4.203 4.104 4.007 3.909 3.811 3.712 3.612 3.513 3.404 3.311 3.192 3.098 3.022 2.949 2.851 2.748 2.631 2.420 2.212 2.006 1.801 1.595 1.389 1.182 0.975 0.767 0.559 0.350 0.140

-0.073 -0.285 -0.498 -0.714 -0.931 -1.152 -1.375 -1.601 -1.834 -2.075 -2.323 -2.582 -2.859 -3.156 -3.405 -3.500

3.7211 3.7315 3.7418 3.7520 3.7618 3.7708 3.7791 3.7868 3.7940 3.8004 3.8033 3.8061 3.8087 3.8115 3.8142 3.8164 3.8182 3.8195 3.8202 3.8200 3.8188 3.8162 3.8113 3.8047 3.7926 3.7796 3.7662 3.7534 3.7429 3.7375 3.7335 3.7286 3.7254 3.7228 3.7204 3.7180 3.7154 3.7125 3.7096 3.7066 3.7035 3.7004 3.6970 3.6931 3.6892 3.6853 3.6811 3.6766 3.6719 3.6669 3.6615 3.6558 3.6496 3.6429 3.6356 3.6275 3.6183 3.6103 3.6072

4.736 4.720 4.702 4.679 4.653 4.623 4.588 4.551 4.511 4.466 4.442 4.417 4.392 4.367 4.342 4.315 4.286 4.254 4.220 4.182 4.139 4.091 4.029 3.966 3.871 3.782 3.699 3.619 3.539 3.476 3.413 3.310 3.215 3.122 3.030 2.939 2.846 2.752 2.658 2.563 2.467 2.371 2.274 2.173 2.073 1.972 1.869 1.764 1.657 1.548 1.436 1.320 1.199 1.073 0.940 0.797 0.641 0.509 0.459

2.6459 2.6397 2.6415 2.6389 2.6280 2.6091 2.5795 2.5450 2.5064 2.4620

2.4167

2.3800

2.3290

2.2468

2.1557

2.0459

1.9076

1.8280

1.3138 1.2094 1.1354 1.0670 1.0000 0.9338 0.8692 0.8015 0.7353 0.6684 0.6022 0.5376 0.4762 0.4284 0.4493 0.4497 0.2610 0.1465 0.0735 0.0115

-0.0476 -0.1023 -0.1583 -0.2135 -0.2618 -0.3041 -0.3456 -0.3444

2.7127 2.7008 2.6969 2.6886 2.6722 2.6477 2.6128 2.5736 2.5306 2.4823

2.4336

2.3936

2.3396

2.2547

2.1614

2.0500

1.9103

1.8298

2.7795 2.7619 2.7523 2.7384 2.7163 2.6863 2.6461 2.6021 2.5548 2.5026

2.4505

2.4073

2.3501

2.2626

2.1672

2.0540

1.9131

1.8316

2.8463 2.8231 2.8078 2.7881 2.7605 2.7249 2.6795 2.6306 2.5790 2.5230

2.4674

2.4210

2.3607

2.2706

2.1730

2.0581

1.9159

1.8334

1.3145 1.2099 1.1358 1.0671 1.0000 0.9336 0.8690 0.8012 0.7349 0.6679 0.6017 0.5371 0.4756 0.4278 0.4486 0.4490 0.2603 0.1457 0.0727 0.0107

-0.0484 -0.1031 -0.1591 -0.2144 -0.2626 -0.3050 -0.3465 -0.3452

1.3153 1.2104 1.1361 1.0672 1.0000 0.9335 0.8687 0.8009 0.7345 0.6675 0.6012 0.5365 0.4750 0.4272 0.4480 0.4483 0.2596 0.1450 0.0719 0.0099

-0.0492 -0.1040 -0.1599 -0.2152 -0.2635 -0.3058 -0.3474 -0.3461

1.3160 1.2109 1.1364 1.0674 1.0000 0.9334 0.8685 0.8006 0.7341 0.6670 0.6007 0.5360 0.4744 0.4265 0.4473 0.4476 0.2588 0.1442 0.0712 0.0091

-0.0500 -0.1048 -0.1608 -0.2160 -0.2643 -0.3067 -0.3482 -0.3469

2.9131 2.8842 2.8632 2.8379 2.8047 2.7635 2.7128 2.6592 2.6032 2.5433

2.4842

2.4347

2.3713

2.2785

2.1787

2.0622

1.9187

1.8353

1.5919 1.5930 1.5942 1.5953 1.5964

1.3168 1.2114 1.1367 1.0675 1.0000 0.9333 0.8683 0.8003 0.7337 0.6666 0.6002 0.5354 0.4738 0.4259 0.4466 0.4469 0.2581 0.1434 0.0704 0.0083

-0.0508 -0.1056 -0.1616 -0.2169 -0.2651 -0.3075 -0.3491 -0.3478

2.9800 2.9453 2.9187 2.8877 2.8489 2.8022 2.7462 2.6877 2.6274 2.5636

2.5011

2.4484

2.3819

2.2864

2.1845

2.0662

1.9215

1.8371

1.5976

1.3175 1.2119 1.1370 1.0677 1.0000 0.9332 0.8681 0.7999 0.7334 0.6661 0.5997 0.5348 0.4732 0.4252 0.4459 0.4462 0.2573 0.1427 0.0696 0.0075

-0.0516 -0.1064 -0.1624 -0.2177 -0.2660 -0.3084 -0.3499 -0.3487

174



^0 a CM (S\ (T\

My B — V Mass logTc// log^f x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

[Fe/H] = -1.66 [O/Fe] = +0.63 F =

11.800 1.565 11.600 1.534 11.400 1.502 11.200 1.470 11.000 1.438 10.800 1.408 10.600 1.381 10.400 1.356 10.200 1.332 10.000 1.308 9.800 1.285 9.600 1.263 9.400 1.240 9.200 1.215 9.000 1.187 8.800 1.157 8.600 1.125 8.400 1.091 8.200 1.053 8.000 1.010 7.800 0.964 7.600 0.917 7.400 0.869 7.200 0.824 7.000 0.778 6.800 0.733 6.600 0.688 6.400 0.643 6.200 0.601 6.000 0.565 5.800 0.534 5.600 0.507 5.400 0.483 5.200 0.459 5.000 0.436 4.800 0.417 4.701 0.409 4.600 0.401 4.499 0.393 4.400 0.385 4.301 0.378 4.200 0.372 4.101 0.367 4.000 0.364 3.900 0.362 3.800 0.362 3.697 0.366 3.600 0.373 3.490 0.387 3.400 0.406 3.284 0.443 3.200 0.484 3.125 0.530 3.000 0.571 2.907 0.588 2.800 0.601 2.600 0.616 2.400 0.628 2.200 0.638 2.000 0.647 1.800 0.655 1.600 0.666 1.400 0.676 1.200 0.688 1.000 0.701

0.1608 10.557 0.1688 10.417 0.1775 10.275 0.1871 10.129 0.1978 9.979 0.2099 9.824 0.2243 9.664 0.2408 9.501 0.2596 9.335 0.2804 9.169 0.3040 9.001 0.3308 8.832 0.3605 8.662 0.3902 8.493 0.4166 8.328 0.4402 8.163 0.4622 7.999 0.4827 7.835 0.5016 7.674 0.5190 7.516 0.5355 7.360 0.5516 7.202 0.5674 7.044 0.5833 6.883 0.5993 6.720 0.6156 6.554 0.6320 6.385 0.6486 6.214 0.6655 6.038 0.6829 5.854 0.7005 5.664 0.7189 5.472 0.7364 5.277 0.7529 5.082 0.7681 4.887 0.7819 4.692 0.7883 4.594 0.7945 4.496 0.8004 4.397 0.8067 4.300 0.8128 4.203 0.8186 4.104 0.8237 4.007 0.8285 3.909 0.8328 3.810 0.8367 3.711 0.8402 3.609 0.8431 3.512 0.8459 3.402 0.8479 3.309 0.8501 3.187 0.8516 3.090 0.8531 2.992 0.8544 2.842 0.8550 2.739 0.8556 2.624 0.8565 2.414 0.8572 2.208 0.8579 2.002 0.8584 1.796 0.8589 1.591 0.8593 1.384 0.8596 1.177 0.8599 0.970 0.8602 0.761

3.5652 5.186 3.5702 5.171 3.5751 5.156 3.5798 5.139 3.5845 5.122 3.5889 5.104 3.5930 5.085 3.5967 5.065 3.6004 5.046 3.6041 5.028 3.6078 5.011 3.6114 4.994 3.6150 4.978 3.6190 4.961 3.6235 4.941 3.6283 4.919 3.6334 4.894

. 3.6388 4.869 3.6452 4.847 3.6525 4.828 3.6606 4.811 3.6694 4.797 3.6789 4.783 3.6888 4.771 3.6991 4.758 3.7095 4.745 3.7201 4.731 3.7305 4.716 3.7408 4.698 3.7510 4.676 3.7607 4.650 3.7695 4.620 3.7778 4.585 3.7855 4.548 3.7926 4.507 3.7988 4.461 3.8016 4.437 3.8042 4.412 3.8067 4.385 3.8095 4.361 3.8120 4.335 3.8141 4.307 3.8156 4.277 3.8166 4.245 3.8170 4.209 3.8164 4.169 3.8148 4.124 3.8117 4.074 3.8059 4.008 3.7986 3.943 3.7849 3.840 3.7692 3.740 3.7516 3.630 3.7384 3.518 3.7339 3.460 3.7306 3.400 3.7266 3.301 3.7236 3.207 3.7212 3.115 3.7188 3.024 3.7164 2.932 3.7136 2.839 3.7108 2.745 3.7079 2.650 3.7048 2.555

2.9090 3.2727 2.9206 3.2737 2.9367 3.2789 2.9600 3.2908 2.9907 3.3093 3.0272 3.3328 3.0648 3.3561 3.0950 3.3709 3.1099 3.3696 3.1250 3.3679 3.1464 3.3717 3.1624 3.3695 3.1525 3.3412 3.0900 3.2617 3.0041 3.1614 2.9407 3.0859 2.8923 3.0270 2.8400 2.9653 2.7864 2.9032 2.7413 2.8507 2.7117 2.8143 2.6901 2.7862 2.6746 2.7645 2.6652 2.7491 2.6583 2.7364 2.6528 2.7250 2.6462 2.7127 2.6401 2.7010 2.6398 2.6951 2.6388 2.6885 2.6298 2.6739 2.6111 2.6497 2.5844 2.6178 2.5515 2.5801 2.5134 2.5376 2.4696 2.4899

2.4268 2.4437

2.3948 2.4084

2.3346 2.3450

2.2507 2.2585

2.1592 2.1648

2.0440 2.0479

1.9114 1.9141

1.8581 1.8598

1.5055 1.5066

1.2948 1.2955 1.2040 1.2045 1.1361 1.1364 1.0663 1.0665 1.0000 1.0000 0.9353 0.9351 0.8695 0.8693 0.8017 0.8014 0.7364 0.7360 0.6691 0.6686

0.2352

3.6364 4.0002 3.6269 3.9801 3.6212 3.9635 3.6217 3.9526 3.6280 3.9468 3.6384 3.9441 3.6475 3.9390 3.6469 3.9230 3.6294 3.8893 3.6109 3.8539 3.5972 3.8227 3.5767 3.7839 3.5299 3.7187 3.4335 3.6053 3.3188 3.4763 3.2312 3.3765 3.1617 3.2964 3.0905 3.2158 3.0201 3.1370 2.9601 3.0695 2.9168 3.0194 2.8823 2.9785 2.8545 2.9444 2.8330 2.9170 2.8144 2.8925 2.7973 2.8695 2.7792 2.8458 2.7619 2.8228 2.7504 2.8057 2.7382 2.7879 2.7181 2.7622 2.6883 2.7268 2.6511 2.6845 2.6086 2.6372 2.5618 2.5860 2.5103 2.5306

2.4605 2.4774

2.4219 2.4354

2.3554 2.3658

2.2663 2.2740

2.1704 2.1761

2.0519 2.0558

1.9168 1.9196

1.8615 1.8633

1.5077 1.5087

1.2962 1.2969 1.2050 1.2055 1.1367 1.1370 1.0666 1.0668 1.0000 1.0000 0.9350 0.9349 0.8690 0.8688 0.8011 0.8008 0.7356 0.7352 0.6682 0.6677

4.3641 4.7280 4.3335 4.6869 4.3060 4.6485 4.2837 4.6148 4.2657 4.5847 4.2499 4.5558 4.2305 4.5222 4.1991 4.4754 4.1492 4.4092 4.0970 4.3403 4.0483 4.2740 3.9913 4.1987 3.9077 4.0966 3.7772 3.9491 3.6337 3.7913 3.5219 3.6673 3.4311 3.5659 3.3411 3.4664 3.2540 3.3709 3.1790 3.2884 3.1220 3.2246 3.0746 3.1708 3.0344 3.1244 3.0010 3.0849 2.9706 3.0487 2.9418 3.0141 2.9123 2.9789 2.8837 2.9447 2.8610 2.9163 2.8376 2.8874 2.8064 2.8506 2.7654 2.8040 2.7178 2.7512 2.6658 2.6943 2.6102 2.6345 2.5509 2.5713

2.4943 2.5111

2.4490 2.4625

2.3762 2.3866

2.2818 2.2896

2.1817 2.1873

2.0598 2.0638

1.9223 1.9250

1.8650 1.8667

1.5098 1.5108

1.2977 1.2984 1.2060 1.2065 1.1373 1.1376 1.0669 1.0670 1.0000 1.0000 0.9348 0.9347 0.8686 0.8684 0.8005 0.8002 0.7349 0.7345 0.6673 0.6668

175



œ Mv B-V Mass Mhol logTc// log 5 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

^ 0.800 0.715 £ 0.600 0.731 ^ 0.400 0.750 S 0.200 0.771 2 0.000 0.794

-0.200 0.818 -0.400 0.846 -0.600 0.877 -0.800 0.911 -1.000 0.949 -1.200 0.992 -1.400 1.041 -1.600 1.096 -1.800 1.160 -2.000 1.235 -2.200 1.325 -2.400 1.431 -2.525 1.508 -2.551 1.524

0.8604 0.553 0.8606 0.343 0.8608 0.132 0.8609 - 0.081 0.8611 - 0.294 0.8612 - 0.508 0.8613 - 0.725 0.8614 - 0.945 0.8615 -1.167 0.8615 - 1.392 0.8616 -1.623 0.8616 - 1.861 0.8617 - 2.107 0.8617 - 2.362 0.8617 - 2.634 0.8617 - 2.927 0.8618 - 3.247 0.8618 - 3.473 0.8618 - 3.521

3.7017 2.459 3.6985 2.362 3.6949 2.263 3.6908 2.162 3.6869 2.061 3.6828 1.959 3.6784 1.855 3.6737 1.748 3.6687 1.640 3.6634 1.528 3.6577 1.413 3.6515 1.293 3.6448 1.168 3.6376 1.037 3.6295 0.896 3.6204 0.742 3.6099 0.572 3.6022 0.451 3.6005 0.425

0.6032 0.6027 0.5398 0.5393 0.4844 0.4838 0.4602 0.4596 0.5216 0.5210 0.3904 0.3897 0.2291 0.2284 0.1408 0.1401 0.0746 0.0738 0.0142 0.0134

-0.0424 -0.0432 -0.0974 -0.0982 -0.1548 -0.1556 -0.2059 -0.2067 -0.2492 -0.2500 -0.2932 -0.2941 -0.3207 -0.3215 -0.2909 -0.2918

0.6022 0.6017 0.5387 0.5382 0.4832 0.4826 0.4590 0.4583 0.5203 0.5196 0.3890 0.3883 0.2276 0.2269 0.1393 0.1386 0.0730 0.0723 0.0126 0.0118

-0.0440 -0.0448 -0.0990 -0.0998 -0.1564 -0.1572 -0.2075 -0.2083 -0.2508 -0.2517 -0.2949 -0.2958 -0.3224 -0.3232 -0.2926 -0.2935

0.6012 0.6007 0.5376 0.5371 0.4820 0.4814 0.4577 0.4571 0.5190 0.5183 0.3876 0.3869 0.2262 0.2254 0.1378 0.1371 0.0715 0.0707 0.0110 0.0102

-0.0456 -0.0464 -0.1006 -0.1014 -0.1580 -0.1588 -0.2092 -0.2100 -0.2525 -0.2534 -0.2966 -0.2974 -0.3241 -0.3249 -0.2943 -0.2952

[Fe/H] = —1.48 [O/Fe] = +0.60 Y = 0.2354

12.000 1.597 11.800 1.567 11.600 1.536 11.400 1.506 11.200 1.477 11.000 1.449 10.800 1.422 10.600 1.397 10.400 1.374 10.200 1.351 10.000 1.329 9.800 1.307 9.600 1.285 9.400 1.261 9.200 1.236 9.000 1.208 8.800 1.178 8.600 1.146 8.400 1.110 8.200 1.070 8.000 1.027 7.800 0.981 7.600 0.934 7.400 0.886 7.200 0.839 7.000 0.793 6.800 0.748 6.600 0.704 6.400 0.659 6.200 0.616 6.000 0.579 5.800 0.548 5.600 0.521 5.400 0.496 5.200 0.473 5.000 0.450 4.800 0.431 4.701 0.422 4.600 0.414 4.500 0.406 4.400 0.399 4.301 0.392 4.200 0.387 4.101 0.382 4.000 0.380

0.1598 10.632 0.1677 10.495 0.1761 10.355 0.1854 10.213 0.1956 10.067 0.2071 9.918 0.2203 9.763 0.2359 9.604 0.2534 9.442 0.2731 9.278 0.2953 9.113 0.3207 8.947 0.3489 8.779 0.3779 8.614 0.4052 8.449 0.4301 8.284 0.4525 8.121 0.4731 7.960 0.4921 7.801 0.5098 7.645 0.5265 7.490 0.5426 7.336 0.5583 7.181 0.5738 7.025 0.5894 6.866 0.6052 6.705 0.6213 6.541 0.6376 6.373 0.6541 6.204 0.6709 6.030 0.6882 5.850 0.7057 5.663 0.7240 5.472 0.7415 5.279 0.7579 5.085 0.7732 4.889 0.7872 4.693 0.7936 4.596 0.7999 4.497 0.8065 4.399 0.8130 4.301 0.8192 4.204 0.8249 4.105 0.8300 4.007 0.8348 3.908

3.5575 5.182 3.5624 5.168 3.5672 5.153 3.5719 5.137 3.5765 5.120 3.5809 5.103 3.5851 5.085 3.5890 5.066 3.5927 5.048 3.5963 5.029 3.6000 5.012 3.6035 4.995 3.6071 4.979 3.6110 4.963 3.6152 4.944 3.6196 4.922 3.6244 4.898 3.6296 4.874 3.6356 4.851 3.6423 4.831 3.6499 4.813 3.6581 4.798 3.6671 4.784 3.6766 4.771 3.6867 4.760 3.6970 4.748 3.7076 4.736 3.7182 4.723 3.7286 4.708 3.7389 4.691 3.7490 4.670 3.7586 4.645 3.7673 4.614 3.7754 4.580 3.7829 4.542 3.7900 4.500 3.7961 4.454 3.7988 4.430 3.8012 4.403 3.8037 4.378 3.8062 4.352 3.8083 4.324 3.8100 4.295 3.8113 4.264 3.8119 4.229

x = —0.5 x = 0.0

2.5435 2.9100 2.5653 2.9213 2.5904 2.9357 2.6197 2.9539 2.6573 2.9798 2.7035 3.0135 2.7522 3.0486 2.7993 3.0812 2.8357 3.1020 2.8687 3.1187 2.9079 3.1409 2.9461 3.1612 2.9577 3.1547 2.9323 3.1122 2.8805 3.0452 2.8240 2.97^8 2.7725 2.9131 2.7255 2.8565 2.6845 2.8070 2.6488 2.7635 2.6204 2.7280 2.6006 2.7017 2.5880 2.6829 2.5792 2.6681 2.5785 2.6616 2.5791 2.6565 2.5808 2.6524 2.5807 2.6467 2.5805 2.6410 2.5847 2.6397 2.5902 2.6397 2.5885 2.6324 2.5767 2.6151 2.5583 2.5916 2.5315 2.5601 2.4985 2.5227 2.4598 2.4801

2.4240 2.4407

2.3952 2.4085

2.3271 2.3372

2.2470 2.2545

x = 0.5 x = 1.0

3.2765 3.6431 3.2774 3.6336 3.2811 3.6266 3.2882 3.6225 3.3024 3.6250 3.3236 3.6337 3.3452 3.6417 3.3631 3.6450 3.3683 3.6347 3.3687 3.6189 3.3739 3.6071 3.3765 3.5918 3.3518 3.5490 3.2921 3.4722 3.2101 3.3749 3.1277 3.2795 3.0538 3.1946 2.9875 3.1185 2.9294 3.0518 2.8782 2.9929 2.8357 2.9434 2.8028 2.9040 2.7779 2.8728 2.7570 2.8460 2.7447 2.8279 2.7338 2.8112 2.7241 2.7957 2.7127 2.7788 2.7015 2.7619 2.6946 2.7496 2.6892 2.7386 2.6764 2.7203 2.6536 2.6920 2.6249 2.6581 2.5886 2.6171 2.5469 2.5711 2.5004 2.5207

2.4575 2.4743

2.4218 2.4351

2.3474 2.3576

2.2621 2.2697

x = 1.5 x = 2.0

4.0098 4.3765 3.9899 4.3463 3.9722 4.3178 3.9570 4.2915 3.9478 4.2706 3.9439 4.2542 3.9384 4.2352 3.9271 4.2092 3.9012 4.1678 3.8691 4.1194 3.8403 4.0736 3.8072 4.0226 3.7463 3.9436 3.6522 3.8324 3.5398 3.7048 3.4314 3.5834 3.3353 3.4761 3.2496 3.3806 3.1743 3.2968 3.1077 3.2225 3.0511 3.1589 3.0052 3.1063 2.9677 3.0627 2.9349 3.0239 2.9110 2.9941 2.8886 2.9660 2.8674 2.9391 2.8448 2.9109 2.8224 2.8830 2.8046 2.8596 2.7881 2.8376 2.7643 2.8083 2.7305 2.7690 2.6914 2.7247 2.6456 2.6742 2.5953 2.6195 2.5410 2.5613

2.4911 2.5078

2.4484 2.4617

2.3677 2.3779

2.2772 2.2848

176



Mv B-V Mass Mbol x — —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

3.900 3.800 3.696 3.600 3.490 3.400 3.315 3.253 3.200 3.117 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.502 -2.504

12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400

0.380 0.382 0.388 0.398 0.417 0.440 0.476 0.513 0.551 0.580 0.605 0.626 0.639 0.649 0.658 0.667 0.677 0.687 0.698 0.711 0.724 0.740 0.758 0.779 0.801 0.825 0.851 0.880 0.912 0.947 0.987 1.032 1.083 1.140 1.206 1.284 1.376 1.485 1.546 1.547

1.627 1.598 1.568 1.539 1.510 1.482 1.456 1.433 1.411 1.389 1.369 1.349 1.330. 1.309 1.285 1.258 1.229 1.199 1.166 1.130 1.090 1.047 1.002 0.956 0.908

0.8391 0.8429 0.8464 0.8493 0.8520 0.8540 0.8558 0.8572 0.8584 0.8594 0.8603 0.8614 0.8622 0.8630 0.8636 0.8641 0.8646 0.8650 0.8653 0.8656 0.8658 0.8660 0.8662 0.8664 0.8665 0.8667 0.8669 0.8670 0.8670 0.8671 0.8671 0.8672 0.8672 0.8673 0.8673 0.8673 0.8674 0.8674 0.8674 0.8674

0.1602 0.1680 0.1764 0.1855 0.1956 0.2068 0.2194 0.2341 0.2507 0.2696 0.2911 0.3155 0.3426 0.3711 0.3983 0.4227 0.4451 0.4662 0.4858 0.5040 0.5211 0.5373 0.5530 0.5684 0.5837

3.809 3.710 3.607 3.511 3.400 3.307 3.213 3.135 3.061 2.959 2.827 2.613 2.405 2.199 1.994 1.788 1.582 1.375 1.167 0.959 0.750 0.541 0.329 0.117

- 0.097 - 0.311 - 0.528 - 0.747 • 0.968

1.192 1.421

■ 1.657 1.900 2.151 2.416 2.699 3.004

■ 3.348 3.543 3.547

3.8117 3.8106 3.8082 3.8042 3.7969 3.7884 3.7756 3.7613 3.7481 3.7390 3.7323 3.7267 3.7234 3.7208 3.7184 3.7160 3.7134 3.7106 3.7077 3.7047 3.7016 3.6984 3.6947 3.6907 3.6866 3.6826 3.6783 3.6737 3.6688 3.6636 3.6581 3.6521 3.6456 3.6387 3.6310 3.6224 3.6127 3.6013 3.5945 3.5944

4.191 4.149 4.099 4.047 3.974 3.904 3.817 3.729 3.647 3.570 3.491 3.384 3.288 3.195 3.104 3.012 2.919 2.825 2.731 2.636 2.540 2.443 2.345 2.243 2.142 2.040 1.936 1.830 1.722 1.612 1.498 1.380 1.257 1.129 0.992 0.845 0.684 0.500 0.396 0.393

2.1546

2.0409

1.9354

1.8355

1.4241 1.2840 1.2030 1.1328 1.0642 1.0000 0.9319 0.8656 0.7981 0.7322 0.6649 0.6006 0.5407 0.4914 0.5239 0.5365 0.3253 0.2082 0.1352 0.0738 0.0157

-0.0402 -0.0993 -0.1537 -0.2005 -0.2483 -0.2869 -0.2983 -0.2397

2.1600

2.0447

1.9380

2.1655

2.0486

1.9405

1.8370 1.8386

1.4251 1.2847 1.2035 1.1330 1.0643 1.0000 0.9317 0.8654 0.7978 0.7318 0.6644 0.6001 0.5402 0.4909 0.5233 0.5358 0.3246 0.2075 0.1345 0.0731 0.0150

-0.0409 -0.1001 -0.1545 -0.2013 -0.2491 -0.2878 -0.2991 -0.2405

1.4261 1.2854 1.2039 1.1333 1.0644 1.0000 0.9316 0.8652 0.7975 0.7314 0.6640 0.5996 0.5396 0.4903 0.5227 0.5352 0.3239 0.2068 0.1338 0.0723 0.0142

-0.0417 -0.1008 -0.1553 -0.2021 -0.2499 -0.2886 -0.2999 -0.2414

[Fe/H] = -1.26 [O/Fe] = +0.55 Y = 0.2358

10.689 10.556 10.419 10.280 10.138 9.992 9.843 9.689 9.531 9.371 9.208 9.044 8.879 8.716 8.554 8.394 8.234 8.074 7.916 7.761 7.608 7.456 7.305 7.153 6.999

3.5497 3.5544 3.5591 3.5637 3.5683 3.5726 3.5768 3.5808 3.5845 3.5882 3.5917 3.5951 3.5987 3.6024 3.6065 3.6109 3.6156 3.6205 3.6259 3.6320 3.6388 3.6465 3.6548 3.6638 3.6734

5.175 5.161 5.147 5.132 5.116 5.099 5.082 5.064 5.046 5.028 5.010 4.993 4.977 4.962 4.944 4.923 4.901 4.876 4.853 4.831 4.812 4.795 4.780 4.767 4.755

2.5518 2.5733 2.5980 2.6264 2.6600 2.6994 2.7434 2.7892 2.8304 2.8683 2.9074 2.9430 2.9614 2.9458 2.8927 2.8344 2.7923 2.7553 2.7138 2.6740 2.6424 2.6173 2.5983 2.5890 2.5830

2.9202 2.9314 2.9455 2.9629 2.9850 3.0123 3.0434 3.0751 3.1014 3.1235 3.1461 3.1643 3.1649 3.1322 3.0638 2.9924 2.9390 2.8920 2.8415 2.7937 2.7548 2.7231 2.6978 2.6826 2.6707

3.2887 3.2896 3.2931 3.2996 3.3102 3.3253 3.3433 3.3612 3.3726 3.3789 3.3848 3.3856 3.3684 3.3186 3.2349 3.1505 3.0858 3.0287 2.9693 2.9134 2.8673 2.8288 2.7973 2.7761 2.7584

2.1709

2.0524

1.9431

1.8402

1.4271 1.2861 1.2044 1.1336 1.0646 1.0000 0.9315 0.8650 0.7972 0.7310 0.6636 0.5991 0.5391 0.4897 0.5220 0.5345 0.3232 0.2060 0.1330 0.0716 0.0134

-0.0425 -0.1016 -0.1561 -0.2029 -0.2507 -0.2894 -0.3008 -0.2422

3.6572 3.6479 3.6408 3.6363 3.6354 3.6384 3.6434 3.6473 3.6438 3.6343 3.6236 3.6070 3.5721 3.5050 3.4060 3.3086 3.2326 3.1654 3.0970 3.0331 2.9798 2.9346 2.8968 2.8697 2.8462

2.1764

2.0562

1.9457

1.8418

1.4281 1.2868 1.2049 1.1339 1.0647 1.0000 0.9314 0.8648 0.7969 0.7307 0.6631 0.5987 0.5386 0.4891 0.5214 0.5338 0.3225 0.2053 0.1323 0.0708 0.0127

-0.0433 -0.1024 -0.1569 -0.2037 -0.2515 -0.2902 -0.3016 -0.2430

4.0259 4.0062 3.9886 3.9730 3.9606 3.9515 3.9436 3.9335 3.9150 3.8898 3.8625 3.8285 3.7758 3.6916 3.5772 3.4667 3.3794 3.3022 3.2248 3.1528 3.0923 3.0404 2.9964 2.9632 2.9340

177

x = 2.0

2.1818

2.0600

1.9482

1.8434

1.4290 1.2875 1.2054 1.1342 1.0648 1.0000 0.9313 0.8646 0.7966 0.7303 0.6627 0.5982 0.5380 0.4886 0.5208 0.5332 0.3218 0.2046 0.1316 0.0701 0.0119

-0.0440 -0.1032 -0.1577 -0.2045 -0.2523 -0.2910 -0.3024 -0.2439

4.3946 4.3647 4.3365 4.3099 4.2860 4.2647 4.2438 4.2197 4.1864 4.1453 4.1014 4.0500 3.9795 3.8782 3.7485 3.6249 3.5262 3.4390 3.3526 3.2726 3.2048 3.1462 3.0959 3.0568 3.0217


TABLE 2—Continued

00 My B-V Mass Mioi logTe^y log^ x = —0.5 x = 0.0 x = 0.5 x = 1.0 x — 1.5 x = 2.0

7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.700 4.600 4.501 4.400 4.301 4.200 4.100 4.000 3.899 3.800 3.694 3.600 3.480 3.400 3.349 3.301 3.200 3.111 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.308 -2.315

0.861 0.815 0.770 0.726 0.682 0.639 0.599 0.568 0.540 0.515 0.492 0.470 0.460 0.450 0.441 0.432 0.425 0.418 0.413 0.408 0.405 0.404 0.406 0.410 0.420 0.433 0.463 0.498 0.539 0.579 0.616 0.634 0.647 0.661 0.671 0.680 0.689 0.699 0.709 0.720 0.732 0.745 0.761 0.780 0.801 0.824 0.848 0.875 0.905 0.937 0.974 1.015 1.060 1.112 1.171 1.240 1.322 1.420 1.538 1.614 1.620

0.5991 0.6149 0.6308 0.6470 0.6634 0.6800 0.6969 0.7149 0.7329 0.7502 0.7667 0.7821 0.7893 0.7962 0.8031 0.8102 0.8170 0.8238 0.8299 0.8356 0.8408 0.8455 0.8499 0.8536 0.8572 0.8599 0.8630 0.8651 0.8666 0.8679 0.8692 0.8699 0.8705 0.8715 0.8724 0.8731 0.8737 0.8742 0.8746 0.8750 0.8753 0.8756 0.8759 0.8761 0.8763 0.8764 0.8766 0.8768 0.8769 0.8770 0.8771 0.8771 0.8772 0.8772 0.8773 0.8773 0.8773 0.8774 0.8774 0.8774 0.8774

6.842 6.683 6.521 6.356 6.188 6.018 5.841 5.658 5.471 5.280 5.087 4.892 4.794 4.696 4.598 4.499 4.402 4.302 4.205 4.106 4.007 3.908 3.808 3.710 3.605 3.510 3.386 3.296 3.225 3.152 3.027 2.925 2.806 2.596 2.390 2.184 1.978 1.771 1.565 1.357 1.149 0.940 0.729 0.516 0.303 0.088

-0.128 -0.347 -0.568 -0.791 -1.018 -1.252 -1.493 -1.742 -2.003 -2.282 -2.582 -2.920 -3.310 -3.568 -3.589

3.6834 3.6937 3.7042 3.7148 3.7253 3.7356 3.7457 3.7551 3.7638 3.7720 3.7794 3.7860 3.7890 3.7919 3.7946 3.7973 3.7996 3.8016 3.8032 3.8045 3.8052 3.8052 3.8044 3.8025 3.7988 3.7939 3.7833 3.7708 3.7564 3.7433 3.7330 3.7282 3.7248 3.7209 3.7182 3.7157 3.7132 3.7107 3.7081 3.7052 3.7022 3.6992 3.6957 3.6917 3.6876 3.6834 3.6791 3.6745 3.6696 3.6645 3.6589 3.6529 3.6465 3.6395 3.6318 3.6232 3.6136 3.6022 3.5882 3.5786 3.5777

4.744 4.733 4.721 4.709 4.695 4.678 4.659 4.634 4.605 4.572 4.533 4.490 4.467 4.443 4.419 4.394 4.368 4.339 4.310 4.278 4.245 4.208 4.167 4.122 4.067 4.010 3.920 3.835 3.750 3.669 3.578 3.518 3.458 3.359 3.266 3.174 3.082 2.989 2.896 2.802 2.707 2.611 2.513 2.412 2.311 2.208 2.104 1.998 1.891 1.781 1.668 1.550 1.428 1.301 1.166 1.019 0.861 0.680 0.468 0.327 0.315

2.5843 2.5854 2.5866 2.5867 2.5855 2.5883 2.5940 2.5951 2.5848 2.5701 2.5488 2.5169

1.3715 1.2764 1.2026 1.1347 1.0680 1.0000 0.9317 0.8666 0.7983 0.7321 0.6712 0.6085 0.5574 0.5935 0.6243 0.3964 0.2736 0.2020 0.1416 0.0844 0.0245

-0.0321 -0.0822 -0.1326 -0.1759 -0.2018 -0.2158 -0.1360

2.6663 2.6618 2.6575 2.6520 2.6454 2.6428 2.6432 2.6388 2.6231 2.6034 2.5774 2.5412

2.4802 2.5005

2.4503

2.4152

2.3408

2.2617

2.1675

2.0587

2.0473

2.4668

2.4282

2.3506

2.2690

2.1727

2.0623

2.0496

1.3724 1.2770 1.2031 1.1349 1.0681 1.0000 0.9316 0.8664 0.7980 0.7318 0.6708 0.6080 0.5569 0.5929 0.6237 0.3958 0.2730 0.2013 0.1409 0.0836 0.0238

-0.0329 -0.0829 -0.1333 -0.1767 -0.2026 -0.2166 -0.1368

2.7484 2.7382 2.7284 2.7174 2.7054 2.6974 2.6924 2.6825 2.6614 2.6366 2.6059 2.5654

2.5208

2.4834

2.4412

2.3605

2.2763

2.1779

2.0659

2.0518

1.6163 1.6176 1.6189

1.3734 1.2777 1.2035 1.1352 1.0683 1.0000 0.9314 0.8662 0.7978 0.7314 0.6704 0.6075 0.5564 0.5923 0.6231 0.3951 0.2723 0.2007 0.1402 0.0829 0.0230

-0.0337 -0.0837 -0.1341 -0.1775 -0.2034 -0.2174 -0.1376

2.8305 2.8147 2.7993 2.7828 2.7654 2.7520 2.7416 2.7262 2.6998 2.6699 2.6345 2.5896

2.5412

2.4999

2.4541

2.3704

2.2836

2.1832

2.0695

2.0540

1.6202

1.3743 1.2784 1.2040 1.1355 1.0684 1.0000 0.9313 0.8660 0.7975 0.7310 0.6700 0.6071 0.5558 0.5918 0.6225 0.3945 0.2716 0.2000 0.1394 0.0822 0.0223

-0.0344 -0.0845 -0.1349 -0.1783 -0.2042 -0.2182 -0.1384

2.9126 2.8912 2.8702 2.8482 2.8253 2.8066 2.7909 2.7699 2.7381 2.7031 2.6630 2.6139

2.5615

2.5165

2.4671

2.3803

2.2909

2.1884

2.0731

2.0563

1.6215

1.3752 1.2790 1.2044 1.1358 1.0685 1.0000 0.9312 0.8658 0.7972 0.7307 0.6696 0.6066 0.5553 0.5912 0.6219 0.3938 0.2709 0.1993 0.1387 0.0815 0.0215

-0.0352 -0.0852 -0.1356 -0.1790 -0.2050 -0.2190 -0.1392

2.9947 2.9676 2.9411 2.9136 2.8853 2.8612 2.8401 2.8137 2.7764 2.7364 2.6916 2.6381

2.5818

2.5330

2.4801

2.3902

2.2982

2.1936

2.0768

2.0585

1.6228

1.3761 1.2797 1.2049 1.1360 1.0687 1.0000 0.9311 0.8656 0.7969 0.7303 0.6692 0.6061 0.5548 0.5907 0.6213 0.3932 0.2703 0.1986 0.1380 0.0807 0.0208

-0.0359 -0.0860 -0.1364 -0.1798 -0.2058 -0.2198 -0.1400

178



\—i 00

^0 a CM (S\ (T\

My B — V Mass Mbol log?«// log^ x = —0.5 x = 0.0 x = 0.5

[Fe/H] = -1.03 [O/Fe] = +0.50 Y = 0.2368

12.600 1.690 0.1566 12.400 1.662 0:i636 12.200 1.634 0.1712 12.000 1.604 0.1794 11.800 1.575 0.1884 11.600 1.547 0.1984 11.400 1.519 0.2097 11.200 1.493 0.2226 11.000 1.469 0.2373 10.800 1.446 0.2538 10.600 1.426 0.2720 10.400 1.406 0.2925 10.200 1.388 0.3160 10.000 1.370 0.3422 9.800 1.351 0.3695 9.600 1.330 0.3958 9.400 1.308 0.4201 9.200 1.282 0.4426 9.000 1.254 0.4638 8.800 1.224 0.4837 8.600 1.190 0.5022 8.400 1.152 0.5195 8.200 1.112 0.5358 8.000 1.070 0.5516 7.800 1.026 0.5671 7.600 0.981 0.5823 7.400 0.935 0.5977 7.200 0.888 0.6131 7.000 0.841 0.6288 6.800 0.795 0.6446 6.600 0.752 0.6606 6.400 0.710 0.6769 6.200 0.665 0.6933 6.000 0.624 0.7106 5.800 0.591 0.7285 5.600 0.562 0.7460 5.400 0.536 0.7631 5.200 0.513 0.7795 5.000 0.492 0.7950 4.901 0.482 0.8026 4.800 0.473 0.8104 4.700 0.465 0.8178 4.600 0.457 0.8250 4.501 0.449 0.8321 4.400 0.443 0.8389 4.301 0.439 0.8451 4.200 0.436 0.8509 4.100 0.435 0.8562 4.000 0.435 0.8610 3.898 0.438 0.8654 3.800 0.444 0.8691 3.687 0.459 0.8730 3.600 0.479 0.8757 3.518 0.514 0.8783 3.478 0.552 0.8800 3.454 0.590 0.8813 3.400 0.627 0.8825 3.320 0.654 0.8834 3.200 0.674 0.8844 3.000 0.690 0.8855 2.800 0.702 0.8865 2.600 0.711 0.8873 2.400 0.719 0.8880 2.200 0.728 0.8886 2.000 0.738 0.8890

10.839 3.5363 5.172 10.715 3.5409 5.159 10.588 3.5455 5.147 10.457 3.5501 5.133 10.323 3.5546 5.119 10.184 3.5591 5.104 10.042 3.5633 5.088 9.895 3.5674 5.071 9.744 3.5713 5.054 9.590 3.5750 5.037 9.435 3.5787 5.020 9.279 3.5823 5.003 9.119 3.5858 4.987 8.958 3.5893 4.971 8.798 3.5931 4.955 8.641 3.5971 4.939 8.485 3.6014 4.919 8.328 3.6059 4.897 8.172 3.6106 4.874 8.016 3.6157 4.850 7.863 3.6213 4.828 7.713 3.6277 4.808 7.565 3.6348 4.790 7.417 3.6425 4.774 7.268 3.6508 4.760 7.118 3.6597 4.748 6.966 3.6691 4.736 6.812 3.6790 4.725 6.655 3.6893 4.714 6.496 3.6999 4.703 6.334 3.7105 4.692 6.169 3.7211 4.679 6.002 3.7316 4.664 5.829 3.7414 4.645 5.650 3.7507 4.621 5.466 3.7595 4.593 5.279 3.7677 4.561 5.088 3.7752 4.524 4.894 3.7818 4.481 4.797 3.7845 4.458 4.698 3.7871 4.432 4.600 3.7894 4.407 4.501 3.7917 4.380 4.404 3.7938 4.353 4.304 3.7954 4.323 4.206 3.7966 4.292 4.107 3.7972 4.258 4.008 3.7974 4.222 3.909 3.7970 4.183 3.808 3.7956 4.139 3.711 3.7931 4.092 3.597 3.7879 4.028 3.507 3.7809 3.965 3.413 3.7689 3.880 3.354 3.7562 3.807 3.306 3.7443 3.741 3.227 3.7337 3.668 3.127 3.7264 3.599 2.992 3.7210 3.524 2.780 3.7166 3.422 2.572 3.7134 3.326 2.365 3.7108 3.234 2.159 3.7085 3.142 1.954 3.7061 3.051 1.747 3.7035 2.958

2.5328 2.9100 3.2872 2.5548 2.9224 3.2900 2.5766 2.9342 3.2920 2.6033 2.9508 3.2983 2.6355 2.9723 3.3091 2.6734 2.9989 3.3245 2.7162 3.0297 3.3431 2.7598 3.0603 3.3609 2.8014 3.0881 3.3749 2.8328 3.1050 3.3772 2.8642 3.1212 3.3783 2.9026 3.1438 3.3851 2.9429 3.1674 3.3920 2.9610 3.1684 3.3759 2.9443 3.1352 3.3262 2.9014 3.0774 3.2535 2.8515 3.0146 3.1776 2.8120 2.9637 3.1153 2.7765 2.9180 3.0594 2.7372 2.8695 3.0019 2.6969 2.8210 2.9452 2.6615 2.7783 2.8951 2.6373 2.7474 2.8574 2.6189 2.7226 2.8263 2.6043 2.7020 2.7997 2.5969 2.6888 2.7807 2.5949 2.6812 2.7675 2.5928 2.6736 2.7543 2.5946 2.6698 2.7450 2.5930 2.6628 2.7327 2.5937 2.6582 2.7227 2.5935 2.6527 2.7120 2.5955 2.6495 2.7035 2.6043 2.6530 2.7016 2.6027 2.6459 2.6892 2.5950 2.6332 2.6713 2.5822 2.6155 2.6487 2.5635 2.5921 2.6207 2.5394 2.5637 2.5880

2.5051 2.5252 2.5454

2.4817 2.4979 2.5142

2.4309 2.4435 2.4562

2.3584 2.3680 2.3776

2.2813 2.2883 2.2954

2.1905 2.1955 2.2005

2.1394 2.1426 2.1459

1.9975 1.9994 2.0013

1.4820 1.4832 1.4844 1.3583 1.3591 1.3600 1.2773 1.2779 1.2786 1.2052 1.2056 1.2061 1.1371 1.1373 1.1376 1.0658 1.0660 1.0661 1.0000 1.0000 1.0000

x = 1.0 x = 1.5 x = 2.0

3.6646 4.0421 4.4197 3.6577 4.0255 4.3935 3.6498 4.0077 4.3656 3.6459 3.9935 4.3413 3.6460 3.9830 4.3200 3.6501 3.9758 4.3015 3.6567 3.9704 4.2841 3.6616 3.9623 4.2631 3.6618 3.9487 4.2357 3.6495 3.9219 4.1943 3.6355 3.8927 4.1501 3.6265 3.8679 4.1094 3.6167 3.8415 4.0664 3.5835 3.7911 3.9988 3.5172 3.7083 3.8994 3.4296 3.6057 3.7820 3.3407 3.5038 3.6670 3.2670 3.4188 3.5705 3.2010 3.3425 3.4841 3.1343 3.2666 3.3991 3.0694 3.1936 3.3178 3.0120 3.1288 3.2457 2.9675 3.0775 3.1876 2.9300 3.0338 3.1375 2.8974 2.9951 3.0929 2.8727 2.9646 3.0566 2.8537 2.9400 3.0263 2.8350 2.9158 2.9965 2.8203 2.8956 2.9708 2.8025 2.8724 2.9422 2.7872 2.8518 2.9163 2.7712 2.8305 2.8897 2.7576 2.8116 2.8656 2.7503 2.7990 2.8477 2.7325 2.7758 2.8191 2.7094 2.7475 2.7857 2.6819 2.7151 2.7483 2.6493 2.6779 2.7065 2.6123 2.6366 2.6610

2.5656 2.5857 2.6059

2.5304 2.5467 2.5629

2.4689 2.4816 2.4943

2.3872 2.3968 2.4064

2.3024 2.3094 2.3165

2.2055 2.2104 2.2154

2.1492 2.1524 2.1557

2.0032 2.0051 2.0070

1.4855 1.4867 1.4878 1.3608 1.3617 1.3626 1.2792 1.2798 1.2804 1.2065 1.2069 1.2074 1.1378 1.1381 1.1384 1.0662 1.0663 1.0664 1.0000 1.0000 1.0000

179



00 Mv B-V Mass Mb0i log 'I'c.f f 1°&9 x — —0.5 x — 0.0 x — 0.5 x = 1.0 x = 1.5 x = 2.0

1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.103 -2.106

0.748 0.760 0.775 0.792 0.811 0.833 0.856 0.882 0.909 0.940 0.973 1.010 1.050 1.096 1.147 1.207 1.274 1.354 1.450 1.569 1.663 1.666

0.8895 0.8898 0.8901 0.8904 0.8906 0.8908 0.8910 0.8913 0.8915 0.8916 0.8917 0.8918 0.8918 0.8919 0.8919 0.8920 0.8920 0.8921 0.8921 0.8921 0.8922 0.8922

1.539 1.331 1.120 0.908 0.695 0.479 0.263 0.043

- 0.178 - 0.401 - 0.628 ■ 0.861 ■ 1.099 - 1.345 1.602 1.874 2.162

• 2.478 2.834 3.261 3.607 3.619

3.7008 3.6979 3.6944 3.6905 3.6866 3.6823 3.6780 3.6734 3.6684 3.6632 3.6577 3.6519 3.6456 3.6389 3.6316 3.6235 3.6146 3.6045 3.5925 3.5774 3.5646 3.5642

2.864 2.769 2.671 2.571 2.470 2.367 2.263 2.157 2.049 1.939 1.826 1.710 1.589 1.464 1.332 1.191 1.040 0.874 0.683 0.452 0.262 0.256

0.9316 0.8664 0.8034 0.7368 0.6735 0.6281 0.6881 0.7093 0.4560 0.3394 0.2721 0.2112 0.1489 0.0904 0.0367

-0.0188 -0.0705 -0.1072 -0.1500 -0.0831 0.1070

0.9315 0.8662 0.8032 0.7365 0.6731 0.6277 0.6876 0.7087 0.4554 0.3388 0.2715 0.2105 0.1482 0.0898 0.0360

-0.0195 -0.0712 -0.1079 -0.1507 -0.0838 0.1063

0.9314 0.8660 0.8029 0.7361 0.6727 0.6272 0.6871 0.7082 0.4548 0.3382 0.2708 0.2098 0.1475 0.0891 0.0353

-0.0202 -0.0720 -0.1086 -0.1515 -0.0846

0.1055

0.9313 0.8658 0.8026 0.7358 0.6723 0.6268 0.6867 0.7076 0.4542 0.3375 0.2702 0.2092 0.1469 0.0884 0.0346

-0.0209 -0.0727 -0.1094 -0.1522 -0.0853 0.1047

0.9312 0.8656 0.8024 0.7355 0.6719 0.6264 0.6862 0.7071 0.4536 0.3369 0.2695 0.2085 0.1462 0.0877 0.0339

-0.0216 -0.0734 -0.1101 -0.1530 -0.0861 0.1040

0.9311 0.8654 0.8021 0.7351 0.6715 0.6259 0.6857 0.7065 0.4530 0.3363 0.2689 0.2078 0.1455 0.0870 0.0332

-0.0223 -0.0742 -0.1109 -0.1537 -0.0869

0.1032

[Fe/H] = -0.78 [O/Fe] = +0.39 Y - 0.2391

13.000 1.730 12.800 1.706 12.600 1.681 12.400 1.656 12.200 1.631 12.000 1.605 11.800 1.580 11.600 1.555 11.400 1.530 11.200 1.507 11.000 1.485 10.800 1.463 10.600 1.443 10.400 1.425 10.200 1.408 10.000 1.391 9.800 1.373 9.600 1.354 9.400 1.333 9.200 1.312 9.000 1.286 8.800 1.256 8.600 1.223 8.400 1.187 8.200 1.146 8.000 1.103 7.800 1.058 7.600 1.012 7.400 0.967 7.200 0.923 7.000 0.876 6.800 0.830 6.600 0.786 6.400 0.744 6.200 0.702 6.000 0.661 5.800 0.625 5.600 0.594 5.400 0.567 5.200 0.544 5.000 0.523 4.900 0.514

0.1544 10.958 0.1609 10.842 0.1679 10.725 0.1755 10.604 0.1836 10.480 0.1925 10.353 0.2025 10.220 0.2138 10.082 0.2267 9.939 0.2413 9.792 0.2577 9.641 0.2760 9.489 0.2964 9.335 0.3196 9.179 0.3454 9.022 0.3717 8.866 0.3972 8.713 0.4213 8.559 0.4438 8.405 0.4648 8.252 0.4845 8.101 0.5032 7.951 0.5209 7.803 0.5378 7.657 0.5538 7.512 0.5694 7.368 0.5847 7.224 0.5998 7.078 0.6149 6.930 0.6302 6.779 0.6457 6.626 0.6615 6.469 0.6776 6.309 0.6939 6.147 0.7105 5.981 0.7274 5.811 0.7446 5.636 0.7626 5.456 0.7804 5.271 0.7976 5.083 0.8139 4.892 0.8216 4.795

3.5243 5.165 3.5286 5.154 3.5329 5.143 3.5372 5.131 3.5415 5.118 3.5457 5.105 3.5500 5.090 3.5541 5.075 3.5580 5.059 3.5618 5.043 3.5655 5.026 3.5691 5.009 3.5727 4.993 3.5761 4.977 3.5796 4.962 3.5834 4.947 3.5875 4.930 3.5917 4.911 3.5961 4.890 3.6008 4.867 3.6057 4.845 3.6111 4.823 3.6170 4.802 3.6234 4.783 3.6305 4.767 3.6382 4.752 3.6466 4.739 3.6554 4.727 3.6647 4.716 3.6744 4.705 3.6845 4.694 3.6948 4.683 3.7052 4.672 3.7157 4.659 3.7260 4.644 3.7360 4.626 3.7457 4.605 3.7546 4.579 3.7626 4.548 3.7698 4.510 3.7759 4.467 3.7788 4.444

x = —1.0 x = —0.5

2.1390 2.5241 2.1636 2.5397 2.1903 2.5572 2.2235 2.5809 2.2634 2.6109 2.3074 2.6445 2.3582 2.6844 2.4133 2.7276 2.4715 2.7732 2.5237 2.8118 2.5704 2.8443 2.6176 2.8766 2.6709 2.9143 2.7235 2.9506 2.7513 2.9618 2.7484 2.9430 2.7277 2.9079 2.6987 2.8662 2.6694 2.8255 2.6407 2.7867 2.6149 2.7520 2.5919 2.7207 2.5699 2.6912 2.5481 2.6625 2.5302 2.6381 2.5198 2.6217 2.5134 2.6095 2.5111 2.6017 2.5147 2.5998 2.5185 2.5984 2.5266 2.6012 2.5341 2.6034 2.5414 2.6055 2.5486 2.6075 2.5558 2.6096 2.5645 2.6132 2.5735 2.6171 2.5774 2.6158 2.5717 2.6051 2.5577 2.5864 2.5349 2.5592

x = 0.0 x = 0.5

2.9094 3.2948 2.9159 3.2922 2.9241 3.2912 2.9383 3.2959 2.9585 3.3062 2.9817 3.3190 3.0106 3.3369 3.0421 3.3565 3.0749 3.3767 3.0999 3.3881 3.1181 3.3921 3.1356 3.3947 3.1577 3.4Ö12 3.1777 3.4049 3.1723 3.3829 3.1377 3.3324 3.0882 3.2685 3.0336 3.2011 2.9816 3.1378 2.9328 3.0789 2.8890 3.0260 2.8495 2.9783 2.8124 2.9337 2.7768 2.8912 2.7460 2.8540 2.7236 2.8255 2.7057 2.8018 2.6923 2.7829 2.6850 2.7702 2.6782 2.7580 2.6757 2.7503 2.6727 2.7420 2.6696 2.7337 2.6664 2.7253 2.6634 2.7172 2.6618 2.7105 2.6607 2.7043 2.6543 2.6927 2.6385 2.6719 2.6151 2.6438 2.5835 2.6078

x = 1.0 x = 1.5

3.6803 4.0659 3.6686 4.0450 3.6583 4.0255 3.6535 4.0112 3.6539 4.0017 3.6564 3.9938 3.6632 3.9896 3.6711 3.9857 3.6786 3.9805 3.6764 3.9648 3.6661 3.9402 3.6538 3.9130 3.6448 3.8885 3.6321 3.8595 3.5936 3.8043 3.5272 3.7220 3.4489 3.6293 3.3687 3.5363 3.2940 3.4503 3.2250 3.3712 3.1631 3.3002 3.1071 3.2360 3.0550 3.1764 3.0055 3.1199 2.9619 3.0699 2.9274 3.0294 2.8980 2.9941 2.8735 2.9641 2.8553 2.9405 2.8379 2.9177 2.8248 2.8994 2.8113 2.8806 2.7978 2.8619 2.7843 2.8432 2.7710 2.8248 2.7592 2.8079 2.7479 2.7915 2.7312 2.7696 2.7054 2.7388 2.6725 2.7012 2.6321 2.6565

180



00 Mv B-V Mass Mboi log Tejj log51 x = —1.0 x — —0.5 x = 0.0 x — 0.5 x = 1.0

4.800 4.701 4.600 4.501 4.400 4.301 4.200 4.100 4.000 3.896 3.800 3.651 3.600 3.587 3.571 3.519 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.770 -1.839

13.200 13.000 12.800 12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200

0.505 0.496 0.489 0.482 0.477 0.474 0.472 0.471 0.473 0.478 0.488 0.527 0.576 0.614 0.652 0.689 0.718 0.741 0.753 0.762 0.770 0.779 0.788 0.801 0.815 0.831 0.849 0.869 0.892 0.917 0.944 0.973 1.004 1.038 1.076 1.119 1.167 1.221 1.282 1.352 1.433 1.530 1.641 1.720

1.744 1.722 1.699 1.676 1.652 1.629 1.605 1.582 1.559 1.536 1.515 1.493 1.472 1.453 1.434 1.417 1.400 1.382 1.364 1.345 1.325

0.8292 0.8364 0.8438 0.8510 0.8581 0.8645 0.8706 0.8762 0.8812 0.8860 0.8900 0.8959 0.8988 0.9003 0.9015 0.9027 0.9040 0.9055 0.9066 0.9076 0.9084 0.9091 0.9096 0.9101 0.9106 0.9109 0.9113 0.9115 0.9118 0.9120 0.9124 0.9125 0.9127 0.9128 0.9129 0.9129 0.9130 0.9131 0.9131 0.9132 0.9132 0.9133 0.9133 0.9133

0.1542 0.1606 0.1674 0.1746 0.1823 0.1907 0.2000 0.2107 0.2230 0.2368 0.2523 0.2695 0.2887 0.3102 0.3344 0.3604 0.3867 0.4115 0.4343 0.4558 0.4764

4.698 4.601 4.502 4.404 4.305 4.207 4.108 4.009 3.910 3.806 3.709 3.549 3.474 3.437 3.394 3.314 3.171 2.953 2.744 2.538 2.331 2.125 1.918 1.709 1.498 1.286 1.073 0.858 0.638 0.417 0.194

- 0.032 - 0.263 - 0.498 -0.738 -0.986 - 1.245 - 1.515 - 1.801 - 2.112 - 2.453 - 2.847 -3.301 - 3.650

3.7814 3.7837 3.7858 3.7875 3.7887 3.7895 3.7898 3.7896 3.7888 3.7867 3.7831 3.7699 3.7545 3.7431 3.7326 3.7229 3.7151 3.7089 3.7056 3.7032 3.7009 3.6986 3.6961 3.6931 3.6897 3.6861 3.6823 3.6781 3.6735 3.6686 3.6636 3.6583 3.6527 3.6468 3.6405 3.6339 3.6267 3.6189 3.6105 3.6009 3.5900 3.5770 3.5612 3.5486

4.419 4.394 4.366 4.338 4.307 4.274 4.238 4.201 4.160 4.113 4.062 3.948 3.858 3.798 3.739 3.669 3.581 3.470 3.374 3.282 3.191 3.099 3.007 2.911 2.814 2.715 2.614 2.512 2.405 2.297 2.188 2.077 1.962 1.845 1.724 1.598 1.465 1.326 1.179 1.016 0.836 0.626 0.381 0.191

2.5144

2.5018

2.4413

2.3743

2.3025

2.2304

2.2767

1.6000 1.4347 1.3444 1.2703 1.2016 1.1319 1.0657 1.0000 0.9326 0.8652 0.8001 0.7409 0.7058 0.8069 0.7402 0.5020 0.4027 0.3334 0.2699 0.2097 0.1502 0.0869 0.0329

-0.0137 -0.0657 -0.0684

0.0654

2.5347

2.5183

2.4542

2.3840

2.3095

2.2352

2.2795

1.6015 1.4358 1.3453 1.2710 1.2020 1.1322 1.0658 1.0000 0.9325 0.8650 0.7999 0.7406 0.7054 0.8065 0.7397 0.5015 0.4021 0.3327 0.2692 0.2091 0.1495 0.0862 0.0322

-0.0144 -0.0664 -0.0691

0.0646

2.5549

2.5347

2.4670

2.3937

2.3166

2.2401

2.2823

1.6030 1.4369 1.3461 1.2716 1.2024 1.1324 1.0659 1.0000 0.9324 0.8648 0.7996 0.7403 0.7050 0.8060 0.7391 0.5009 0.4015 0.3321 0.2686 0.2084 0.1488 0.0855 0.0314

-0.0152 -0.0671 -0.0699

0.0638

[Fe/H] = -0.65 [O/Fe] = +0.30 Y = 0.2413

11.001 10.889 10.775 10.660 10.542 10.420 10.294 10.161 10.024 9.881 9.734 9.585 9.435 9.281 9.125 8.971 8.819 8.667 8.516 8.364 8.213

3.5186 3.5228 3.5270 3.5312 3.5353 3.5394 3.5435 3.5475 3.5513 3.5551 3.5587 3.5624 3.5660 3.5695 3.5729 3.5765 3.5804 3.5846 3.5890 3.5935 3.5982

5.159 5.149 5.138 5.127 5.115 5.102 5.089 5.074 5.059 5.043 5.027 5.011 4.995 4.979 4.962 4.947 4.933 4.916 4.896 4.875 4.852

2.1355 2.1564 2.1793 2.2108 2.2465 2.2880 2.3378 2.3936 2.4502 2.5064 2.5526 2.5968 2.6451 2.6972 2.7395 2.7603 2.7480 2.7123 2.6827 2.6616 2.6390

2.5239 2.5359 2.5498 2.5721 2.5984 2.6300 2.6694 2.7138 2.7584 2.8015 2.8339 2.8637 2.8972 2.9336 2.9598 2.9644 2.9370 2.8877 2.8464 2.8148 2.7826

2.9123 2.9155 2.9205 2.9336 2.9504 2.9721 3.0010 3.0342 3.0666 3.0966 3.1152 3.1307 3.1493 3.1701 3.1801 3.1686 3.1260 3.0633 3.0102 2.9679 2.9262

2.5752

2.5512

2.4799

2.4034

2.3237

2.2450

2.2851

1.6045 1.4381 1.3470 1.2722 1.2029 1.1327 1.0660 1.0000 0.9323 0.8647 0.7993 0.7399 0.7046 0.8056 0.7386 0.5003 0.4009 0.3315 0.2679 0.2077 0.1481 0.0847 0.0307

-0.0159 -0.0679 -0.0706

0.0631

3.3009 3.2951 3.2912 3.2951 3.3025 3.3143 3.3326 3.3546 3.3749 3.3919 3.3967 3.3978 3.4014 3.4066 3.4004 3.3728 3.3150 3.2389 3.1739 3.1212 3.0698

2.5955

2.5676

2.4928

2.4131

2.3307

2.2499

2.2879

1.6060 1.4392 1.3478 1.2728 1.2033 1.1329 1.0662 1.0000 0.9322 0.8645 0.7991 0.7396 0.7042 0.8051 0.7381 0.4998 0.4003 0.3309 0.2673 0.2071 0.1474 0.0840 0.0300

-0.0166 -0.0686 -0.0714

0.0623

3.6896 3.6749 3.6620 3.6568 3.6547 3.6565 3.6644 3.6750 3.6832 3.6872 3.6782 3.6650 3.6536 3.6432 3.6209 3.5771 3.5041 3.4145 3.3377 3.2744 3.2135

181

x — 1.5

2.6157

2.5841

2.5057

2.4228

2.3378

2.2548

2.2907

1.6075 1.4403 1.3487 1.2734 1.2037 1.1332 1.0663 1.0000 0.9321 0.8643 0.7988 0.7393 0.7038 0.8047 0.7376 0.4992 0.3997 0.3302 0.2666 0.2064 0.1467 0.0833 0.0293

-0.0173 -0.0694 -0.0721

0.0616

4.0784 4.0547 4.0328 4.0185 4.0069 3.9988 3.9962 3.9956 3.9916 3.9825 3.9597 3.9322 3.9059 3.8799 3.8414 3.7814 3.6933 3.5901 3.5016 3.4277 3.3571


TABLE 2—Continued

Mv B - V Mass Mboi logTe// log^ x = -1.0 x = -0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.900 4.800 4.701 4.600 4.501 4.400 4.301 4.200 4.099 4.000 3.893 3.800 3.692 3.658 3.654 3.649 3.600 3.517 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.592 -1.684

1.302 1.273 1.241 1.205 1.165 1.122 1.076 1.030 0.986 0.942 0.897 0.851 0.806 0.764 0.723 0.682 0.644 0.614 0.586 0.561 0.539 0.530 0.521 0.513 0.506 0.500 0.495 0.492 0.490 0.490 0.493 0.502 0.516 0.552 0.593 0.635 0.677 0.718 0.743 0.762 0.778 0.788 0.796 0.805 0.816 0.827 0.841 0.857 0.874 0.894 0.917 0.941 0.966 0.994 1.023 1.056 1.093 1.134 1.180 1.232 1.289 1.356 1.432 1.521 1.632 1.744

0.4958 0.5142 0.5316 0.5482 0.5641 0.5795 0.5947 0.6098 0.6250 0.6403 0.6559 0.6718 0.6879 0.7043 0.7210 0.7379 0.7553 0.7735 0.7912 0.8083 0.8246 0.8324 0.8400 0.8475 0.8554 0.8630 0.8700 0.8766 0.8828 0.8885 0.8936 0.8987 0.9028 0.9076 0.9102 0.9117 0.9130 0.9143 0.9154 0.9165 0.9178 0.9189 0.9198 0.9206 0.9213 0.9219 0.9223 0.9228 0.9231 0.9234 0.9237 0.9240 0.9244 0.9246 0.9247 0.9249 0.9250 0.9250 0.9251 0.9252 0.9253 0.9253 0.9254 0.9254 0.9254 0.9255

8.064 7.916 7.770 7.626 7.484 7.342 7.199 7.054 6.908 6.759 6.607 6.452 6.295 6.134 5.969 5.801 5.628 5.448 5.266 5.079 4.890 4.794 4.697 4.601 4.502 4.404 4.305 4.207 4.108 4.008 3.910 3.802 3.707 3.584 3.529 3.497 3.461 3.379 3.276 3.144 2.931 2.723 2.516 2.309 2.101 1.893 1.683 1.471 1.257 1.040 0.820 0.598 0.375 0.147

-0.084 -0.319 -0.560 -0.810 -1.070 -1.339 -1.624 -1.934 -2.272 -2.660 -3.143 -3.660

3.6032 3.6086 3.6146 3.6211 3.6283 3.6360 3.6442 3.6529 3.6621 3.6716 3.6816 3.6918 3.7021 3.7125 3.7228 3.7329 3.7425 3.7512 3.7594 3.7669 3.7733 3.7760 3.7786 3.7809 3.7828 3.7843 3.7855 3.7862 3.7863 3.7859 3.7846 3.7814 3.7766 3.7650 3.7523 3.7401 3.7288 3.7182 3.7116 3.7067 3.7024 3.6995 3.6972 3.6949 3.6923 3.6895 3.6863 3.6828 3.6790 3.6748 3.6702 3.6653 3.6604 3.6552 3.6497 3.6439 3.6377 3.6312 3.6241 3.6165 3.6082 3.5988 3.5882 3.5755 3.5590 3.5404

4.830 4.808 4.788 4.770 4.754 4.740 4.727 4.715 4.704 4.693 4.682 4.671 4.660 4.648 4.633 4.616 4.596 4.569 4.538 4.503 4.462 4.438 4.414 4.388 4.360 4.331 4.300 4.267 4.230 4.192 4.150 4.096 4.041 3.948 3.876 3.816 3.756 3.682 3.615 3.543 3.441 3.347 3.255 3.164 3.070 2.976 2.880 2.781 2.680 2.577 2.471 2.363 2.254 2.142 2.027 1.910 1.789 1.663 1.531 1.393 1.246 1.084 0.907 0.701 0.441 0.160

2.6137 2.5905 2.5688 2.5476 2.5307 2.5225 2.5183 2.5168 2.5211 2.5264 2.5339 2.5431 2.5490 2.5563 2.5640 2.5712 2.5800 2.5804 2.5743 2.5626 2.5434

2.5279

2.5146

2.4526

2.3903

2.3218

2.2771

2.7486 2.7174 2.6885 2.6606 2.6375 2.6234 2.6136 2.6067 2.6056 2.6057 2.6080 2.6119 2.6126 2.6149 2.6175 2.6197 2.6234 2.6187 2.6076 2.5913 2.5678

2.5482

2.5311

2.4654

2.3999

2.3288

2.2818

2.8835 2.8444 2.8082 2.7736 2.7444 2.7244 2.7090 2.6966 2.6902 2.6849 2.6820 2.6808 2.6763 2.6735 2.6710 2.6681 2.6668 2.6569 2.6409 2.6200 2.5922

2.5685

2.5475

2.4781

2.4095

2.3357

2.2864

3.0184 2.9714 2.9280 2.8867 2.8512 2.8254 2.8043 2.7865 2.7747 2.7642 2.7561 2.7496 2.7400 2.7321 2.7245 2.7166 2.7102 2.6952 2.6743 2.6487 2.6165

2.5888

2.5639

2.4909

2.4190

2.3426

2.2911

3.1534 3.0985 3.0477 2.9998 2.9581 2.9264 2.8997 2.8764 2.8593 2.8435 2.8302 2.8185 2.8038 2.7907 2.7780 2.7650 2.7535 2.7334 2.7076 2.6774 2.6409

2.6091

2.5803

2.5036

2.4286

2.3495

2.2957

1.5420 1.4225 1.3410 1.2706 1.2015 1.1357 1.0660 1.0000 0.9334 0.8671 0.8066 0.7587 0.8235 0.8722 0.5904 0.4713 0.3980 0.3352 0.2745 0.2104 0.1461 0.0916 0.0402

-0.0116 -0.0295 0.1167

1.5434 1.4235 1.3418 1.2712 1.2019 1.1359 1.0661 1.0000 0.9333 0.8670 0.8063 0.7584 0.8231 0.8718 0.5899 0.4708 0.3974 0.3346 0.2738 0.2098 0.1454 0.0909 0.0395

-0.0123 -0.0302 0.1160

1.5448 1.4246 1.3426 1.2718 1.2023 1.1362 1.0662 1.0000 0.9332 0.8668 0.8061 0.7580 0.8227 0.8713 0.5894 0.4702 0.3968 0.3339 0.2732 0.2091 0.1447 0.0902 0.0388

-0.0130 -0.0309 0.1152

1.5462 1.4257 1.3434 1.2724 1.2027 1.1364 1.0664 1.0000 0.9331 0.8666 0.8058 0.7577 0.8223 0.8708 0.5888 0.4696 0.3963 0.3333 0.2725 0.2085 0.1441 0.0895 0.0381

-0.0138 -0.0317 0.1145

1.5476 1.4267 1.3442 1.2730 1.2031 1.1367 1.0665 1.0000 0.9330 0.8664 0.8056 0.7574 0.8220 0.8704 0.5883 0.4691 0.3957 0.3327 0.2719 0.2078 0.1434 0.0888 0.0374

-0.0145 -0.0324 0.1138

3.2883 3.2255 3.1675 3.1129 3.0649 3.0274 2.9950 2.9663 2.9438 2.9228 2.9043 2.8874 2.8675 2.8493 2.8316 2.8135 2.7969 2.7717 2.7410 2.7061 2.6653

2.6295

2.5967

2.5164

2.4382

2.3565

2.3004

2.2546 2.2572 2.2598 2.2624 2.2649 2.2675

1.5490 1.4278 1.3450 1.2736 1.2035 1.1369 1.0666 1.0000 0.9329 0.8662 0.8053 0.7571 0.8216 0.8699 0.5878 0.4685 0.3951 0.3321 0.2713 0.2072 0.1427 0.0882 0.0367

-0.0152 -0.0331 0.1130

182


19 9

2ApJ

S. ,

.81 n

.163

B

TABLE 2—Continued

My B — V Mass logTeyy logp x=—1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

[Fe/H] = -0.47 [O/Fe] = +0.23 F =

13.400 1.752 13.200 1.731 13.000 1.710 12.800 1.689 12.600 1.668 12.400 1.647 12.200 1.626 12.000 1.606 11.800 1.585 11.600 1.566 11.400 1.546 11.200 1.526 11.000 1.507 10.800 1.487 10.600 1.469 10.400 1.450 10.200 1.431 10.000 1.413 9.800 1.397 9.600 1.379 9.400 1.362 9.200 1.343 9.000 1.322 8.800 1.297 8.600 1.267 8.400 1.232 8.200 1.193 8.000 1.151 7.800 1.106 7.600 1.059 7.400 1.015 7.200 0.972 7.000 0.929 6.800 0.883 6.600 0.838 6.400 0.795 6.200 0.753 6.000 0.714 5.800 0.677 5.600 0.645 5.400 0.616 5.200 0.590 5.101 0.578 5.000 0.567 4.902 0.557 4.800 0.548 4.701 0.541 4.600 0.535 4.501 0.530 4.400 0.526 4.300 0.523 4.200 0.522 4.098 0.524 4.000 0.530 3.879 0.544 3.800 0.567 3.754 0.606 3.754 0.647 3.767 0.687 3.767 0.727 3.722 0.767 3.600 0.798 3.400 0.819 3.200 0.831 3.000 0.840

0.1564 11.016 0.1629 10.905 0.1695 10.795 0.1767 10.683 0.1843 10.569 0.1926 10.452 0.2018 10.332 0.2122 10.206 0.2241 10.074 0.2376 9.937 0.2529 9.795 0.2697 9.650 0.2883 9.504 0.3093 9.354 0.3330 9.202 0.3583 9.051 0.3836 8.902 0.4081 8.753 0.4315 8.604 0.4535 8.454 0.4743 8.306 0.4941 8.158 0.5130 8.011 0.5310 7.867 0.5482 7.724 0.5646 7.583 0.5805 7.443 0.5959 7.303 0.6112 7.162 0.6265 7.019 0.6418 6.875 0.6573 6.728 0.6731 6.579 0.6891 6.427 0.7054 6.271 0.7218 6.113 0.7385 5.951 0.7556 5.784 0.7738 5.612 0.7917 5.436 0.8092 5.256 0.8263 5.071 0.8345 4.979 0.8426 4.884 0.8504 4.791 0.8589 4.694 0.8671 4.598 0.8753 4.500 0.8829 4.403 0.8902 4.304 0.8969 4.206 0.9032 4.107 0.9091 4.006 0.9144 3.907 0.9204 3.781 0.9244 3.693 0.9277 3.626 0.9295 3.600 0.9308 3.582 0.9320 3.550 0.9334 3.472 0.9349 3.324 0.9365 3.107 0.9377 2.896 0.9388 2.689

3.5125 5.147 3.5167 5.137 3.5208 5.127 3.5248 5.116 3.5288 5.104 3.5327 5.092 3.5365 5.080 3.5402 5.066 3.5439 5.052 3.5474 5.036 3.5509 5.021 3.5544 5.005 3.5580 4.990 3.5615 4.974 3.5649 4.959 3.5685 4.945 3.5723 4.930 3.5763 4.914 3.5805 4.895 3.5848 4.874 3.5895 4.853 3.5945 4.831 3.5997 4.810 3.6053 4.789 3.6113 4.770 3.6180 4.753 3.6251 4.738 3.6327 4.723 3.6407 4.710 3.6492 4.698 3.6581 4.686 3.6674 4.675 3.6771 4.664 3.6871 4.654 3.6973 4.642 3.7076 4.630 3.7179 4.616 3.7279 4.600 3.7372 4.578 3.7460 4.553 3.7542 4.524 3.7616 4.488 3.7649 4.469 3.7682 4.448 3.7712 4.427 3.7738 4.403 3.7757 4.376 3.7773 4.348 3.7786 4.318 3.7794 4.285 3.7799 4.251 3.7799 4.214 3.7790 4.173 3.7768 4.128 3.7720 4.061 3.7645 3.997 3.7527 3.925 3.7412 3.870 3.7304 3.820 3.7199 3.765 3.7100 3.695 3.7019 3.604 3.6966 3.497 3.6933 3.400 3.6908 3.308

2.1520 2.5419 2.1683 2.5494 2.1896 2.5619 2.2145 2.5778 2.2496 2.6037 2.2901 2.6347 2.3389 2.6732 2.3947 2.7182 2.4537 2.7654 2.5104 2.8093 2.5542 2.8396 2.5962 2.8676 2.6448 2.9017 2.6998 2.9414 2.7421 2.9678 2.7552 2.9651 2.7469 2.9421 2.7288 2.9106 2.7059 2.8756 2.6799 2.8387 2.6560 2.8051 2.6358 2.7760 2.6157 2.7478 2.5947 2.7192 2.5744 2.6920 2.5564 2.6676 2.5426 2.6478 2.5356 2.6350 2.5334 2.6273 2.5334 2.6220 2.5368 2.6202 2.5443 2.6224 2.5496 2.6226 2.5578 2.6257 2.5628 2.6256 2.5686 2.6264 2.5749 2.6277 2.5840 2.6319 2.5911 2.6338 2.5926 2.6304 2.5913 2.6243 2.5817 2.6102

2.5669 2.5911

2.5605 2.5806

2.5355 2.5515

2.4743 2.4866

2.4178 2.4270

2.3618 2.3683

2.5104 2.5140

1.6716 1.6733 1.5065 1.5078 1.4157 1.4167 1.3409 1.3417

0.2454

2.9318 3.3219 2.9305 3.3118 2.9342 3.3066 2.9412 3.3047 2.9578 3.3121 2.9793 3.3239 3.0077 3.3422 3.0417 3.3653 3.0771 3.3889 3.1082 3.4072 3.1251 3.4106 3.1391 3.4107 3.1586 3.4156 3.1831 3.4249 3.1936 3.4194 3.1752 3.3853 3.1374 3.3327 3.0924 3.2743 3.0453 3.2151 2.9976 3.1565 2.9542 3.1034 2.9162 3.0565 2.8798 3.0119 2.8438 2.9684 2.8096 2.9273 2.7788 2.8900 2.7530 2.8582 2.7345 2.8340 2.7213 2.8153 2.7106 2.7992 2.7035 2.7869 2.7006 2.7787 2.6956 2.7686 2.6936 2.7615 2.6884 2.7513 2.6842 2.7421 2.6806 2.7335 2.6797 2.7276 2.6765 2.7193 2.6682 2.7059 2.6573 2.6903 2.6387 2.6672

2.6154 2.6396

2.6007 2.6207

2.5676 2.5836

2.4990 2.5113

2.4362 2.4454

2.3748 2.3813

2.5176 2.5212

1.6750 1.6766 1.5090 1.5103 1.4177 1.4187 1.3424 1.3432

3.7121 4.1024 3.6931 4.0745 3.6791 4.0517 3.6682 4.0319 3.6665 4.0209 3.6687 4.0135 3.6768 4.0114 3.6890 4.0127 3.7007 4.0126 3.7063 4.0055 3.6962 3.9819 3.6823 3.9540 3.6727 3.9299 3.6667 3.9086 3.6454 3.8714 3.5955 3.8057 3.5281 3.7235 3.4562 3.6382 3.3849 3.5548 3.3155 3.4745 3.2526 3.4018 3.1967 3.3370 3.1440 3.2761 3.0930 3.2176 3.0450 3.1626 3.0013 3.1125 2.9635 3.0687 2.9335 3.0330 2.9093 3.0033 2.8878 2.9764 2.8702 2.9536 2.8569 2.9351 2.8417 2.9147 2.8294 2.8973 2.8142 2.8770 2.7999 2.8578 2.7864 2.8393 2.7754 2.8233 2.7620 2.8048 2.7437 2.7815 2.7234 2.7564 2.6957 2.7242

2.6638 2.6881

2.6408 2.6609

2.5996 2.6157

2.5237 2.5361

2.4546 2.4638

2.3878 2.3944

2.5248 2.5284

1.6783 1.6800 1.5116 1.5129 1.4197 1.4207 1.3439 1.3447

183


19 9

2ApJ

S. .

.81.

.16

3B

BERGBUSCH & VANDENBERG

TABLE 2—Continued

184

Mv B — V Mass Mboi logTcjj logg x = —1.0 x = —0.5 x = 0.0 x = 0.5 a; = 1.0 x = 1.5

2.800 0.850 2.600 0.860 2.400 0.872 2.200 0.885 2.000 0.901 1.800 0.918 1.600 0.939 1.400 0.961 1.200 0.985 1.000 1.009 0.800 1.035 0.600 1.064 0.400 1.096 0.200 1.133 0.000 1.174

-0.200 1.220 -0.400 1.270 -0.600 1.328 -0.800 1.394 -1.000 1.469 -1.200 1.561 -1.380 1.678 -1.460 1.784

0.9396 2.481 0.9404 2.274 0.9410 2.064 0.9416 1.854 0.9420 1.641 0.9424 1.425 0.9428 1.206 0.9431 0.985 0.9433 0.761 0.9438 0.535 0.9440 0.305 0.9442 0.072 0.9443 -0.166 0.9445 -0.412 0.9446 -0.668 0.9446 -0.932 0.9447 -1.209 0.9448 -1.505 0.9448 -1.826 0.9449 -2.183 0.9449 -2.608 0.9450 -3.162 0.9450 -3.690

3.6884 3.215 3.6860 3.123 3.6833 3.029 3.6802 2.933 3.6768 2.834 3.6729 2.732 3.6686 2.628 3.6640 2.521 3.6591 2.411 3.6542 2.302 3.6490 2.189 3.6435 2.074 3.6377 1.956 3.6315 1.833 3.6248 1.703 3.6175 1.569 3.6097 1.427 3.6010 1.274 3.5911 1.106 3.5797 0.917 3.5656 0.691 3.5460 0.391 3.5263 0.101

1.2722 1.2727 1.2017 1.2021 1.1405 1.1407 1.0677 1.0678 1.0000 1.0000 0.9348 0.9347 0.8737 0.8735 0.8276 0.8274 0.9124 0.9121 0.9493 0.9489 0.6554 0.6550 0.5376 0.5371 0.4661 0.4656 0.4038 0.4032 0.3401 0.3396 0.2728 0.2722 0.2114 0.2108 0.1580 0.1573 0.1009 0.1003 0.0608 0.0601 0.0372 0.0366 0.2236 0.2229

1.2733 1.2738 1.2025 1.2029 1.1409 1.1412 1.0679 1.0680 1.0000 1.0000 0.9346 0.9345 0.8733 0.8732 0.8271 0.8269 0.9118 0.9114 0.9485 0.9481 0.6545 0.6540 0.5366 0.5361 0.4650 0.4645 0.4027 0.4021 0.3390 0.3384 0.2716 0.2710 0.2101 0.2095 0.1567 0.1561 0.0996 0.0990 0.0594 0.0588 0.0359 0.0352 0.2222 0.2216

1.2744 1.2749 1.2033 1.2036 1.1414 1.1416 1.0682 1.0683 1.0000 1.0000 0.9344 0.9343 0.8730 0.8728 0.8266 0.8264 0.9111 0.9108 0.9477 0.9473 0.6536 0.6531 0.5356 0.5351 0.4640 0.4634 0.4015 0.4010 0.3378 0.3372 0.2704 0.2698 0.2089 0.2083 0.1554 0.1548 0.0983 0.0976 0.0581 0.0575 0.0345 0.0339 0.2209 0.2202

Besides the usual information—namely, Mv, B - V, Mass (in solar units), (assuming = 4.72), log Tee, and log g (in cgs units)—these tables contain the predicted luminosity functions for several choices of x. [Recall from § 2.1 that the number of stars in a mass interval + dJl) is assumed to be proportional to ^~(1+XK] The log </) values give the logarithm of the numbers of stars per unit magnitude interval in bins centered on the tabulated Mv’s: moreover, they have been normalized to 10 stars in the 0.2 mag interval 1.9 < My <2.1. Note that all of the bins have the same width, except- ing the brightest one which spans what remains of the upper red-giant branch once all of the fainter bins have been defined. Because there appears to be a considerable variation in the power-law mass function exponent among globulars having a similar metallicity (e.g., see Richer & Fahlman 1991 ), as well as some tendency for x to vary inversely with [Fe/H] (see McClure et al. 1986, 1988, but see Richer et ai. 1991 and Piotto 1991 ), we have opted to vary the assumed range in jc ( in Tables 2-4) from 0.0 < x < 2.5 when [Fe/H] < -1.66, to -0.5 < x < 2.0 when -1.66 < [Fe/H] < -0.78, and to -1.0 < x < 1.5 when [Fe/H] > -0.78.

Some final comments concerning the tables: to better delin- eate the morphology of the isochrones in the vicinity of the turnoff, particularly of those having a relatively flat subgiant branch (the connecting segment between the turnoff and the lower RGB), additional points were judiciously inserted at intermediate magnitudes. The last point on each isochrone gives the location of the RGB tip and also marks the upper boundary of the brightest bin for which the luminosity function has been tabulated. No luminosity function data are provided for these extra points, which are useful only for the definition of the isochrones.

3.1. Isochrone Considerations

Figure 7 illustrates on the theoretical plane all of the 14 Gyr isochrones that have been computed in this investigation. Also

plotted are the upper RGB ridge fines for three GCs that have been derived by Frogel, Persson, & Cohen (1981) using V- K photometry, as well as the location of Groombridge 1830, the Population II subdwarf standard with the most well determined parameters (see Paper I and van Altena et al. 1988). Given that the metalficities of M92, Ml3, and 47 Tue are be- lieved to near [Fe/H] = -2.2, -1.5, and -0.7, respectively (see Zinn 1985), and that [Fe/H] = -1.4 seems to be a reasonably good estimate of Gmb 1830’s iron content (see Vanden- Berg 1988), the fact that the observations are closely matched by the appropriate theoretical locus indicates that the reff scale of the calculations agrees well with empirical determinations. To be sure, the comparison of the RGBs would be slightly different had isochrones for some other age been plotted. But, in fact, Frogel et al. assumed a particular distance scale for the GCs, which may or may not be correct. So it is entirely possible that the GC fiducials should be adjusted to somewhat brighter or fainter luminosities (as well as horizontally if the inferred ^eff’s suffer from some inaccuracies). Of course, the same criti- cisms can be directed to the theoretical isochrones in view of continuing uncertainties in the bolometric corrections, the treatment of convection, etc. The point of these remarks is that a comparison of predicted and observed RGBs cannot be used to argue for or against a particular age. All that can really be said of Figure 7 is that there is no obvious problem with the models on the (M^, log ^eff) -plane and that it is very encouraging that a single choice for the mixing-length parameter (a = 1.5) seems to be valid for both dwarfs and giants ( see Straniero & Chieffi 1991).

Figure 8 shows that there is comparably good agreement on the CMD. The observed properties of Gmb 1830 (HD 103095 ) are as given by van Altena et al. ( 1988 ) while the GC fiducials were taken directly from, or are based on photometry provided by Stetson & Harris ( 1988) and Buonanno, Corsi, & Fusi Pecci (1985) for M92; Richer & Fahlman (1986) and Sandage ( 1970) for Ml3; and Hesser et al. ( 1987) for 47 Tue.


TABLE 3 Isochrones and Luminosity Functions for 14 Gyr

log<¿

a Mv B-V Mass Mbd logTe// log^ X = 0.0 x = 0.5 X = 1.0 x = 1.5 x = 2.0 x = 2.5

[Fe/H] = -2.26 [O/Fe] = +0.75 Y = 11.400 1.491 11.200 1.449 11.000 1.409 10.800 1.369 10.600 1.333 10.400 1.303 10.200 1.276 10.000 1.251 9.800 1.227 9.600 1.203 9.400 1.178 9.200 1.154 9.000 1.129 8.800 1.101 8.600 1.069 8.400 1.035 8.200 0.998 8.000 0.959 7.800 0.915 7.600 0.869 7.400 0.827 7.200 0.784 7.000 0.740 6.800 0.693 6.600 0.647 6.400 0.604 6.200 0.564 6.000 0.529 5.800 0.498 5.600 0.472 5.400 0.447 5.200 0.426 5.000 0.406 4.800 0.387 4.700 0.379 4.600 0.370 4.500 0.363 4.400 0.356 4.300 0.350 4.200 0.345 4.101 0.340 4.000 0.337 3.900 0.335 3.800 0.336 3.698 0.339 3.600 0.346 3.493 0.359 3.400 0.376 3.292 0.406 3.200 0.437 3.103 0.470 3.000 0.502 2.909 0.522 2.800 0.539 2.600 0.560 2.400 0.574 2.200 0.586 2.000 0.598 1.800 0.607 1.600 0.616 1.400 0.625

0.1580 10.434 0.1665 10.282 0.1756 10.127 0.1857 9.970 0.1970 9.810 0.2099 9.647 0.2253 9.479 0.2433 9.308 0.2638 9.136 0.2866 8.963 0.3123 8.790 0.3413 8.616 0.3735 8.441 0.4043 8.267 0.4308 8.097 0.4547 7.927 0.4768 7.758 0.4971 7.591 0.5158 7.425 0.5333 7.260 0.5501 7.094 0.5665 6.927 0.5827 6.758 0.5989 6.587 0.6152 6.413 0.6316 6.236 0.6482 6.053 0.6652 5.860 0.6820 5.663 0.6981 5.464 0.7140 5.268 0.7288 5.074 0.7421 4.880 0.7541 4.686 0.7595 4.589 0.7647 4.492 0.7695 4.395 0.7742 4.297 0.7786 4.200 0.7828 4.102 0.7866 4.005 0.7901 3.906 0.7932 3.808 0.7960 3.709 0.7985 3.607 0.8007 3.509 0.8029 3.400 0.8045 3.305 0.8060 3.191 0.8072 3.091 0.8083 2.980 0.8092 2.860 0.8099 2.758 0.8104 2.640 0.8113 2.428 0.8120 2.220 0.8125 2.013 0.8131 1.807 0.8135 1.602 0.8139 1.396 0.8142 1.191

3.5826 5.199 3.5877 5.181 3.5926 5.162 3.5975 5.143 3.6022 5.123 3.6066 5.103 3.6107 5.083 3.6144 5.064 3.6181 5.044 3.6219 5.027 3.6257 5.010 3.6295 4.994 3.6332 4.978 3.6374 4.959 3.6422 4.938 3.6475 4.915 3.6531 4.890 3.6595 4.867 3.6668 4.846 3.6749 4.827 3.6837 4.809 3.6931 4.793 3.7030 4.777 3.7132 4.761 3.7235 4.744 3.7338 4.726 3.7441 4.705 3.7545 4.681 3.7644 4.653 3.7736 4.620 3.7820 4.585 3.7895 4.546 3.7965 4.505 3.8032 4.461 3.8063 4.438 3.8093 4.414 3.8120 4.388 3.8145 4.362 3.8169 4.335 3.8189 4.306 3.8205 4.276 3.8216 4.243 3.8219 4.206 3.8212 4.166 3.8194 4.119 3.8161 4.068 3.8103 4.002 3.8034 3.937 3.7919 3.846 3.7794 3.757 3.7631 3.648 3.7494 3.546 3.7423 3.477 3.7375 3.411 3.7321 3.305 3.7285 3.208 3.7257 3.114 3.7231 3.022 3.7207 2.930 3.7181 2.838 3.7155 2.745

2.9681 3.3238 2.9813 3.3258 2.9977 3.3305 3.0186 3.3392 3.0478 3.3555 3.0869 3.3806 3.1283 3.4068 3.1595 3.4215 3.1736 3.4181 3.1866 3.4130 3.2020 3.4097 3.2152 3.4037 3.1967 3.3660 3.1100 3.2622 3.0248 3.1630 2.9641 3.0906 2.9078 3.0239 2.8529 2.9599 2.8048 2.9038 2.7670 2.8586 2.7394 2.8243 2.7185 2.7970 2.7033 2.7757 2.6941 2.7605 2.6832 2.7438 2.6761 2.7310 2.6756 2.7248 2.6652 2.7088 2.6445 2.6827 2.6161 2.6492 2.5733 2.6015 2.5327 2.5565 2.4859 2.5057 2.4355 2.4519

2.3850 2.3984

2.3408 2.3515

2.2867 2.2950

2.2004 2.2066

2.1020 2.1067

1.9801 1.9834

1.8285 1.8308

1.7055 1.7071

1.5353 1.5364

1.3046 1.3053 1.2046 1.2051 1.1315 1.1318 1.0676 1.0678 1.0000 1.0000 0.9346 0.9345 0.8665 0.8662 0.8007 0.8004

0.2350

3.6797 4.0356 3.6704 4.0151 3.6634 3.9964 3.6600 3.9808 3.6633 3.9712 3.6745 3.9685 3.6854 3.9641 3.6835 3.9456 3.6626 3.9073 3.6395 3.8661 3.6175 3.8254 3.5922 3.7809 3.5354 3.7048 3.4146 3.5669 3.3013 3.4396 3.2171 3.3436 3.1401 3.2562 3.0670 3.1741 3.0028 3.1018 2.9503 3.0420 2.9092 2.9942 2.8756 2.9541 2.8480 2.9204 2.8270 2.8934 2.8044 2.8650 2.7859 2.8408 2.7740 2.8233 2.7525 2.7962 2.7210 2.7593 2.6824 2.7156 2.6298 2.6581 2.5803 2.6042 2.5256 2.5455 2.4683 2.4847

2.4117 2.4251

2.3622 2.3729

2.3033 2.3115

2.2129 2.2192

2.1113 2.1160

1.9868 1.9902

1.8332 1.8355

1.7087 1.7103

1.5374 1.5385

1.3061 1.3068 1.2056 1.2061 1.1321 1.1324 1.0679 1.0680 1.0000 1.0000 0.9344 0.9343 0.8660 0.8658 0.8001 0.7998

4.3916 4.7478 4.3598 4.7047 4.3295 4.6626 4.3016 4.6226 4.2792 4.5873 4.2625 4.5567 4.2429 4.5218 4.2078 4.4701 4.1520 4.3968 4.0927 4.3195 4.0334 4.2415 3.9696 4.1584 3.8744 4.0440 3.7194 3.8719 3.5780 3.7164 3.4701 3.5967 3.3724 3.4887 3.2812 3.3883 3.2008 3.2999 3.1338 3.2255 3.0791 3.1641 3.0326 3.1112 2.9928 3.0653 2.9599 3.0264 2.9257 2.9863 2.8957 2.9506 2.8725 2.9218 2.8398 2.8835 2.7975 2.8358 2.7487 2.7819 2.6864 2.7146 2.6280 2.6518 2.5654 2.5853 2.5012 2.5176

2.4385 2.4518

2.3835 2.3942

2.3198 2.3281

2.2254 2.2317

2.1206 2.1253

1.9935 1.9969

1.8379 1.8402

1.7118 1.7134

1.5395 1.5406

1.3075 1.3082 1.2066 1.2070 1.1327 1.1330 1.0682 1.0683 1.0000 1.0000 0.9342 0.9340 0.8656 0.8654 0.7995 0.7992


TABLE 3—Continued

00 Mv B — V Mass Mid logTeyy log^ x = 0.0 x = 0.5 a: = 1.0 x = 1.5 x = 2.0 x = 2.5

1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.600 -2.719 -2.738

11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.800 4.700 4.600 4.501 4.400 4.301 4.200 4.101 4.000

0.635 0.646 0.660 0.674 0.690 0.707 0.727 0.749 0.772 0.798 0.827 0.859 0.894 0.932 0.974 1.021 1.075 1.136 1.206 1.288 1.343 1.352

1.536 1.498 1.460 1.423 1.387 1.353 1.323 1.298 1.273 1.249 1.225 1.202 1.178 1.153 1.123 1.091 1.056 1.019 0.978 0.933 0.886 0.841 0.798 0.753 0.707 0.661 0.617 0.576 0.541 0.511 0.485 0.460 0.438 0.418 0.399 0.391 0.383 0.375 0.369 0.363 0.358 0.354 0.352

0.8145 0.8147 0.8149 0.8151 0.8152 0.8154 0.8155 0.8156 0.8157 0.8158 0.8158 0.8159 0.8159 0.8160 0.8160 0.8160 0.8161 0.8161 0.8161 0.8161 0.8161 0.8161

0.1571 0.1651 0.1739 0.1834 0.1942 0.2063 0.2204 0.2370 0.2561 0.2774 0.3016 0.3294 0.3602 0.3907 0.4181 0.4424 0.4646 0.4850 0.5038 0.5213 0.5380 0.5542 0.5702 0.5861 0.6021 0.6181 0.6343 0.6506 0.6673 0.6838 0.7000 0.7162 0.7310 0.7445 0.7565 0.7620 0.7672 0.7722 0.7769 0.7815 0.7857 0.7895 0.7929

0.985 0.778 0.570 0.362 0.153

- 0.056 - 0.267 - 0.479 - 0.691 - 0.905 - 1.122 - 1.340 - 1.560 - 1.782 - 2.008 ■ 2.239 - 2.477 - 2.722 - 2.974 - 3.238 ■ 3.402 3.429

3.7127 3.7099 3.7068 3.7038 3.7006 3.6973 3.6937 3.6900 3.6863 3.6824 3.6784 3.6741 3.6697 3.6652 3.6604 3.6553 3.6499 3.6442 3.6381 3.6316 3.6274 3.6267

2.652 2.558 2.463 2.368 2.271 2.174 2.076 1.976 1.876 1.775 1.673 1.568 1.463 1.356 1.246 1.133 1.017 0.896 0.771 0.639 0.557 0.543

0.7330 0.6669 0.5997 0.5332 0.4675 0.4044 0.3532 0.3587 0.3345 0.1807 0.0712

-0.0006 -0.0647 -0.1248 -0.1825 -0.2367 -0.2915 -0.3455 -0.3958 -0.4344 -0.3845

0.7327 0.6665 0.5992 0.5327 0.4670 0.4038 0.3526 0.3580 0.3338 0.1800 0.0704

-0.0013 -0.0654 -0.1256 -0.1833 -0.2375 -0.2923 -0.3463 -0.3966 -0.4352 -0.3854

0.7323 0.6660 0.5987 0.5322 0.4664 0.4032 0.3519 0.3574 0.3331 0.1792 0.0697

-0.0021 -0.0662 -0.1263 -0.1841 -0.2383 -0.2932 -0.3471 -0.3974 -0.4361 -0.3862

[Fe/H] = -2.03 [O/Fe] = +0.70 Y = 0.2350

10.520 10.374 10.225 10.072 9.916 9.757 9.594 9.427 9.258 9.088 8.917 8.744 8.570 8.399 8.230 8.061 7.893 7.727 7.564 7.402 7.239 7.077 6.912 6.745 6.576 6.404 6.229 6.048 5.858 5.664 5.467 5.271 5.077 4.883 4.688 4.591 4.493 4.396 4.298 4.201 4.102 4.005 3.906

3.5746 3.5796 3.5846 3.5895 3.5942 3.5987 3.6029 3.6068 3.6106 3.6144 3.6181 3.6218 3.6254 3.6295 3.6340 3.6389 3.6443 3.6502 3.6570 3.6647 3.6732 3.6823 3.6919 3.7019 3.7122 3.7226 3.7330 3.7433 3.7535 3.7632 3.7722 3.7805 3.7880 3.7948 3.8011 3.8041 3.8070 3.8096 3.8119 3.8140 3.8158 3.8169 3.8175

5.199 5.182 5.164 5.146 5.128 5.108 5.089 5.069 5.050 5.032 5.015 4.999 4.983 4.966 4.945 4.922 4.898 4.874 4.852 4.833 4.816 4.800 4.785 4.770 4.755 4.739 4.722 4.702 4.678 4.650 4.617 4.582 4.543 4.500 4.455 4.431 4.406 4.381 4.353 4.325 4.296 4.263 4.228

2.9605 2.9745 2.9913 3.0114 3.0379 3.0738 3.1119 3.1472 3.1664 3.1819 3.2052 3.2222 3.2067 3.1434 3.0600 2.9907 2.9317 2.8754 2.8251 2.7858 2.7549 2.7324 2.7160 2.7037 2.6952 2.6858 2.6769 2.6765 2.6677 2.6491 2.6245 2.5865 2.5464 2.4996 2.4494

2.4016

2.3607

2.2942

2.2051

3.3182 3.3214 3.3270 3.3353 3.3495 3.3721 3.3958 3.4154 3.4179 3.4160 3.4211 3.4191 3.3845 3.3037 3.2055 3.1238 3.0541 2.9884 2.9298 2.8831 2.8453 2.8163 2.7938 2.7755 2.7611 2.7460 2.7315 2.7255 2.7113 2.6874 2.6577 2.6147 2.5702 2.5194 2.4657

2.4149

2.3713

2.3023

2.2113

3.6760 3.6684 3.6627 3.6593 3.6612 3.6705 3.6798 3.6837 3.6695 3.6502 3.6370 3.6160 3.5623 3.4640 3.3510 3.2569 3.1765 3.1014 3.0346 2.9804 2.9357 2.9003 2.8715 2.8472 2.8271 2.8062 2.7862 2.7746 2.7549 2.7257 2.6909 2.6430 2.5940 2.5393 2.4821

2.4282

2.3819

2.3105

2.2174

0.7319 0.6656 0.5982 0.5316 0.4658 0.4026 0.3513 0.3567 0.3324 0.1785 0.0690

-0.0028 -0.0670 -0.1271 -0.1849 -0.2391 -0.2940 -0.3479 -0.3982 -0.4369 -0.3870

4.0340 4.0155 3.9986 3.9835 3.9729 3.9690 3.9639 3.9521 3.9212 3.8845 3.8531 3.8130 3.7402 3.6244 3.4966 3.3901 3.2990 3.2145 3.1394 3.0777 3.0262 2.9842 2.9493 2.9190 2.8930 2.8664 2.8408 2.8237 2.7985 2.7640 2.7241 2.6713 2.6179 2.5592 2.4985

2.4415

2.3924

2.3187

2.2236

0.7315 0.6652 0.5977 0.5311 0.4652 0.4020 0.3507 0.3560 0.3317 0.1778 0.0682

-0.0036 -0.0677 -0.1279 -0.1856 -0.2399 -0.2948 -0.3487 -0.3990 -0.4377 -0.3878

4.3920 4.3626 4.3345 4.3076 4.2847 4.2676 4.2480 4.2206 4.1729 4.1188 4.0692 4.0101 3.9182 3.7849 3.6422 3.5232 3.4214 3.3276 3.2442 3.1750 3.1166 3.0682 3.0271 2.9908 2.9590 2.9267 2.8955 2.8729 2.8422 2.8023 2.7574 2.6996 2.6417 2.5790 2.5148

0.7312 0.6647 0.5972 0.5305 0.4646 0.4013 0.3500 0.3553 0.3310 0.1771 0.0675

-0.0043 -0.0685 -0.1287 -0.1864 -0.2407 -0.2956 -0.3495 -0.3998 -0.4385 -0.3887

4.7501 4.7099 4.6705 4.6319 4.5967 4.5662 4.5323 4.4891 4.4248 4.3533 4.2855 4.2073 4.0963 3.9454 3.7878 3.6564 3.5439 3.4407 3.3490 3.2724 3.2071 3.1522 3.1049 3.0626 3.0250 2.9870 2.9501 2.9220 2.8858 2.8406 2.7906 2.7279 2.6655 2.5989 2.5312

2.4548 2.4681

2.4030

2.3268

2.2298

2.4135

2.3350

2.2359

186



oo My B — V Mass M^oi log<7 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

3.900 3.800 3.696 3.600 3.492 3.400 3.297 3.200 3.113 3.000 2.902 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.593 -2.687

11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000

0.352 0.354 0.359 0.369 0.386 0.406 0.439 0,473 0.506 0.535 0.551 0.565 0.583 0.595 0.606 0.616 0.625 0.634 0.644 0.655 0.667 0.680 0.695 0.711 0.730 0.751 0.773 0.798 0.826 0.856 0.890 0.928 0.970 1.017 1.070 1.130 1.200 1.283 1.377 1.426

1.566 1.535 1.501 1.467 1.433 1.401 1.372 1.345 1.320 1.296 1.272 1.250 1.227 1.204 1.176 1.145 1.112 1.078 1.041 0.999 0.954 0.906 0.860 0.814 0.770

0.7960 0.7987 0.8013 0.8036 0.8057 0.8073 0.8087 0.8100 0.8110 0.8119 0.8125 0.8130 0.8138 0.8144 0.8150 0.8155 0.8159 0.8163 0.8166 0.8169 0.8171 0.8173 0.8175 0.8176 0.8178 0.8179 0.8180 0.8181 0.8182 0.8183 0.8183 0.8183 0.8184 0.8184 0.8184 0.8185 0.8185 0.8185 0.8185 0.8185

0.1568 0.1646 0.1728 0.1819 0.1921 0.2037 0.2171 0.2328 0.2508 0.2709 0.2936 0.3197 0.3495 0.3801 0.4077 0.4317 0.4539 0.4748 0.4941 0.5119 0.5285 0.5445 0.5602 0.5757 0.5913

3.807 3.708 3.604 3.508 3.398 3.303 3.192 3.083 2.980 2.850 2.744 2.633 2.423 2.216 2.009 1.804 1.598 1.393 1.187 0.980 0.773 0.565 0.356 0.147

-0.064 ■ 0.275 ■ 0.488 0.701 0.917 1.135 1.356 1.578 1.805 2.037 2.276 2.523 2.779 3.050 3.329 3.469

3.8173 3.8160 3.8134 3.8094 3.8026 3.7947 3.7820 3.7669 3.7530 3.7426 3.7380 3.7343 3.7297 3.7266 3.7240 3.7215 3.7191 3.7166 3.7139 3.7111 3.7082 3.7051 3.7020 3.6988 3.6953 3.6916 3.6878 3.6839 3.6798 3.6754 3.6708 3.6660 3.6609 3.6555 3.6497 3.6434 3.6367 3.6294 3.6215 3.6174

4.189 4.146 4.096 4.042 3.972 3.903 3.809 3.706 3.609 3.516 3.456 3.397 3.295 3.200 3.107 3.015 2.924 2.832 2.738 2.645 2.550 2.455 2.359 2.263 2.165 2.065 1.965 1.864 1.761 1.657 1.550 1.442 1.331 1.217 1.097 0.974 0.845 0.707 0.564 0.491

2.1028

1.9729

1.8277

1.7265

1.4704

1.2928 1.2039 1.1327 1.0684 1.0000 0.9353 0.8686 0.8014 0.7332 0.6676 0.5990 0.5338 0.4696 0.4134 0.3927 0.4131 0.2864 0.1491 0.0670 0.0010

-0.0602 -0.1187 -0.1732 -0.2286 -0.2831 -0.3321 -0.3753 -0.4021

2.1073

1.9762

1.8300

1.7280

1.4713

1.2935 1.2044 1.1330 1.0685 1.0000 0.9352 0.8684 0.8011 0.7328 0.6671 0.5985 0.5333 0.4691 0.4128 0.3921 0.4125 0.2857 0.1484 0.0663 0.0003

-0.0610 -0.1194 -0.1740 -0.2294 -0.2839 -0.3328 -0.3761 -0.4029

2.1119

1.9794

1.8322

1.7295

1.4723

1.2941 1.2049 1.1333 1.0686 1.0000 0.9351 0.8682 0.8008 0.7324 0.6667 0.5980 0.5327 0.4685 0.4122 0.3914 0.4118 0.2850 0.1477 0.0655

-0.0005 -0.0617 -0.1202 -0.1748 -0.2302 -0.2846 -0.3336 -0.3769 -0.4037

[Fe/H] = -1.78 [O/Fe] = +0.66 Y = 0.2351

10.592 10.451 10.308 10.161 10.011 9.856 9.697 9.533 9.367 9.200 9.032 8.862 8.690 8.519 8.351 8.187 8.021 7.856 7.693 7.533 7.374 7.215 7.055 6.893 6.729

3.5666 3.5716 3.5766 3.5814 3.5862 3.5907 3.5950 3.5989 3.6026 3.6064 3.6101 3.6138 3.6173 3.6210 3.6254 3.6303 3.6355 3.6409 3.6470 3.6541 3.6621 3.6708 3.6801 3.6900 3.7002

5.195 5.179 5.163 5.146 5.129 5.111 5.092 5.072 5.053 5.035 5.018 5.001 4.985 4.968 4.949 4.927 4.904 4.879 4.855 4.835 4.817 4.801 4.787 4.773 4.760

2.9577 2.9700 2.9855 3.0061 3.0332 3.0681 3.1093 3.1442 3.1648 3.1776 3.2003 3.2271 3.2268 3.1734 3.0822 3.0095 2.9603 2.9111 2.8568 2.8071 2.7724 2.7462 2.7270 2.7144 2.7037

3.3170 3.3189 3.3237 3.3330 3.3483 3.3704 3.3977 3.4175 3.4220 3.4181 3.4232 3.4315 3.4122 3.3408 3.2344 3.1490 3.0889 3.0300 2.9670 2.9096 2.8679 2.8351 2.8099 2.7913 2.7748

3.6764 3.6678 3.6619 3.6600 3.6634 3.6728 3.6862 3.6909 3.6793 3.6586 3.6462 3.6361 3.5977 3.5084 3.3867 3.2886 3.2176 3.1488 3.0772 3.0121 2.9634 2.9242 2.8927 2.8682 2.8459

2.1165

1.9826

1.8344

1.7310

1.4733

1.2948 1.2053 1.1336 1.0688 1.0000 0.9350 0.8680 0.8005 0.7321 0.6663 0.5976 0.5322 0.4679 0.4116 0.3908 0.4112 0.2843 0.1470 0.0648

-0.0012 -0.0625 -0.1210 -0.1756 -0.2310 -0.2854 -0.3344 -0.3777 -0.4045

4.0359 4.0169 4.0001 3.9870 3.9786 3.9753 3.9748 3.9644 3.9366 3.8992 3.8694 3.8407 3.7832 3.6760 3.5390 3.4283 3.3463 3.2678 3.1874 3.1146 3.0589 3.0132 2.9755 2.9451 2.9170

2.1210

1.9859

1.8367

1.7325

1.4743

1.2955 1.2058 1.1339 1.0689 1.0000 0.9349 0.8678 0.8002 0.7317 0.6659 0.5971 0.5317 0.4674 0.4110 0.3902 0.4105 0.2836 0.1463 0.0641

-0.0020 -0.0632 -0.1217 -0.1763 -0.2318 -0.2862 -0.3352 -0.3785 -0.4053

4.3956 4.3661 4.3385 4.3142 4.2939 4.2779 4.2635 4.2380 4.1941 4.1399 4.0926 4.0454 3.9689 3.8436 3.6913 3.5680 3.4750 3.3867 3.2976 3.2171 3.1545 3.1022 3.0584 3.0220 2.9881

2.1256

1.9891

1.8389

1.7340

1.4753

1.2962 1.2063 1.1341 1.0690 1.0000 0.9348 0.8676 0.7999 0.7313 0.6654 0.5966 0.5311 0.4668 0.4104 0.3895 0.4098 0.2829 0.1456 0.0633

-0.0027 -0.0640 -0.1225 -0.1771 -0.2325 -0.2870 -0.3360 -0.3793 -0.4061

4.7553 4.7153 4.6769 4.6414 4.6092 4.5805 4.5523 4.5116 4.4516 4.3806 4.3158 4.2502 4.1546 4.0114 3.8437 3.7077 3.6037 3.5056 3.4079 3.3197 3.2500 3.1912 3.1413 3.0989 3.0592

187


TABLE 3—Continued

Mv B -V Mass Mbol logTc// log^ x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.701 4.600 4.501 4.400 4.300 4.200 4.100 4.000 3.899 3.800 3.694 3.600 3.489 3.400 3.294 3.200 3.110 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.547 -2.594

0.724 0.678 0.634 0.593 0.557 0.527 0.500 0.477 0.453 0.433 0.424 0.415 0.407 0.399 0.392 0.385 0.380 0.376 0.374 0.373 0.374 0.378 0.386 0.399 0.421 0.448 0.488 0.530 0.554 0.574 0.595 0.610 0.620 0.630 0.639 0.648 0.657 0.668 0.679 0.692 0.706 0.722 0.740 0.761 0.783 0.807 0.834 0.864 0.898 0.935 0.977 1.024 1.077 1.138 1.209 1.294 1.393 1.477 1.505

0.6069 0.6227 0.6385 0.6546 0.6710 0.6874 0.7038 0.7201 0.7350 0.7486 0.7548 0.7607 0.7663 0.7716 0.7767 0.7816 0.7862 0.7904 0.7942 0.7976 0.8007 0.8038 0.8065 0.8086 0.8107 0.8122 0.8138 0.8151 0.8159 0.8166 0.8176 0.8184 0.8190 0.8196 0.8201 0.8205 0.8208 0.8212 0.8214 0.8216 0.8218 0.8220 0.8221 0.8223 0.8224 0.8225 0.8226 0.8227 0.8227 0.8228 0.8228 0.8229 0.8229 0.8229 0.8230 0.8230 0.8230 0.8230 0.8230

6.561 6.392 6.219 6.042 5.856 5.664 5.470 5.275 5.080 4.885 4.788 4.690 4.593 4.494 4.397 4.299 4.201 4.102 4.004 3.905 3.806 3.707 3.602 3.507 3.393 3.299 3.179 3.062 2.958 2.836 2.623 2.415 2.208 2.003 1.797 1.592 1.386 1.179 0.972 0.764 0.555 0.346 0.135

-0.077 -0.289 -0.503 -0.719 -0.938 -1.159 -1.382 -1.610 -1.845 -2.087 -2.338 -2.600 -2.881 -3.184 -3.426 -3.509

3.7106 3.7211 3.7315 3.7417 3.7518 3.7613 3.7701 3.7782 3.7857 3.7923 3.7953 3.7982 3.8009 3.8034 3.8059 3.8080 3.8096 3.8109 3.8116 3.8115 3.8108 3.8091 3.8057 3.8008 3.7921 3.7822 3.7655 3.7494 3.7415 3.7359 3.7302 3.7266 3.7239 3.7215 3.7192 3.7168 3.7141 3.7113 3.7084 3.7054 3.7023 3.6991 3.6956 3.6917 3.6879 3.6839 3.6797 3.6752 3.6704 3.6653 3.6599 3.6540 3.6477 3.6410 3.6335 3.6252 3.6159 3.6081 3.6053

4.746 4.732 4.715 4.696 4.673 4.645 4.612 4.576 4.538 4.494 4.471 4.446 4.421 4.395 4.369 4.341 4.311 4.279 4.244 4.206 4.165 4.121 4.066 4.010 3.931 3.854 3.740 3.630 3.557 3.486 3.379 3.281 3.188 3.097 3.006 2.914 2.821 2.727 2.633 2.538 2.442 2.346 2.248 2.147 2.047 1.946 1.843 1.737 1.630 1.520 1.407 1.290 1.168 1.040 0.906 0.760 0.602 0.474 0.429

2.6970 2.6875 2.6802 2.6782 2.6733 2.6599 2.6385 2.6036 2.5621 2.5160

2.3810

2.3027

2.2124

2.1033

1.9699

1.8548

1.4100 1.2853 1.2055 1.1349 1.0693 1.0000 0.9360 0.8681 0.8008 0.7324 0.6662 0.5991 0.5351 0.4772 0.4466 0.4824 0.3874 0.2272 0.1350 0.0667 0.0056

-0.0528 -0.1073 -0.1645 -0.2186 -0.2652 -0.3085 -0.3481 -0.3389

2.7624 2.7473 2.7346 2.7272 2.7169 2.6982 2.6717 2.6319 2.5859 2.5358

2.8278 2.8072 2.7890 2.7762 2.7605 2.7366 2.7050 2.6602 2.6097 2.5557

2.4665 2.4829 2.4992

2.4217 2.4349

2.3915

2.3108

2.2185

2.1077

1.9730

1.8569

2.4482

2.4020

2.3189

2.2246

2.1121

1.9761

2.8932 2.8670 2.8434 2.8251 2.8041 2.7750 2.7382 2.6885 2.6336 2.5756

2.5156

2.4615

2.4124

2.3269

2.2307

2.1165

1.9792

1.8590 1.8612

2.9586 2.9269 2.8978 2.8741 2.8477 2.8133 2.7715 2.7168 2.6574 2.5955

2.5320

2.4747

2.4229

2.3350

2.2368

2.1210

1.9823

1.8633

1.4110 1.2859 1.2059 1.1352 1.0695 1.0000 0.9359 0.8678 0.8005 0.7321 0.6658 0.5986 0.5346 0.4766 0.4460 0.4818 0.3868 0.2266 0.1343 0.0660 0.0049

-0.0535 -0.1080 -0.1652 -0.2193 -0.2660 -0.3093 -0.3489 -0.3397

1.4119 1.2866 1.2064 1.1354 1.0696 1.0000 0.9358 0.8676 0.8002 0.7317 0.6653 0.5982 0.5341 0.4761 0.4455 0.4812 0.3862 0.2259 0.1336 0.0653 0.0041

-0.0543 -0.1088 -0.1660 -0.2201 -0.2668 -0.3101 -0.3497 -0.3405

1.4128 1.2872 1.2068 1.1357 1.0697 1.0000 0.9357 0.8674 0.7999 0.7314 0.6649 0.5977 0.5336 0.4755 0.4449 0.4806 0.3855 0.2252 0.1329 0.0646 0.0034

-0.0550 -0.1095 -0.1667 -0.2208 -0.2675 -0.3109 -0.3505 -0.3413

1.4138 1.2879 1.2073 1.1360 1.0698 1.0000 0.9356 0.8672 0.7997 0.7310 0.6645 0.5972 0.5331 0.4750 0.4443 0.4799 0.3849 0.2245 0.1323 0.0639 0.0027

-0.0557 -0.1103 -0.1675 -0.2216 -0.2683 -0.3116 -0.3512 -0.3420

3.0241 2.9867 2.9522 2.9231 2.8914 2.8517 2.8047 2.7451 2.6813 2.6154

2.5484

2.4880

2.4334

2.3430

2.2428

2.1254

1.9854

1.8654

1.7044 1.7058 1.7072 1.7086 1.7100 1.7113

1.4147 1.2886 1.2077 1.1363 1.0700 1.0000 0.9355 0.8670 0.7994 0.7307 0.6641 0.5968 0.5326 0.4744 0.4437 0.4793 0.3842 0.2239 0.1316 0.0632 0.0020

-0.0565 -0.1110 -0.1682 -0.2224 -0.2691 -0.3124 -0.3520 -0.3428

188



oo My B — V Mass ^bol l°g^e// x = 0.0 x — 0.5 x = 1.0 x — 1.5 x = 2.0 x = 2.5

[Fe/H] = -1.66 [O/Fe] = +0.63 Y =

11.800 1.565 S 11.600 1.534 2 11.400 1.502

11.200 1.470 11.000 1.438 10.800 1.409 10.600 1.381 10.400 1.356 10.200 1.332 10.000 1.308 9.800 1.285 9.600 1.263 9.400 1.240 9.200 1.215 9.000 1.187 8.800 1.157 8.600 1.125 8.400 1.091 8.200 1.052 8.000 1.010 7.800 0.964 7.600 0.917 7.400 0.869 7.200 0.824 7.000 0.778 6.800 0.733 6.600 0.688 6.400 0.644 6.200 0.602 6.000 0.566 5.800 0.535 5.600 0.509 5.400 0.485 5.200 0.462 5.000 0.441 4.901 0.432 4.800 0.423 4.700 0.415 4.600 0.408 4.501 0.401 4.400 0.395 4.301 0.390 4.200 0.386 4.100 0.384 4.000 0.385 3.899 0.386 3.800 0.391 3.693 0.401 3.600 0.416 3.487 0.443 3.400 0.473 3.301 0.514 3.200 0.556 3.104 0.576 3.000 0.594 2.800 0.612 2.600 0.624 2.400 0.634 2.200 0.643 2.000 0.652 1.800 0.661 1.600 0.671 1.400 0.682 1.200 0.693 1.000 0.706

0.1604 10.557 0.1684 10.417 0.1770 10.274 0.1864 10.128 0.1970 9.978 0.2091 9.823 0.2233 9.664 0.2398 9.500 0.2586 9.334 0.2794 9.168 0.3031 9.001 0.3301 8.832 0.3597 8.662 0.3891 8.493 0.4153 8.328 0.4387 8.164 0.4604 7.999 0.4806 7.835 0.4992 7.674 0.5163 7.516 0.5325 7.360 0.5482 7.202 0.5636 7.044 0.5790 6.883 0.5944 6.720 0.6100 6.554 0.6258 6.385 0.6416 6.213 0.6575 6.038 0.6738 5.853 0.6902 5.664 0.7065 5.471 0.7227 5.277 0.7376 5.082 0.7512 4.887 0.7574 4.790 0.7634 4.691 0.7690 4.594 0.7744 4.495 0.7796 4.398 0.7846 4.299 0.7892 4.202 0.7934 4.103 0.7972 4.004 0.8007 3.905 0.8042 3.805 0.8071 3.707 0.8099 3.600 0.8119 3.506 0.8141 3.389 0.8155 3.294 0.8172 3.177 0.8184 3.052 0.8191 2.943 0.8198 2.828 0.8207 2.617 0.8214 2.409 0.8221 2.204 0.8226 1.998 0.8231 1.793 0.8235 1.587 0.8239 1.381 0.8242 1.173 0.8244 0.966 0.8247 0.758

3.5652 5.185 3.5701 5.170 3.5750 5.154 3.5798 5.137 3.5844 5.119 3.5888 5.101 3.5929 5.082 3.5967 5.063 3.6003 5.044 3.6040 5.026 3.6077 5.009 3.6114 4.993 3.6150 4.977 3.6190 4.960 3.6235 4.940 3.6283 4.917 3.6334 4.893 3.6389 4.868 3.6452 4.845 3.6525 4.826 3.6606 4.809 3.6695 4.794 3.6789 4.780 3.6888 4.767 3.6991 4.754 3.7095 4.741 3.7200 4.727 3.7304 4.711 3.7406 4.691 3.7506 4.669 3.7601 4.641 3.7689 4.609 3.7769 4.573 3.7843 4.534 3.7908 4.490 3.7938 4.467 3.7965 4.442 3.7991 4.416 3.8015 4.389 3.8038 4.362 3.8057 4.334 3.8073 4.303 3.8083 4.270 3.8087 4.234 3.8083 4.195 3.8074 4.153 3.8054 4.108 3.8014 4.050 3.7958 3.991 3.7859 3.906 3.7743 3.823 3.7576 3.710 3.7433 3.603 3.7374 3.536 3.7324 3.471 3.7279 3.369 3.7246 3.273 3.7221 3.181 3.7199 3.090 3.7175 2.999 3.7150 2.907 3.7123 2.814 3.7095 2.720 3.7066 2.625 3.7036 2.530

2.9653 3.3204 2.9771 3.3217 2.9932 3.3270 3.0169 3.3393 3.0480 3.3584 3.0856 3.3830 3.1245 3.4076 3.1568 3.4245 3.1723 3.4237 3.1872 3.4217 3.2097 3.4266 3.2249 3.4234 3.2092 3.3892 3.1459 3.3091 3.0621 3.2110 2.9977 3.1346 2.9482 3.0746 2.8957 3.0127 2.8412 2.9500 2.7951 2.8965 2.7639 2.8585 2.7412 2.8295 2.7238 2.8061 2.7136 2.7901 2.7045 2.7753 2.6984 2.7635 2.6900 2.7496 2.6818 2.7360 2.6785 2.7273 2.6732 2.7167 2.6604 2.6987 2.6397 2.6729 2.6078 2.6361 2.5671 2.5910 2.5217 2.5416

2.4731 2.4895

2.4336 2.4469

2.3881 2.3985

2.3063 2.3144

2.2166 2.2226

2.1032 2.1075

1.9728 1.9758

1.8797 1.8817

1.6523 1.6536

1.3898 1.3907 1.2729 1.2735 1.2038 1.2043 1.1346 1.1349 1.0673 1.0675 1.0000 1.0000 0.9351 0.9349 0.8671 0.8669 0.8011 0.8008 0.7331 0.7328 0.6677 0.6673

0.2352

3.6755 4.0308 3.6664 4.0112 3.6609 3.9949 3.6619 3.9845 3.6689 3.9794 3.6804 3.9780 3.6908 3.9741 3.6923 3.9602 3.6752 3.9268 3.6563 3.8910 3.6435 3.8605 3.6219 3.8205 3.5694 3.7495 3.4724 3.6357 3.3600 3.5090 3.2716 3.4086 3.2010 3.3275 3.1298 3.2469 3.0587 3.1675 2.9979 3.0994 2.9532 3.0479 2.9179 3.0062 2.8884 2.9707 2.8665 2.9430 2.8460 2.9167 2.8286 2.8938 2.8091 2.8687 2.7902 2.8443 2.7761 2.8249 2.7602 2.8037 2.7371 2.7754 2.7062 2.7394 2.6645 2.6928 2.6149 2.6388 2.5615 2.5814

2.5059 2.5223

2.4601 2.4734

2.4090 2.4195

2.3224 2.3305

2.2287 2.2347

2.1118 2.1161

1.9788 1.9818

1.8837 1.8857

1.6550 1.6563

1.3916 1.3925 1.2742 1.2748 1.2047 1.2051 1.1351 1.1354 1.0676 1.0677 1.0000 1.0000 0.9348 0.9347 0.8667 0.8665 0.8006 0.8003 0.7324 0.7321 0.6669 0.6664

4.3861 4.7415 4.3560 4.7010 4.3289 4.6631 4.3072 4.6300 4.2901 4.6008 4.2756 4.5733 4.2575 4.5410 4.2282 4.4962 4.1784 4.4302 4.1257 4.3606 4.0776 4.2948 4.0192 4.2180 3.9298 4.1102 3.7991 3.9625 3.6581 3.8072 3.5456 3.6826 3.4539 3.5804 3.3640 3.4811 3.2764 3.3852 3.2008 3.3023 3.1426 3.2373 3.0946 3.1830 3.0531 3.1354 3.0195 3.0960 2.9875 3.0582 2.9589 3.0241 2.9283 2.9879 2.8985 2.9527 2.8737 2.9225 2.8472 2.8908 2.8137 2.8521 2.7726 2.8059 2.7211 2.7495 2.6627 2.6865 2.6014 2.6213

2.5387 2.5551

2.4867 2.5000

2.4299 2.4404

2.3385 2.3465

2.2407 2.2468

2.1204 2.1247

1.9848 1.9878

1.8878 1.8898

1.6576 1.6589

1.3934 1.3943 1.2755 1.2761 1.2056 1.2060 1.1357 1.1360 1.0678 1.0680 1.0000 1.0000 0.9346 0.9345 0.8663 0.8661 0.8000 0.7997 0.7317 0.7314 0.6660 0.6656

189



Mv B — V Mass Mfjol l°g^e// x — 0.0 x = 0.5 a; = 1.0 x = 1.5 x = 2.0

0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.516 -2.532

12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.700 4.600 4.501 4.400 4.301 4.200 4.100

0.721 0.737 0.757 0.779 0.802 0.827 0.856 0.887 0.922 0.962 1.006 1.057 1.113 1.179 1.257 1.350 1.459 1.532 1.542

1.597 1.566 1.536 1.506 1.477 1.449 1.422 1.397 1.374 1.351 1.329 1.307 1.285 1.261 1.235 1.208 1.178 1.145 1.109 1.069 1.026 0.981 0.934 0.886 0.839 0.793 0.748 0.704 0.659 0.616 0.580 0.549 0.522 0.499 0.476 0.455 0.445 0.437 0.429 0.422 0.416 0.410 0.406 0.403 0.402

0.8249 0.8250 0.8252 0.8253 0.8254 0.8256 0.8256 0.8257 0.8258 0.8258 0.8259 0.8259 0.8259 0.8260 0.8260 0.8260 0.8260 0.8260 0.8260

0.1594 0.1672 0.1756 0.1847 0.1948 0.2063 0.2194 0.2348 0.2524 0.2721 0.2944 0.3199 0.3483 0.3769 0.4039 0.4286 0.4509 0.4712 0.4899 0.5073 0.5237 0.5394 0.5548 0.5699 0.5850 0.6003 0.6157 0.6312 0.6468 0.6626 0.6787 0.6950 0.7117 0.7278 0.7428 0.7564 0.7627 0.7688 0.7745 0.7800 0.7853 0.7904 0.7949 0.7991 0.8032

0.549 0.339 0.127

■ 0.086 •0.299 - 0.514 • 0.732 - 0.952 - 1.175 ■ 1.401 - 1.634 - 1.874 - 2.122 - 2.381 ■ 2.657 - 2.954 * 3.283 - 3.498 - 3.529

3.7004 3.6972 3.6934 3.6894 3.6855 3.6813 3.6768 3.6720 3.6670 3.6616 3.6558 3.6495 3.6428 3.6354 3.6271 3.6178 3.6070 3.5997 3.5986

10.632 10.494 10.354 10.212 10.066 9.917 9.762 9.603 9.441 9.278 9.113 8.946 8.779 8.614 8.449 8.284 8.121 7.960 7.802 7.645 7.491 7.337 7.181 7.025 6.866 6.704 6.541 6.374 6.204 6.030 5.849 5.663 5.472 5.279 5.084 4.889 4.792 4.693 4.595 4.497 4.399 4.300 4.202 4.103 4.005

3.5575 3.5623 3.5671 3.5718 3.5764 3.5808 3.5850 3.5889 3.5926 3.5963 3.5999 3.6035 3.6071 3.6110 3.6153 3.6197 3.6244 3.6297 3.6356 3.6424 3.6499 3.6581 3.6671 3.6766 3.6867 3.6970 3.7076 3.7182 3.7286 3.7388 3.7488 3.7582 3.7667 3.7744 3.7817 3.7883 3.7913 3.7939 3.7962 3.7984 3.8004 3.8021 3.8033 3.8041 3.8042

2.434 2.337 2.237 2.136 2.035 1.932 1.828 1.720 1.611 1.499 1.383 1.262 1.136 1.003 0.859 0.703 0.528 0.413 0.396

0.5999 0.5385 0.4862 0.4862 0.5081 0.3388 0.2092 0.1315 0.0675 0.0080

-0.0480 -0.1047 -0.1612 -0.2107 -0.2545 -0.2978 -0.3191 -0.2752

0.5994 0.5380 0.4856 0.4856 0.5075 0.3382 0.2085 0.1308 0.0668 0.0073

-0.0487 -0.1054 -0.1619 -0.2115 -0.2552 -0.2986 -0.3198 -0.2760

0.5990 0.5375 0.4851 0.4850 0.5069 0.3375 0.2078 0.1301 0.0661 0.0066

-0.0494 -0.1061 -0.1626 -0.2122 -0.2560 -0.2993 -0.3206 -0.2768

[Fe/H] = -1.48

5.181 5.166 5.151 5.135 5.118 5.101 5.082 5.064 5.045 5.027 5.010 4.994 4.978 4.962 4.943 4.921 4.897 4.872 4.850 4.829 4.811 4.795 4.781 4.768 4.756 4.744 4.732 4.719 4.703 4.685 4.663 4.636 4.604 4.567 4.528 4.484 4.460 4.435 4.408 4.381 4.353 4.322 4.291 4.257 4.220

2.6088 2.6307 2.6560 2.6857 2.7227 2.7703 2.8204 2.8689 2.9068 2.9399 2.9800 3.0188 3.0258 2.9961 2.9467 2.8916 2.8384 2.7898 2.7480 2.7116 2.6824 2.6620 2.6479 2.6377 2.6343 2.6327 2.6320 2.6303 2.6276 2.6285 2.6319 2.6262 2.6127 2.5872 2.5529 2.5124

2.4702

2.4389

2.3854

2.3051

2.9668 2.9783 2.9930 3.0117 3.0370 3.0722 3.1088 3.1427 3.1649 3.1817 3.2046 3.2254 3.2143 3.1675 3.1031 3.0351 2.9708 2.9127 2.8624 2.8183 2.7822 2.7553 2.7352 2.7191 2.7100 2.7028 2.6966 2.6895 2.6815 2.6771 2.6753 2.6645 2.6459 2.6155 2.5767 2.5323

2.4866

2.4521

2.3958

2.3131

3.3249 3.3261 3.3301 3.3377 3.3515 3.3741 3.3972 3.4165 3.4231 3.4235 3.4293 3.4321 3.4028 3.3390 3.2596 3.1787 3.1033 3.0355 2.9767 2.9251 2.8821 2.8487 2.8224 2.8005 2.7857 2.7730 2.7612 2.7487 2.7354 2.7258 2.7188 2.7028 2.6790 2.6439 2.6006 2.5523

2.5030

2.4653

2.4062

2.3210

0.5985 0.5370 0.4846 0.4844 0.5063 0.3369 0.2072 0.1294 0.0654 0.0059

-0.0501 -0.1069 -0.1634 -0.2130 -0.2567 -0.3001 -0.3214 -0.2775

0.5981 0.5365 0.4840 0.4839 0.5057 0.3362 0.2065 0.1287 0.0647 0.0052

-0.0508 -0.1076 -0.1641 -0.2137 -0.2575 -0.3008 -0.3221 -0.2783

[O/Fe] = +0.60 Y = 0.2354

x = —0.5 x = 0.0 x — 0.5 a? = 1.0 x = 1.5

3.6830 3.6739 3.6673 3.6638 3.6660 3.6762 3.6858 3.6904 3.6814 3.6655 3.6541 3.6390 3.5915 3.5106 3.4161 3.3223 3.2358 3.1584 3.0911 3.0318 2.9819 2.9421 2.9097 2.8819 2.8614 2.8431 2.8258 2.8079 2.7893 2.7744 2.7622 2.7411 2.7122 2.6722 2.6245 2.5722

2.5194

2.4786

2.4166

2.3290

4.0412 4.0218 4.0045 3.9900 3.9805 3.9783 3.9744 3.9643 3.9397 3.9075 3.8790 3.8458 3.7801 3.6822 3.5727 3.4660 3.3683 3.2813 3.2055 3.1386 3.0817 3.0355 2.9970 2.9633 2.9371 2.9133 2.8905 2.8672 2.8432 2.8231 2.8057 2.7795 2.7454 2.7005 2.6484 2.5921

2.5358

2.4918

2.4270

2.3370

190

x = 2.5

0.5976 0.5360 0.4835 0.4833 0.5051 0.3356 0.2058 0.1280 0.0640 0.0045

-0.0516 -0.1083 -0.1649 -0.2145 -0.2582 -0.3016 -0.3229 -0.2791

x = 2.0

4.3995 4.3698 4.3419 4.3163 4.2952 4.2805 4.2631 4.2384 4.1981 4.1495 4.1040 4.0528 3.9689 3.8539 3.7294 3.6096 3.5009 3.4043 3.3200 3.2454 3.1816 3.1289 3.0843 3.0448 3.0128 2.9834 2.9551 2.9264 2.8971 2.8718 2.8492 2.8178 2.7786 2.7288 2.6723 2.6121

2.5522

2.5051

2.4374

2.3450


TABLE 3—Continued

My B-V Mass Mbol logTeff logg x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0

4.000 3.898 3.800 3.693 3.600 3.485 3.400 3.326 3.200 3.107 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.394 -2.488

12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200

0.402 0.406 0.412 0.427 0.445 0.480 0.518 0.558 0.591 0.608 0.621 0.636 0.646 0.655 0.663 0.673 0.683 0.693 0.704 0.717 0.730 0.746 0.766 0.786 0.809 0.833 0.860 0.889 0.922 0.959 1.000 1.046 1.098 1.156 1.225 1.305 1.399 1.508 1.563

1.627 1.598 1.568 1.539 1.510 1.482 1.456 1.433 1.411 1.389 1.369 1.349 1.330 1.309 1.284 1.258 1.229 1.199 1.165 1.129 1.090 1.047 1.002 0.956 0.908 0.861

0.8070 0.8105 0.8134 0.8161 0.8182 0.8204 0.8221 0.8233 0.8245 0.8251 0.8257 0.8266 0.8273 0.8279 0.8285 0.8289 0.8293 0.8297 0.8300 0.8302 0.8304 0.8306 0.8308 0.8309 0.8311 0.8312 0.8313 0.8314 0.8315 0.8315 0.8316 0.8316 0.8317 0.8317 0.8317 0.8317 0.8318 0.8318 0.8318

0.1598 0.1675 0.1759 0.1849 0.1949 0.2060 0.2186 0.2331 0.2497 0.2686 0.2901 0.3146 0.3419 0.3702 0.3972 0.4215 0.4437 0.4645 0.4839 0.5018 0.5186 0.5346 0.5499 0.5649 0.5798 0.5947

3.906 3.805 3.707 3.599 3.504 3.381 3.279 3.182 3.036 2.932 2.816 2.607 2.400 2.195 1.990 1.784 1.577 1.371 1.163 0.955 0.746 0.536 0.324 0.111

- 0.102 - 0.317 - 0.535 - 0.754 - 0.976 - 1.201 - 1.431 - 1.669 ■ 1.913 - 2.167 - 2.436 - 2.723 - 3.033 - 3.376 ■ 3.557

3.8036 3.8022 3.7995 3.7941 3.7874 3.7745 3.7598 3.7462 3.7362 3.7317 3.7281 3.7244 3.7215 3.7192 3.7170 3.7145 3.7119 3.7092 3.7063 3.7033 3.7002 3.6970 3.6931 3.6892 3.6852 3.6811 3.6767 3.6720 3.6671 3.6619 3.6562 3.6502 3.6437 3.6366 3.6288 3.6201 3.6102 3.5988 3.5926

4.180 4.136 4.088 4.024 3.960 3.861 3.762 3.670 3.572 3.512 3.452 3.354 3.260 3.169 3.079 2.987 2.893 2.800 2.706 2.611 2.515 2.418 2.318 2.217 2.116 2.013 1.909 1.803 1.694 1.583 1.469 1.349 1.226 1.096 0.957 0.808 0.644 0.461 0.364

2.2138

2.1025

1.9825

1.9024

1.5452

1.3630 1.2727 1.2011 1.1321 1.0654 1.0000 0.9317 0.8636 0.7975 0.7290 0.6627 0.6000 0.5420 0.5144 0.5739 0.4545 0.2874 0.1954 0.1278 0.0671 0.0100

-0.0480 -0.1067 -0.1598 -0.2067 -0.2552 -0.2906 -0.3012

2.2197

2.1066

1.9853

1.9042

1.5464

1.3639 1.2734 1.2015 1.1324 1.0655 1.0000 0.9316 0.8634 0.7972 0.7287 0.6623 0.5995 0.5415 0.5139 0.5733 0.4539 0.2867 0.1947 0.1271 0.0665 0.0093

-0.0488 -0.1074 -0.1605 -0.2074 -0.2559 -0.2913 -0.3019

2.2256

2.1108

1.9882

1.9061

1.5476

1.3647 1.2740 1.2019 1.1327 1.0657 1.0000 0.9315 0.8632 0.7969 0.7284 0.6619 0.5991 0.5411 0.5134 0.5728 0.4533 0.2861 0.1941 0.1265 0.0658 0.0086

-0.0495 -0.1081 -0.1612 -0.2081 -0.2566 -0.2921 -0.3027

2.2315

2.1150

2.2373

2.1191

19911 1.9940

2.2432

2.1233

1.9968

[Fe/H] = —1.26 [O/Fe] = +0.55 Y = 0.2358

10.689 10.555 10.419 10.279 10.137 9.991 9.842 9.688 9.530 9.370 9.207 9.043 8.879 8.716 8.554 8.394 8.234 8.074 7.916 7.761 7.608 7.456 7.305 7.153 6.998 6.842

3.5497 3.5544 3.5590 3.5637 3.5682 3.5726 3.5767 3.5807 3.5845 3.5881 3.5916 3.5951 3.5987 3.6024 3.6065 3.6109 3.6156 3.6205 3.6259 3.6320 3.6388 3.6465 3.6547 3.6638 3.6733 3.6834

5.174 5.160 5.145 5.129 5.113 5.097 5.079 5.062 5.044 5.026 5.008 4.992 4.976 4.961 4.943 4.922 4.899 4.875 4.851 4.829 4.810 4.793 4.777 4.764 4.752 4.741

2.6192 2.6408 2.6657 2.6947 2.7279 2.7685 2.8137 2.8602 2.9025 2.9400 2.9802 3.0180 3.0337 3.0131 2.9614 2.9044 2.8601 2.8210 2.7794 2.7400 2.7078 2.6819 2.6614 2.6497 2.6422 2.6410

2.9792 2.9906 3.0050 3.0232 3.0449 3.0734 3.1056 3.1382 3.1655 3.1872 3.2107 3.2309 3.2288 3.1910 3.1242 3.0542 2.9986 2.9496 2.8991 2.8518 2.8124 2.7799 2.7532 2.7357 2.7225 2.7158

3.3394 3.3406 3.3445 3.3517 3.3620 3.3783 3.3976 3.4162 3.4286 3.4345 3.4413 3.4440 3.4240 3.3691 3.2871 3.2040 3.1372 3.0782 3.0189 2.9637 2.9171 2.8779 2.8451 2.8217 2.8028 2.7906

1.9080 1.9098 1.9117

1.5488 1.5500 1.5512

1.3656 1.2746 1.2023 1.1329 1.0658 1.0000 0.9314 0.8630 0.7967 0.7280 0.6616 0.5986 0.5406 0.5129 0.5722 0.4527 0.2855 0.1934 0.1258 0.0651 0.0079

-0.0502 -0.1089 -0.1620 -0.2089 -0.2574 -0.2928 -0.3034

3.6996 3.6906 3.6840 3.6802 3.6791 3.6834 3.6897 3.6944 3.6917 3.6818 3.6720 3.6571 3.6192 3.5472 3.4500 3.3539 3.2758 3.2069 3.1387 3.0755 3.0217 2.9760 2.9369 2.9077 2.8832 2.8654

1.3665 1.2752 1.2028 1.1332 1.0659 1.0000 0.9313 0.8628 0.7964 0.7277 0.6612 0.5982 0.5401 0.5123 0.5717 0.4521 0.2849 0.1928 0.1251 0.0644 0.0072

-0.0509 -0.1096 -0.1627 -0.2096 -0.2581 -0.2935 -0.3042

4.0599 4.0407 4.0236 4.0089 3.9964 3.9885 3.9819 3.9726 3.9550 3.9292 3.9027 3.8703 3.8145 3.7254 3.6129 3.5038 3.4145 3.3356 3.2585 3.1873 3.1264 3.0740 3.0288 2.9937 2.9635 2.9402

1.3674 1.2759 1.2032 1.1335 1.0660 1.0000 0.9312 0.8626 0.7961 0.7274 0.6608 0.5978 0.5396 0.5118 0.5711 0.4515 0.2842 0.1921 0.1245 0.0637 0.0066

-0.0516 -0.1103 -0.1634 -0.2103 -0.2588 -0.2943 -0.3049

4.4203 4.3909 4.3632 4.3376 4.3137 4.2937 4.2741 4.2508 4.2183 4.1767 4.1335 4.0836 4.0099 3.9036 3.7759 3.6538 3.5532 3.4643 3.3783 3.2992 3.2311 3.1721 3.1207 3.0797 3.0439 3.0151

191

American Astronomical Society • Provided by the NASA Astrophysics Data System

TABLE 3—Continued

Mv B-V Mass Mbol l°g^e// x ~ "“0*5 x — 0.0 x — 0.5 x = 1.0 x = 1.5 x = 2.0

7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.701 4.600 4.501 4.400 4.301 4.200 4.100 4.000 3.896 3.800 3.686 3.600 3.524 3.471 3.400 3.316 3.200 3.000 2.80Ö 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.194 -2.288

0.814 0.770 0.726 0.683 0.639 0.601 0.568 0.541 0.517 0.496 0.475 0.465 0.456 0.448 0.441 0.435 0.431 0.427 0.425 0.425 0.427 0.434 0.444 0.464 0.489 0.523 0.559 0.593 0.619 0.639 0.658 0.669 0.678 0.687 0.696 0.705 0.715 0.726 0.738 0.751 0.769 0.788 0.810 0.832 0.857 0.885 0.915 0.948 0.985 1.027 1.074 1.127 1.189 1.260 1.344 1.447 1.564 1.634

0.6099 0.6252 0.6407 0.6562 0.6719 0.6878 0.7039 0.7206 0.7367 0.7517 0.7654 0.7718 0.7779 0.7837 0.7896 0.7950 0.8001 0.8052 0.8099 0.8141 0.8179 0.8214 0.8242 0.8272 0.8292 0.8309 0.8322 0.8333 0.8342 0.8350 0.8361 0.8369 0.8376 0.8382 0.8388 0.8392 0.8396 0.8399 0.8402 0.8405 0.8407 0.8408 0.8410 0.8412 0.8414 0.8415 0.8416 0.8416 0.8417 0.8417 0.8418 0.8418 0.8419 0.8419 0.8419 0.8420 0.8420 0.8420

6.683 6.521 6.356 6.188 6.017 5.841 5.658 5.470 5.279 5.086 4.891 4.794 4.695 4.598 4.499 4.401 4.302 4.204 4.105 4.005 3.907 3.803 3.707 3.591 3.498 3.408 3.335 3.242 3.140 3.011 2.798 2.590 2.385 2.179 1.973 1.767 1.560 1.352 1.144 0.935 0.723 0.511 0.297 0.082

-0.135 -0.354 -0.575 -0.799 -1.028 -1.264 -1.506 -1.758 -2.023 -2.306 -2.612 -2.961 -3.351 -3.594

3.6937 3.7042 3.7147 3.7251 3.7353 3.7453 3.7548 3.7633 3.7710 3.7779 3.7843 3.7871 3.7897 3.7922 3.7943 3.7959 3.7972 3.7982 3.7987 3.7983 3.7972 3.7947 3.7908 3.7836 3.7747 3.7623 3.7500 3.7394 3.7323 3.7269 3.7219 3.7189 3.7165 3.7140 3.7116 3.7091 3.7065 3.7037 3.7007 3.6977 3.6940 3.6900 3.6859 3.6818 3.6775 3.6728 3.6679 3.6627 3.6571 3.6510 3.6445 3.6374 3.6296 3.6208 3.6109 3.5990 3.5851 3.5759

4.729 4.717 4.704 4.689 4.672 4.651 4.626 4.595 4.559 4.519 4.474 4.450 4.424 4.399 4.370 4.341 4.309 4.277 4.241 4.202 4.161 4.111 4.058 3.985 3.913 3.828 3.751 3.671 3.603 3.530 3.425 3.331 3.239 3.147 3.056 2.963 2.870 2.776 2.681 2.585 2.486 2.385 2.283 2.181 2.077 1.971 1.863 1.752 1.638 1.520 1.397 1.268 1.131 0.982 0.820 0.633 0.422 0.288

2.6418 2.6405 2.6396 2.6357 2.6355 2.6373 2.6348 2.6226 2.6023 2.5711 2.5330

2.4949

2.4686

2.4039

2.3227

2.2298

2.1205

2.0500

1.8217

1.4751 1.3459 1.2719 1.2039 1.1354 1.0688 1.0000 0.9327 0.8653 0.7978 0.7325 0.6709 0.6106 0.5808 0.6504 0.5410 0.3582 0.2620 0.1959 0.1362 0.0776 0.0174

-0.0383 -0.0878 -0.1397 -0.1794 -0.2079 -0.1979

2.7111 2.7045 2.6983 2.6891 2.6839 2.6805 2.6729 2.6557 2.6306 2.5950 2.5530

2.5114

2.4819

2.4143

2.3304

2.2355

2.1244

2.0527

1.8234

1.4762 1.3467 1.2725 1.2043 1.1356 1.0689 1.0000 0.9326 0.8651 0.7976 0.7322 0.6706 0.6102 0.5803 0.6499 0.5405 0.3576 0.2614 0.1953 0.1356 0.0770 0.0168

-0.0390 -0.0885 -0.1404 -0.1801 -0.2087 -0.1986

2.7805 2.7684 2.7569 2.7425 2.7322 2.7238 2.7111 2.6888 2.6589 2.6190 2.5731

2.5279

2.4952

2.4247

2.3382

2.2411

2.1284

2.0553

1.4774 1.3475 1.2731 1.2047 1.1359 1.0690 1.0000 0.9325 0.8650 0.7973 0.7318 0.6702 0.6097 0.5799 0.6494 0.5399 0.3570 0.2608 0.1947 0.1350 0.0763 0.0161

-0.0397 -0.0892 -0.1411 -0.1808 -0.2094 -0.1993

2.8499 2.8324 2.8156 2.7960 2.7805 2.7670 2.7493 2.7219 2.6873 2.6430 2.5931

2.5444

2.5085

2.4351

2.3460

2.2468

2.1324

2.0579

2.9193 2.8964 2.8743 2.8495 2.8288 2.8103 2.7875 2.7550 2.7156 2.6670 2.6132

2.5609

2.5218

2.4455

2.3538

2.2524

2.1363

2.0605

1.4785 1.3483 1.2737 1.2051 1.1361 1.0691 1.0000 0.9324 0.8648 0.7971 0.7315 0.6698 0.6093 0.5794 0.6489 0.5394 0.3564 0.2602 0.1941 0.1343 0.0757 0.0154

-0.0404 -0.0899 -0.1418 -0.1815 -0.2101 -0.2000

1.4796 1.3492 1.2743 1.2055 1.1364 1.0693 1.0000 0.9323 0.8646 0.7968 0.7312 0.6694 0.6089 0.5789 0.6484 0.5388 0.3558 0.2596 0.1934 0.1337 0.0750 0.0147

-0.0410 -0.0906 -0.1425 -0.1822 -0.2108 -0.2008

2.9887 2.9604 2.9330 2.9029 2.8772 2.8535 2.8257 2.7882 2.7440 2.6909 2.6332

2.5774

2.5350

2.4559

2.3616

2.2580

2.1403

2.0631

1.8250 1.8266 1.8283 1.8299

1.4807 1.3500 1.2749 1.2059 1.1366 1.0694 1.0000 0.9322 0.8644 0.7965 0.7309 0.6691 0.6085 0.5785 0.6479 0.5383 0.3553 0.2590 0.1928 0.1330 0.0744 0.0141

-0.0417 -0.0912 -0.1432 -0.1829 -0.2115 -0.2015

192



^0 a CM (S\ (T\ \ 1

My B — V Mass Mbol l°S^c// x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0

[Fe/H] = —1.03 [O/Fe] = +0.50 Y =

12.600 1.690 12.400 1.662 12.200 1.634 12.000 1.604 11.800 1.575 11.600 1.546 11.400 1.519 11.200 1.493 11.000 1.469 10.800 1.446 10.600 1.426 10.400 1.406 10.200 1.388 10.000 1.370 9.800 1.351 9.600 1.330 9.400 1.307 9.200 1.282 9.000 1.254 8.800 1.223 8.600 1.189 8.400 1.152 8.200 1.112 8.000 1.069 7.800 1.025 7.600 0.980 7.400 0.935 7.200 0.888 7.000 0.841 6.800 0.795 6.600 0.752 6.400 0.710 6.200 0.666 6.000 0.625 5.800 0.593 5.600 0.565 5.400 0.539 5.200 0.517 5.100 0.508 5.000 0.498 4.901 0.489 4.800 0.481 4.701 0.473 4.600 0.466 4.501 0.460 4.400 0.456 4.300 0.454 4.200 0.453 4.099 0.455 4.000 0.459 3.891 0.468 3.800 0.483 3.696 0.512 3.637 0.546 3.600 0.581 3.532 0.627 3.400 0.665 3.200 0.688 3.000 0.700 2.800 0.710 2.600 0.718 2.400 0.726 2.200 0.735 2.000 0.744 1.800 0.755

0.1563 10.839 0.1633 10.714 0.1707 10.587 0.1788 10.456 0.1878 10.322 0.1977 10.183 0.2089 10.041 0.2217 9.894 0.2363 9.743 0.2528 9.589 0.2710 9.434 0.2915 9.278 0.3151 9.119 0.3414 8.958 0.3686 8.798 0.3947 8.641 0.4189 8.485 0.4412 8.328 0.4622 8.172 0.4818 8.016 0.5001 7.863 0.5170 7.713 0.5331 7.565 0.5487 7.417 0.5638 7.268 0.5787 7.119 0.5936 6.966 0.6085 6.812 0.6236 6.655 0.6387 6.496 0.6540 6.334 0.6694 6.169 0.6849 6.001 0.7007 5.829 0.7176 5.649 0.7339 5.465 0.7497 5.277 0.7646 5.087 0.7717 4.991 0.7785 4.893 0.7850 4.796 0.7913 4.697 0.7975 4.600 0.8039 4.501 0.8099 4.403 0.8155 4.303 0.8207 4.205 0.8254 4.106 0.8297 4.006 0.8335 3.907 0.8372 3.798 0.8400 3.705 0.8430 3.591 0.8448 3.516 0.8461 3.458 0.8476 3.359 0.8489 3.198 0.8502 2.981 0.8512 2.772 0.8520 2.565 0.8527 2.360 0.8533 2.154 0.8538 1.948 0.8542 1.741 0.8546 1.534

3.5363 5.171 3.5409 5.158 3.5455 5.145 3.5500 5.131 3.5546 5.117 3.5590 5.102 3.5633 5.085 3.5673 5.069 3.5712 5.052 3.5749 5.034 3.5786 5.017 3.5822 5.001 3.5858 4.985 3.5893 4.970 3.5930 4.954 3.5971 4.937 3.6014 4.918 3.6059 4.896 3.6106 4.872 3.6157 4.848 3.6213 4.826 3.6277 4.806 3.6348 4.788 3.6425 4.772 3.6508 4.758 3.6597 4.745 3.6691 4.733 3.6790 4.721 3.6893 4.710 3.6998 4.699 3.7104 4.687 3.7210 4.673 3.7313 4.657 3.7412 4.638 3.7501 4.612 3.7586 4.582 3.7666 4.549 3.7737 4.509 3.7768 4.487 3.7796 4.463 3.7821 4.438 3.7844 4.411 3.7866 4.384 3.7885 4.356 3.7901 4.326 3.7911 4.293 3.7915 4.259 3.7914 4.221 3.7906 4.180 3.7890 4.136 3.7855 4.080 3.7803 4.024 3.7700 3.938 3.7585 3.863 3.7472 3.796 3.7342 3.705 3.7238 3.600 3.7175 3.488 3.7140 3.391 3.7113 3.298 3.7090 3.207 3.7067 3.116 3.7044 3.025 3.7019 2.932 3.6992 2.838

2.6020 2.9709 2.6235 2.9829 2.6452 2.9948 2.6721 3.0115 2.7045 3.0333 2.7428 3.0604 2.7864 3.0920 2.8312 3.1240 2.8739 3.1529 2.9065 3.1708 2.9378 3.1870 2.9770 3.2103 3.0187 3.2352 3.0351 3.2343 3.0143 3.1970 2.9715 3.1394 2.9226 3.0776 2.8815 3.0252 2.8441 2.9777 2.8045 2.9290 2.7643 2.8807 2.7290 2.8381 2.7042 2.8066 2.6849 2.7811 2.6686 2.7588 2.6601 2.7447 2.6548 2.7339 2.6516 2.7253 2.6506 2.7190 2.6481 2.7113 2.6460 2.7040 2.6447 2.6977 2.6446 2.6926 2.6499 2.6928 2.6467 2.6846 2.6335 2.6665 2.6149 2.6432 2.5887 2.6128

2.5558 2.5760

2.5268 2.5434

2.4959 2.5092

2.4212 2.4313

2.3434 2.3509

2.2519 2.2573

2.1667 2.1704

2.1034 2.1056

1.6079 1.6093 1.4387 1.4397 1.3493 1.3501 1.2751 1.2756 1.2033 1.2037 1.1368 1.1370 1.0684 1.0685 1.0000 1.0000 0.9322 0.9322

0.2368

3.3399 3.7090 3.3423 3.7018 3.3444 3.6942 3.3510 3.6906 3.3622 3.6912 3.3781 3.6958 3.3977 3.7035 3.4168 3.7097 3.4319 3.7109 3.4352 3.6997 3.4362 3.6855 3.4436 3.6770 3.4517 3.6684 3.4336 3.6330 3.3798 3.5627 3.3074 3.4754 3.2327 3.3877 3.1689 3.3126 3.1113 3.2449 3.0536 3.1781 2.9971 3.1136 2.9472 3.0564 2.9091 3.0116 2.8773 2.9735 2.8491 2.9394 2.8293 2.9139 2.8129 2.8920 2.7989 2.8726 2.7873 2.8557 2.7744 2.8376 2.7621 2.8201 2.7507 2.8037 2.7406 2.7886 2.7358 2.7788 2.7225 2.7604 2.6995 2.7325 2.6716 2.7000 2.6369 2.6610

2.5962 2.6164

2.5600 2.5766

2.5224 2.5357

2.4414 2.4516

2.3584 2.3659

2.2627 2.2681

2.1740 2.1777

2.1079 2.1101

1.6106 1.6120 1.4407 1.4418 1.3508 1.3516 1.2762 1.2767 1.2041 1.2045 1.1373 1.1375 1.0686 1.0687 1.0000 1.0000 0.9321 0.9320

4.0782 4.4476 4.0615 4.4212 4.0439 4.3938 4.0302 4.3699 4.0202 4.3493 4.0137 4.3316 4.0093 4.3152 4.0026 4.2956 3.9901 4.2693 3.9642 4.2289 3.9349 4.1843 3.9105 4.1441 3.8851 4.1019 3.8325 4.0320 3.7456 3.9286 3.6435 3.8116 3.5428 3.6979 3.4563 3.6001 3.3785 3.5121 3.3027 3.4273 3.2301 3.3466 3.1656 3.2748 3.1141 3.2166 3.0698 3.1660 3.0297 3.1200 2.9986 3.0832 2.9711 3.0502 2.9463 3.0201 2.9241 2.9925 2.9008 2.9640 2.8781 2.9362 2.8567 2.9097 2.8366 2.8846 2.8219 2.8649 2.7983 2.8362 2.7655 2.7985 2.7284 2.7568 2.6851 2.7092

2.6366 2.6568

2.5933 2.6099

2.5489 2.5622

2.4617 2.4719

2.3734 2.3810

2.2734 2.2788

2.1814 2.1850

2.1123 2.1146

1.6134 1.6148 1.4428 1.4438 1.3524 1.3532 1.2773 1.2779 1.2049 1.2053 1.1377 1.1380 1.0688 1.0689 1.0000 1.0000 0.9319 0.9318

193


TABLE 3—Continued

Mv B-V Mass Mb<* logTe// logg x — —0.5 x — 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0

1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -1.986 -2.073

13.000 12.800 12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.101 5.000 4.900 4.800

0.767 0.783 0.800 0.820 0.842 0.865 0.891 0.919 0.950 0.984 1.021 1.063 1.109 1.163 1.223 1.293 1.376 1.475 1.595 1.680

1.730 1.706 1.681 1.656 1.631 1.605 1.580 1.555 1.530 1.507 1.485 1.463 1.443 1.425 1.408 1.391 1.372 1.353 1.333 1.312 1.286 1.256 1.223 1.186 1.147 1.103 1.058 1.012 0.968 0.923 0.877 0.830 0.786 0.744 0.702 0.661 0.625 0.595 0.570 0.548 0.538 0.529 0.520 0.512

0.8549 0.8552 0.8554 0.8556 0.8558 0.8560 0.8562 0.8563 0.8564 0.8565 0.8566 0.8566 0.8567 0.8567 0.8568 0.8568 0.8568 0.8569 0.8569 0.8569

0.1541 0.1606 0.1675 0.1750 0.1830 0'1918 0.2017 0.2130 0.2258 0.2403 0.2567 0.2750 0.2955 0.3188 0.3446 0.3708 0.3961 0.4201 0.4424 0.4633 0.4828 0.5013 0.5188 0.5353 0.5512 0.5664 0.5814 0.5961 0.6108 0.6256 0.6404 0.6555 0.6708 0.6863 0.7019 0.7177 0.7338 0.7500 0.7664 0.7822 0.7896 0.7967 0.8036 0.8104

1.325 1.114 0.901 0.688 0.472 0.255 0.035

•0.186 • 0.410 • 0.639 - 0.873 • 1.112 1.360

- 1.621 1.896

• 2.189 2.513

• 2.877 3.308 3.628

3.6961 3.6925 3.6887 3.6847 3.6805 3.6762 3.6715 3.6666 3.6613 3.6558 3.6499 3.6436 3.6368 3.6294 3.6212 3.6121 3.6017 3.5894 3.5741 3.5622

2.742 2.644 2.544 2.443 2.340 2.235 2.129 2.021 1.910 1.797 1.679 1.558 1.432 1.298 1.155 1.002 0.830 0.636 0.402 0.227

0.8678 0.8017 0.7363 0.6781 0.6577 0.7515 0.6032 0.4203 0.3290 0.2658 0.2031 0.1406 0.0831 0.0291

-0.0283 -0.0776 -0.1151 -0.1539 -0.0541

0.8676 0.8015 0.7360 0.6777 0.6573 0.7511 0.6027 0.4198 0.3284 0.2652 0.2025 0.1400 0.0825 0.0285

-0.0290 -0.0782 -0.1158 -0.1546 -0.0548

0.8674 0.8012 0.7357 0.6774 0.6568 0.7506 0.6022 0.4193 0.3279 0.2646 0.2019 0.1394 0.0818 0.0279

-0.0296 -0.0789 -0.1164 -0.1553 -0.0555

10.958 10.842 10.724 10.604 10.480 10.352 10.219 10.081 9.938 9.791 9.640 9.488 9.334 9.178 9.021 8.866 8.713 8.559 8.405 8.252 8.101 7.952 7.803 7.657 7.512 7.368 7.223 7.077 6.929 6.778 6.625 6.469 6.309 6.147 5.981 5.811 5.636 5.455 5.270 5.081 4.987 4.890 4.794 4.697

3.5243 3.5286 3.5329 3.5372 3.5414 3.5457 3.5499 3.5540 3.5579 3.5617 3.5654 3.5690 3.5726 3.5761 3.5796 3.5834 3.5875 3.5917 3.5961 3.6008 3.6057 3.6111 3.6169 3.6234 3.6304 3.6381 3.6464 3.6553 3.6646 3.6743 3.6844 3.6948 3.7052 3.7157 3.7260 3.7359 3.7453 3.7540 3.7616 3.7682 3.7712 3.7741 3.7766 3.7789

5.165 5.153 5.142 5.129 5.116 5.103 5.088 5.073 5.057 5.040 5.023 5.007 4.991 4.975 4.960 4.946 4.929 4.910 4.889 4.866 4.843 4.821 4.800 4.781 4.764 4.749 4.736 4.723 4.712 4.701 4.690 4.679 4.668 4.654 4.639 4.620 4.597 4.569 4.535 4.495 4.473 4.450 4.425 4.399

2.2163 2.2404 2.2670 2.3012 2.3402 2.3842 2.4354 2.4912 2.5497 2.6038 2.6510 2.6987 2.7532 2.8073 2.8329 2.8259 2.8053 2.7777 2.7479 2.7180 2.6913 2.6675 2.6445 2.6226 2.6036 2.5919 2.5839 2.5801 2.5817 2.5838 2.5891 2.5946 2.6000 2.6050 2.6100 2.6156 2.6212 2.6240 2.6136 2.5908

2.5624

2.5453

2.5929 2.6081 2.6254 2.6502 2.6794 2.7131 2.7534 2.7974 2.8433 2.8838 2.9167 2.9495 2.9884 3.0260 3.0349 3.0121 2.9771 2.9368 2.8958 2.8558 2.8201 2.7882 2.7578 2.7290 2.7036 2.6860 2.6723 2.6631 2.6594 2.6563 2.6565 2.6570 2.6573 2.6574 2.6574 2.6582 2.6590 2.6571 2.6420 2.6148

2.5824

2.5616

2.9696 2.9758 2.9840 2.9993 3.0187 3.0421 3.0714 3.1037 3.1370 3.1639 3.1825 3.2004 3.2236 3.2448 3.2370 3.1984 3.1491 3.0960 3.0436 2.9937 2.9490 2.9089 2.8710 2.8354 2.8037 2.7800 2.7607 2.7461 2.7371 2.7288 2.7239 2.7193 2.7147 2.7098 2.7049 2.7009 2.6969 2.6902 2.6704 2.6388

2.6024

2.5779

0.8673 0.8010 0.7354 0.6770 0.6564 0.7502 0.6017 0.4187 0.3273 0.2640 0.2013 0.1387 0.0812 0.0272

-0.0303 -0.0795 -0.1171 -0.1559 -0.0562

0.8671 0.8007 0.7351 0.6767 0.6560 0.7497 0.6012 0.4182 0.3267 0.2634 0.2007 0.1381 0.0806 0.0266

-0.0309 -0.0802 -0.1178 -0.1566 -0.0569

0.8669 0.8005 0.7348 0.6763 0.6556 0.7493 0.6007 0.4176 0.3262 0.2628 0.2001 0.1375 0.0799 0.0259

-0.0316 -0.0809 -0.1184 -0.1573 -0.0576

[Fe/H] = -0.78 [O/Fe] = +0.39 Y = 0.2391

x = —1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

3.3464 3.3436 3.3426 3.3485 3.3581 3.3712 3.3895 3.4101 3.4307 3.4440 3.4484 3.4513 3.4589 3.4637 3.4392 3.3847 3.3210 3.2552 3.1915 3.1315 3.0778 3.0296 2.9842 2.9418 2.9037 2.8741 2.8492 2.8291 2.8148 2.8013 2.7913 2.7816 2.7720 2.7621 2.7524 2.7435 2.7347 2.7233 2.6988 2.6628

2.6224

2.5941

3.7233 3.7114 3.7013 3.6977 3.6975 3.7003 3.7077 3.7165 3.7245 3.7242 3.7143 3.7023 3.6942 3.6826 3.6414 3.5710 3.4930 3.4144 3.3395 3.2694 3.2067 3.1503 3.0975 3.0482 3.0038 2.9682 2.9376 2.9121 2.8925 2.8738 2.8587 2.8440 2.8293 2.8145 2.7999 2.7862 2.7726 2.7564 2.7272 2.6868

2.6424

2.6104

4.1004 4.0793 4.0601 4.0471 4.0370 4.0295 4.0259 4.0230 4.0183 4.0045 3.9803 3.9534 3.9296 3.9015 3.8437 3.7574 3.6651 3.5737 3.4875 3.4074 3.3356 3.2711 3.2108 3.1546 3.1039 3.0624 3.0261 2.9951 2.9702 2.9463 2.9261 2.9064 2.8867 2.8669 2.8474 2.8288 2.8104 2.7895 2.7556 2.7109

2.6623

2.6267

194



Mv B-V Mass Mbol logTe// log^ x — —1.0 a? = —0.5 x = 0.0 x = 0.5 x = 1.0

4.701 4.600 4.501 4.400 4.300 4.200 4.098 4.000 3.881 3.800 3.750 3.721 3.688 3.600 3.510 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.744 -1.788

13.200 13.000 12.800 12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000

0.505 0.498 0.494 0.491 0.490 0.490 0.493 0.500 0.519 0.545 0.585 0.626 0.667 0.704 0.723 0.738 0.752 0.762 0.770 0.777 0.786 0.797 0.809 0.824 0.840 0.858 0.879 0.903 0.927 0.954 0.984 1.015 1.050 1.089 1.133 1.183 1.238 1.301 1.374 1.458 1.562 1.665 1.733

1.744 1.722 1.699 1.676 1.652 1.629 1.605 1.582 1.559 1.537 1.515 1.493 1.473 1.453 1.434 1.417 1.400 1.382 1.364 1.345 1.324 1.301

0.8170 0.8235 0.8294 0.8349 0.8399 0.8445 0.8487 0.8526 0.8571 0.8601 0.8624 0.8640 0.8653 0.8666 0.8674 0.8682 0.8694 0.8704 0.8712 0.8719 0.8725 0.8730 0.8734 0.8738 0.8741 0.8744 0.8746 0.8748 0.8751 0.8753 0.8755 0.8756 0.8757 0.8758 0.8758 0.8759 0.8760 0.8760 0.8760 0.8761 0.8761 0.8761 0.8762

0.1540 0.1602 0.1670 0.1742 0.1818 0.1901 0.1994 0.2099 0.2221 0.2359 0.2514 0.2686 0.2878 0.3092 0.3330 0.3589 0.3855 0.4105 0.4331 0.4544 0.4748 0.4940

4.600 4.501 4.403 4.304 4.205 4.106 4.004 3.906 3.781 3.690 3.618 3.563 3.499 3.382 3.276 3.155 2.944 2.737 2.531 2.325 2.119 1.911 1.702 1.491 1.279 1.065 0.848 0.628 0.407 0.184

- 0.044 - 0.275 -0.511 - 0.753 - 1.004 - 1.266 - 1.540 ■ 1.830 • 2.149 - 2.500 - 2.925 - 3.354 3.657

3.7809 3.7826 3.7837 3.7842 3.7841 3.7837 3.7824 3.7799 3.7732 3.7644 3.7518 3.7398 3.7287 3.7189 3.7139 3.7099 3.7060 3.7033 3.7011 3.6990 3.6967 3.6940 3.6910 3.6877 3.6841 3.6802 3.6760 3.6712 3.6665 3.6614 3.6561 3.6505 3.6446 3.6383 3.6316 3.6243 3.6164 3.6078 3.5979 3.5867 3.5724 3.5574 3.5463

4.372 4.342 4.311 4.276 4.239 4.200 4.156 4.109 4.034 3.964 3.887 3.817 3.748 3.663 3.600 3.537 3.437 3.344 3.253 3.163 3.071 2.978 2.882 2.785 2.686 2.585 2.481 2.374 2.267 2.158 2.046 1.930 1.812 1.691 1.563 1.429 1.289 1.138 0.971 0.786 0.558 0.327 0.161

2.5030

2.4335

2.3637

2.2887

2.3245

1.8045

1.5247 1.4156 1.3404 1.2672 1.2029 1.1327 1.0678 1.0000 0.9337 0.8648 0.8021 0.7514 0.7580 0.8599 0.6279 0.4767 0.3959 0.3294 0.2667 0.2071 0.1453 0.0836 0.0325

-0.0170 -0.0629 -0.0478 0.1711

2.5158

2.4434

2.3711

2.2940

2.3277

2.5287

2.4532

2.3784

2.2993

2.3309

1.8063 1.8081

1.5260 1.4166 1.3411 1.2678 1.2033 1.1330 1.0679 1.0000 0.9336 0.8646 0.8018 0.7511 0.7577 0.8594 0.6274 0.4762 0.3954 0.3289 0.2661 0.2065 0.1447 0.0830 0.0319

-0.0177 -0.0636 -0.0485 0.1704

1.5273 1.4176 1.3419 1.2684 1.2037 1.1332 1.0680 1.0000 0.9335 0.8645 0.8016 0.7508 0.7573 0.8590 0.6269 0.4757 0.3948 0.3283 0.2655 0.2059 0.1441 0.0823 0.0312

-0.0183 -0.0643 -0.0491 0.1697

[Fe/H] = -0.65 [O/Fe] = +0.30 Y = 0.2413

11.001 10.889 10.775 10.659 10.541 10.419 10.292 10.160 10.022 9.879 9.733 9.584 9.434 9.280 9.124 8.969 8.818 8.667 8.516 8.364 8.213 8.064

3.5186 3.5228 3.5270 3.5311 3.5352 3.5393 3.5434 3.5474 3.5512 3.5550 3.5587 3.5623 3.5660 3.5695 3.5728 3.5764 3.5804 3.5846 3.5890 3.5935 3.5982 3.6032

5.159 5.148 5.137 5.125 5.113 5.100 5.087 5.072 5.057 5.041 5.024 5.008 4.993 4.976 4.960 4.945 4.931 4.915 4.895 4.873 4.851 4.828

2.2131 2.2337 2.2564 2.2887 2.3235 2.3649 2.4147 2.4710 2.5285 2.5855 2.6337 2.6784 2.7251 2.7734 2.8158 2.8435 2.8340 2.7934 2.7598 2.7377 2.7152 2.6899

2.5930 2.6048 2.6186 2.6417 2.6672 2.6987 2.7382 2.7832 2.8286 2.8726 2.9070 2.9373 2.9690 3.0017 3.0280 3.0396 3.0149 2.9606 2.9153 2.8826 2.8507 2.8167

2.9730 2.9760 2.9809 2.9949 3.0110 3.0326 3.0617 3.0955 3.1288 3.1598 3.1804 3.1962 3.2130 3.2301 3.2404 3.2358 3.1957 3.1279 3.0708 3.0277 2.9862 2.9436

2.5415

2.4631

2.3858

2.3046

2.3341

2.5544

2.4729

2.3932

2.3099

2.3373

1.8098 1.8116

1.5286 1.4186 1.3426 1.2689 1.2041 1.1334 1.0681 1.0000 0.9334 0.8643 0.8014 0.7505 0.7569 0.8586 0.6264 0.4752 0.3943 0.3277 0.2649 0.2053 0.1434 0.0817 0.0306

-0.0190 -0.0649 -0.0498 0.1690

3.3531 3.3473 3.3433 3.3482 3.3548 3.3666 3.3852 3.4078 3.4291 3.4470 3.4538 3.4553 3.4571 3.4586 3.4528 3.4321 3.3767 3.2952 3.2263 3.1727 3.1217 3.0705

1.5299 1.4196 1.3434 1.2695 1.2044 1.1337 1.0682 1.0000 0.9333 0.8641 0.8011 0.7502 0.7566 0.8582 0.6259 0.4746 0.3937 0.3272 0.2643 0.2047 0.1428 0.0811 0.0299

-0.0196 -0.0656 -0.0505 0.1683

3.7333 3.7186 3.7057 3.7015 3.6987 3.7007 3.7089 3.7202 3.7294 3.7344 3.7273 3.7143 3.7012 3.6872 3.6653 3.6284 3.5577 3.4626 3.3819 3.3178 3.2573 3.1975

195

x = 1.5

2.5673

2.4828

2.4005

2.3152

2.3405

1.8134

1.5312 1.4206 1.3441 1.2700 1.2048 1.1339 1.0683 1.0000 0.9332 0.8640 0.8009 0.7499 0.7562 0.8578 0.6255 0.4741 0.3932 0.3266 0.2637 0.2041 0.1422 0.0804 0.0293

-0.0203 -0.0663 -0.0512

0.1677

4.1136 4.0900 4.0683 4.0549 4.0427 4.0348 4.0326 4.0327 4.0298 4.0217 4.0009 3.9735 3.9454 3.9158 3.8779 3.8248 3.7387 3.6300 3.5375 3.4629 3.3929 3.3244


TABLE 3—Continued

00 My B-V Mass Mm logTeff logg x = —1.0 x = -0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.101 5.000 4.901 4.800 4.701 4.600 4.501 4.400 4.300 4.200 4.094 4.000 3.880 3.822 3.800 3.788 3.767 3.711 3.600 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.566 -1.632

1.273 1.241 1.205 1.165 1.122 1.076 1.030 0.986 0.942 0.897 0.851 0.806 0.765 0.724 0.684 0.647 0.616 0.589 0.565 0.555 0.545 0.537 0.529 0.522 0.517 0.512 0.509 0.509 0.509 0.514 0.525 0.552 0.586 0.622 0.657 0.692 0.726 0.753 0.777 0.788 0.796 0.805 0.814 0.824 0.836 0.850 0.866 0.884 0.905 0.927 0.952 0.977 1.005 1.035 1.068 1.106 1.148 1.196 1.249 1.308 1.377 1.455 1.550 1.654 1.755

0.5121 0.5294 0.5457 0.5613 0.5764 0.5912 0.6060 0.6207 0.6355 0.6504 0.6657 0.6811 0.6966 0.7123 0.7282 0.7443 0.7608 0.7773 0.7929 0.8003 0.8076 0.8145 0.8215 0.8282 0.8347 0.8406 0.8461 0.8513 0.8563 0.8612 0.8653 0.8702 0.8729 0.8746 0.8758 0.8769 0.8780 0.8792 0.8806 0.8817 0.8827 0.8835 0.8841 0.8847 0.8852 0.8856 0.8860 0.8863 0.8866 0.8868 0.8870 0.8874 0.8876 0.8877 0.8878 0.8879 0.8880 0.8880 0.8881 0.8881 0.8882 0.8882 0.8883 0.8883 0.8883

7.916 7.770 7.626 7.484 7.342 7.199 7.055 6.908 6.759 6.607 6.452 6.294 6.133 5.968 5.799 5.626 5.447 5.264 5.077 4.983 4.887 4.792 4.695 4.598 4.500 4.403 4.303 4.204 4.105 3.999 3.902 3.772 3.696 3.652 3.614 3.566 3.483 3.350 3.131 2.922 2.715 2.509 2.302 2.094 1.885 1.675 1.462 1.247 1.030 0.810 0.587 0.363 0.135

-0.098 -0.334 -0.577 -0.830 -1.092 -1.365 -1.655 -1.973 -2.320 -2.734 -3.189 -3.659

3.6087 3.6146 3.6211 3.6283 3.6360 3.6442 3.6529 3.6621 3.6716 3.6815 3.6916 3.7019 3.7122 3.7223 3.7322 3.7418 3.7505 3.7583 3.7653 3.7683 3.7711 3.7737 3.7759 3.7777 3.7792 3.7803 3.7808 3.7807 3.7801 3.7782 3.7744 3.7654 3.7547 3.7441 3.7343 3.7249 3.7162 3.7090 3.7028 3.6997 3.6973 3.6951 3.6928 3.6902 3.6874 3.6842 3.6807 3.6769 3.6726 3.6679 3.6631 3.6582 3.6530 3.6474 3.6416 3.6354 3.6287 3.6216 3.6139 3.6053 3.5957 3.5847 3.5711 3.5554 3.5384

4.807 4.786 4.768 4.752 4.738 4.724 4.712 4.701 4.689 4.678 4.667 4.655 4.641 4.625 4.607 4.585 4.558 4.526 4.488 4.466 4.443 4.419 4.392 4.365 4.335 4.303 4.268 4.231 4.191 4.144 4.092 4.006 3.935 3.875 3.821 3.765 3.698 3.616 3.505 3.409 3.317 3.226 3.135 3.042 2.947 2.850 2.752 2.650 2.546 2.440 2.331 2.223 2.110 1.995 1.877 1.755 1.628 1.494 1.354 1.204 1.039 0.856 0.636 0.391 0.135

2.6662 2.6435 2.6219 2.6035 2.5940 2.5884 2.5856 2.5881 2.5919 2.5976 2.6039 2.6085 2.6133 2.6177 2.6224 2.6260 2.6271 2.6156 2.5954

2.5709

2.5565

2.5124

2.4510

2.3818

2.3235

1.6698 1.4989 1.4117 1.3371 1.2693 1.2010 1.1330 1.0667 1.0000 0.9334 0.8687 0.8077 0.7720 0.8899 0.7897 0.5618 0.4614 0.3924 0.3301 0.2691 0.2026 0.1407 0.0887 0.0336

-0.0123 -0.0216 0.1944

2.7853 2.7553 2.7271 2.7026 2.6873 2.6761 2.6680 2.6653 2.6640 2.6646 2.6659 2.6655 2.6654 2.6650 2.6649 2.6638 2.6601 2.6440 2.6194

2.5909

2.5729

2.5253

2.4609

2.3891

2.3286

2.9043 2.8672 2.8324 2.8017 2.7806 2.7639 2.7504 2.7426 2.7360 2.7316 2.7279 2.7225 2.7176 2.7123 2.7074 2.7016 2.6931 2.6723 2.6435

2.6110

2.5892

2.5382

2.4709

2.3965

2.3337

3.0234 2.9791 2.9376 2.9008 2.8739 2.8517 2.8329 2.8198 2.8081 2.7986 2.7899 2.7796 2.7697 2.7596 2.7499 2.7394 2.7261 2.7007 2.6676

2.6311

2.6056

2.5511

2.4808

2.4038

2.3388

3.1424 3.0909 3.0429 3.0000 2.9672 2.9395 2.9153 2.8970 2.8803 2.8657 2.8519 2.8367 2.8219 2.8069 2.7925 2.7771 2.7591 2.7291 2.6916

2.6511

2.6219

2.5641

2.4908

2.4112

2.3438

1.6714 1.5001 1.4127 1.3378 1.2698 1.2013 1.1333 1.0668 1.0000 0.9333 0.8686 0.8075 0.7717 0.8895 0.7893 0.5613 0.4609 0.3918 0.3296 0.2686 0.2020 0.1401 0.0881 0.0330

-0.0129 -0.0223

0.1937

1.6730 1.5014 1.4136 1.3385 1.2704 1.2017 1.1335 1.0669 1.0000 0.9333 0.8684 0.8072 0.7715 0.8892 0.7889 0.5608 0.4604 0.3913 0.3290 0.2680 0.2014 0.1395 0.0875 0.0324

-0.0135 -0.0229

0.1931

1.6746 1.5026 1.4146 1.3392 1.2709 1.2021 1.1337 1.0670 1.0000 0.9332 0.8682 0.8070 0.7712 0.8888 0.7885 0.5604 0.4599 0.3908 0.3285 0.2674 0.2008 0.1389 0.0869 0.0317

-0.0142 -0.0236 0.1924

1.6763 1.5039 1.4156 1.3400 1.2714 1.2024 1.1339 1.0671 1.0000 0.9331 0.8681 0.8068 0.7709 0.8884 0.7880 0.5599 0.4594 0.3902 0.3279 0.2668 0.2003 0.1383 0.0863 0.0311

-0.0148 -0.0242 0.1918

3.2615 3.2028 3.1481 3.0991 3.0606 3.0273 2.9978 2.9743 2.9524 2.9328 2.9139 2.8937 2.8740 2.8542 2.8350 2.8149 2.7921 2.7575 2.7157

2.6712

2.6383

2.5770

2.5007

2.4186

2.3489

2.3411 2.3440 2.3469 2.3499 2.3528 2.3557

1.6779 1.5051 1.4165 1.3407 1.2720 1.2028 1.1342 1.0672 1.0000 0.9330 0.8679 0.8065 0.7706 0.8881 0.7876 0.5594 0.4589 0.3897 0.3274 0.2663 0.1997 0.1377 0.0857 0.0305

-0.0154 -0.0249 0.1911

196



\—i 00

^0 a CM (S\ (T\ ï—I

Mv B - V Mass Mboi \ogTejf logp x = -1.0 x = -0.5 x = 0.0 x = 0.5

[Fe/H] = -0.47 [O/Fe] = +0.23 Y = 0.2454

13.400 1.752 13.200 1.731 13.000 1.710 12.800 1.689 12.600 1.668 12.400 1.647 12.200 1.626 12.000 1.606 11.800 1.586 11.600 1.566 11.400 1.546 11.200 1.526 11.000 1.507 10.800 1.488 10.600 1.469 10.400 1.450 10.200 1.431 10.000 1.413 9.800 1.396 9.600 1.379 9.400 1.362 9.200 1.343 9.000 1.322 8.800 1.297 8.600 1.267 8.400 1.232 8.200 1.193 8.000 1.151 7.800 1.106 7.600 1.059 7.400 1.015 7.200 0.972 7.000 0.929 6.800 0.884 6.600 0.839 6.400 0.796 6.200 0.755 6.000 0.716 5.800 0.679 5.600 0.648 5.400 0.620 5.200 0.596 5.101 0.584 5.000 0.574 4.901 0.565 4.800 0.557 4.701 0.550 4.600 0.545 4.500 0.542 4.400 0.541 4.299 0.541 4.200 0.544 4.090 0.553 4.000 0.569 3.924 0.603 3.900 0.640 3.901 0.677 3.900 0.715 3.875 0.752 3.800 0.786 3.710 0.804 3.600 0.817 3.400 0.831 3.200 0.840 3.000 0.849

0.1562 11.016 0.1625 10.905 0.1692 10.794 0.1763 10.682 0.1838 10.568 0.1920 10.451 0.2010 10.331 0.2113 10.205 0.2232 10.073 0.2367 9.935 0.2519 9.793 0.2687 9.649 0.2873 9.502 0.3083 9.353 0.3321 9.201 0.3575 9.050 0.3827 8.901 0.4071 8.753 0.4303 8.604 0.4523 8.454 0.4730 8.305 0.4926 8.157 0.5113 8.011 0.5290 7.867 0.5459 7.724 0.5620 7.583 0.5775 7.443 0.5926 7.303 0.6076 7.162 0.6224 7.019 0.6373 6.875 0.6523 6.728 0.6675 6.579 0.6828 6.426 0.6984 6.271 0.7141 6.112 0.7299 5.949 0.7458 5.783 0.7624 5.611 0.7791 5.434 0.7954 5.253 0.8110 5.068 0.8184 4.976 0.8257 4.881 0.8327 4.788 0.8401 4.690 0.8470 4.595 0.8537 4.496 0.8601 4.399 0.8662 4.300 0.8718 4.200 0.8770 4.100 0.8824 3.987 0.8866 3.891 0.8905 3.797 0.8926 3.750 0.8940 3.723 0.8952 3.692 0.8963 3.636 0.8976 3.533 0.8985 3.428 0.8994 3.307 0.9007 3.095 0.9017 2.888 0.9026 2.681

3.5125 5.147 3.5167 5.136 3.5208 5.125 3.5248 5.114 3.5287 5.103 3.5326 5.091 3.5364 5.078 3.5402 5.064 3.5438 5.049 3.5474 5.034 3.5508 5.018 3.5544 5.003 3.5579 4.987 3.5614 4.972 3.5649 4.958 3.5684 4.943 3.5723 4.929 3.5763 4.912 3.5805 4.893 3.5848 4.873 3.5895 4.851 3.5944 4.829 3.5996 4.808 3.6052 4.787 3.6113 4.768 3.6180 4.751 3.6251 4.735 3.6327 4.721 3.6408 4.708 3.6492 4.695 3.6581 4.683 3.6674 4.671 3.6771 4.660 3.6870 4.649 3.6971 4.637 3.7073 4.624 3.7174 4.609 3.7273 4.591 3.7366 4.569 3.7451 4.542 3.7528 4.509 3.7598 4.472 3.7630 4.451 3.7660 4.429 3.7686 4.406 3.7708 4.380 3.7725 4.352 3.7738 4.321 3.7744 4.288 3.7746 4.252 3.7743 4.214 3.7729 4.171 3.7696 4.115 3.7645 4.058 3.7541 3.981 3.7434 3.920 3.7331 3.869 3.7233 3.818 3.7138 3.758 3.7052 3.683 3.7006 3.623 3.6972 3.562 3.6935 3.463 3.6909 3.370 3.6886 3.278

2.2290 2.6106 2.2453 2.6182 2.2665 2.6306 2.2914 2.6466 2.3270 2.6731 2.3669 2.7035 2.4157 2.7422 2.4721 2.7878 2.5315 2.8354 2.5897 2.8809 2.6346 2.9123 2.6771 2.9408 2.7259 2.9750 2.7820 3.0157 2.8249 3.0426 2.8360 3.0379 2.8259 3.0131 2.8078 2.9816 2.7852 2.9469 2.7590 2.9098 2.7340 2.8751 2.7122 2.8445 2.6908 2.8150 2.6688 2.7856 2.6484 2.7583 2.6295 2.7331 2.6145 2.7122 2.6060 2.6981 2.6034 2.6901 2.6013 2.6827 2.6046 2.6809 2.6097 2.6809 2.6142 2.6804 2.6204 2.6817 2.6243 2.6806 2.6269 2.6785 2.6313 2.6781 2.6335 2.6757 2.6398 2.6772 2.6382 2.6708 2.6298 2.6579 2.6128 2.6367

2.5969 2.6169

2.5897 2.6060

2.5369 2.5498

2.4758 2.4855

2.4160 2.4230

2.5015 2.5057

2.0745 2.0767

1.5934 1.5949 1.4867 1.4878 1.4085 1.4094 1.3375 1.3382

2.9923 3.3741 2.9912 3.3642 2.9948 3.3591 3.0020 3.3574 3.0193 3.3655 3.0401 3.3768 3.0688 3.3954 3.1035 3.4193 3.1394 3.4434 3.1721 3.4634 3.1900 3.4678 3.2045 3.4682 3.2241 3.4733 3.2495 3.4833 3.2604 3.4782 3.2399 3.4419 3.2003 3.3875 3.1554 3.3292 3.1086 3.2704 3.0607 3.2116 3.0163 3.1575 2.9768 3.1091 2.9392 3.0634 2.9024 3.0192 2.8683 2.9782 2.8367 2.9403 2.8099 2.9076 2.7901 2.8822 2.7767 2.8634 2.7641 2.8455 2.7572 2.8335 2.7522 2.8234 2.7467 2.8129 2.7429 2.8042 2.7370 2.7934 2.7300 2.7816 2.7249 2.7718 2.7178 2.7599 2.7145 2.7519 2.7034 2.7361 2.6861 2.7142 2.6606 2.6846

2.6369 2.6570

2.6223 2.6386

2.5626 2.5754

2.4952 2.5049

2.4300 2.4369

2.5099 2.5141

2.0790 2.0812

1.5963 1.5978 1.4890 1.4901 1.4102 1.4111 1.3389 1.3396

x = 1.0 x = 1.5

3.7561 4.1381 3.7373 4.1105 3.7235 4.0879 3.7128 4.0684 3.7118 4.0583 3.7136 4.0505 3.7221 4.0488 3.7351 4.0510 3.7474 4.0516 3.7547 4.0461 3.7456 4.0236 3.7321 3.9960 3.7225 3.9718 3.7172 3.9512 3.6961 3.9141 3.6440 3.8462 3.5748 3.7622 3.5031 3.6770 3.4321 3.5939 3.3626 3.5135 3.2986 3.4399 3.2415 3.3738 3.1877 3.3120 3.1360 3.2529 3.0882 3.1982 3.0440 3.1476 3.0053 3.1030 2.9743 3.0664 2.9501 3.0368 2.9270 3.0084 2.9098 2.9861 2.8947 2.9659 2.8791 2.9454 2.8655 2.9268 2.8498 2.9062 2.8332 2.8848 2.8186 2.8654 2.8021 2.8442 2.7893 2.8266 2.7687 2.8013 2.7424 2.7705 2.7086 2.7325

2.6770 2.6970

2.6549 2.6712

2.5883 2.6011

2.5146 2.5243

2.4439 2.4509

2.5183 2.5225

2.0835 2.0858

1.5992 1.6007 1.4913 1.4924 1.4120 1.4129 1.3403 1.3409

197


19 9

2ApJ

S. .

.81.

.16

3B

BERGBUSCH & VANDENBERG

TABLE 3—Continued

198

My B — V Mass logT^fj logg x — —1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

2.800 0.859 2.600 0.869 2.400 0.881 2.200 0.894 2.000 0.910 1.800 0.929 1.600 0.949 1.400 0.972 1.200 0.995 1.000 1.019 0.800 1.046 0.600 1.075 0.400 1.108 0.200 1.146 0.000 1.189

-0.200 1.235 -0.400 1.288 -0.600 1.348 -0.800 1.416 -1.000 1.495 -1.200 1.593 -1.348 1.714 -1.392 1.796

0.9034 2.473 0.9040 2.266 0.9045 2.056 0.9050 1.845 0.9054 1.631 0.9058 1.414 0.9061 1.195 0.9063 0.973 0.9066 0.748 0.9070 0.521 0.9072 0.291 0.9073 0.057 0.9074 -0.183 0.9075 -0.431 0.9076 -0.690 0.9077 -0.957 0.9078 -1.238 0.9078 -1.542 0.9079 -1.872 0.9079 -2.246 0.9080 -2.700 0.9080 -3.282 0.9080 -3.695

3.6863 3.186 3.6839 3.094 3.6811 3.000 3.6781 2.903 3.6746 2.804 3.6706 2.701 3.6663 2.597 3.6616 2.489 3.6568 2.380 3.6519 2.270 3.6467 2.157 3.6412 2.042 3.6354 1.923 3.6291 1.798 3.6222 1.667 3.6149 1.531 3.6069 1.387 3.5979 1.229 3.5877 1.056 3.5756 0.858 3.5602 0.615 3.5393 0.299 3.5236 0.071

1.2679 1.2684 1.2027 1.2030 1.1334 1.1336 1.0673 1.0674 1.0000 1.0000 0.9335 0.9334 0.8746 0.8745 0.8456 0.8454 0.9937 0.9934 0.8394 0.8390 0.6214 0.6209 0.5256 0.5252 0.4587 0.4583 0.3961 0.3956 0.3297 0.3292 0.2632 0.2627 0.2044 0.2039 0.1486 0.1480 0.0936 0.0930 0.0589 0.0583 0.0667 0.0661 0.3330 0.3324

1.2689 1.2694 1.2034 1.2037 1.1338 1.1340 1.0675 1.0676 1.0000 1.0000 0.9333 0.9332 0.8743 0.8742 0.8452 0.8450 0.9931 0.9928 0.8386 0.8383 0.6205 0.6201 0.5247 0.5242 0.4578 0.4573 0.3951 0.3946 0.3286 0.3281 0.2621 0.2616 0.2033 0.2028 0.1475 0.1469 0.0924 0.0918 0.0577 0.0571 0.0655 0.0649 0.3318 0.3312

1.2699 1.2704 1.2040 1.2044 1.1343 1.1345 1.0677 1.0678 1.0000 1.0000 0.9332 0.9331 0.8740 0.8738 0.8448 0.8445 0.9925 0.9922 0.8379 0.8375 0.6197 0.6192 0.5238 0.5233 0.4568 0.4563 0.3941 0.3936 0.3276 0.3270 0.2610 0.2605 0.2022 0.2016 0.1463 0.1457 0.0912 0.0906 0.0565 0.0559 0.0642 0.0636 0.3306 0.3299

The assumed cluster reddenings and distance moduli, which are noted in the figure caption, are within ±0.01 and ±0.10 mag, respectively, of the values adopted in the aforementioned references. Although the clear impression from Figure 8 is that all three globulars have very nearly the same age, it must be appreciated that current distance modulus estimates remain uncertain at the ±0.2 mag level (e.g., Renzini 1986, 1991). This would imply a corresponding age uncertainty of ^ ±3 Gyr.

Indeed, the match between the theory and the M92 fiducial sequence is not entirely satisfactory. If the cluster stars have [Fe/H] ^ -2.2 (the canonical estimate) or even lower (see Peterson, Kurucz, & Carney 1990), then the predicted turnoff color for this metallicity (and age) is too blue. With the choice of ( m - M)v = 14.70 mag, which is close to that required to fit a theoretical zero-age horizontal branch to its observed coun- terpart (e.g., see VandenBerg 1990), the main-sequence data tend to coincide with a 14 Gyr isochrone having -2.03 < [Fe/ H] < -1.78. Although some studies of M92 have argued for such a high iron content (e.g., Pilachowski, Sneden, & Waller- stein 1983), these tend to be in the minority. Alternatively, is it possible that enhancements in the a-nuclei elements—not taken into account in the present models—are responsible for the discrepancy? It is clearly important that the necessary work be carried out to answer this question. Other possibilities are that the reddening to M92 is higher than the usual estimate of E{B - V) = 0.02 mag or that the distance modulus is smaller than the value adopted here (see Sandage & Cacciari 1990), which, while it may pose a difficulty for fits of the horizontal branch models, would alleviate the apparent color problem and lead to a higher inferred age. It is simply not possible to say at the present time what the true situation is. In fact, we would contend that our isochrones are able to reproduce observed CMDs within current uncertainties and, moreover, that it is going to be very difficult to argue convincingly for or against the accuracy of our models (and absolute cluster ages within

±2-3 Gyr from CMD fits) until distance estimates are improved significantly.

To further support our claim that the present isochrones are about as well placed on the CMD as it is possible to make them, we show in Figure 9 a comparison of three of them with the latest data for the Population II parallax standards (Laird, Carney, & Latham 1988). Obviously, the particular age that is assumed is irrelevant since most of the subdwarfs are sufficiently faint that evolutionary effects will be negligible (see Paper I for confirmation of this). Although the error bars are large, the mean of the stellar distribution for each of the two most metal-poor samples is very close to that predicted by the appropriate isochrone. If anything, the latter are slightly too red, rather than too blue, as one might have anticipated from the globular cluster fits shown in Figure 8. In contrast, the [Fe/H] ^ -0.6 subdwarfs are redder than one’s expectation from the theory. Given that Kapteyn’s star (HD 33793), with its [Fe/H] ( = -0.5), and B-V values given by Cayrel de Strobel Sc Bentolila ( 1983), is also to the red of the relevant isochrone (see Fig. 8), there may be some cause for concern here. However, the uncertainties in metallicity estimates are rarely less than ±0.2-0.3 dex, and as the effects on stellar reff’s and colors of a small change in [Fe/H] become systematically larger as the metal abundance increases, it is not clear that the discrepancy is a serious one. We do note that, if the most metal rich isochrones in our grid shouldbt displaced to redder colors, then Figure 8 would suggest that 47 Tue is more metal poor than [Fe/H] = -0.7 (as found in some abundance analyses, e.g., Brown, Wallerstein, & Oke 1990).

A couple of additional points should be made in connection with Figure 8. First, it is apparent that the RGB tip of the [Fe/H] = -0.47 isochrone is just beginning to bend over. This is the expected consequence of the steep dependence of the bolometric corrections in F(BCF)to reff among cool stars (see Paper I ), which is caused by TiO blanketing in K( Kraft 1991). Furthermore, we would expect the Mv of the helium flash


1992

. PQ oo KO

TABLE 4 Isochrones nd Luminosity Functions for 16 Gyr

02.

^0 ft

log^>

My B — V Mass Mboi x ~ 0.0 x = 0.5 jt = 1.0 x — 1.5 x = 2.0 x = 2.5

[Fe/H] = -2.26 [O/Fe] = +0.75 Y - 0.2350

11.400 1.491 11.200 1.449 11.000 1.409 10.800 1.370 10.600 1.333 10.400 1.303 10.200 1.276 10.000 1.251 9.800 1.227 9.600 1.203 9.400 1.178 9.200 1.153 9.000 1.128 8.800 1.101 8.600 1.069 8.400 1.034 8.200 0.998 8.000 0.958 7.800 0.914 7.600 0.869 7.400 0.826 7.200 0.784 7.000 0.740 6.800 0.693 6.600 0.647 6.400 0.603 6.200 0.563 6.000 0.528 5.800 0.498 5.600 0.473 5.400 0.451 5.200 0.430 5.000 0.410 4.901 0.401 4.800 0.392 4.701 0.385 4.600 0.377 4.500 0.371 4.400 0.364 4.301 0.359 4.200 0.355 4.100 0.352 4.000 0.351 3.899 0.353 3.800 0.357 3.694 0.366 3.600 0.380 3.490 0.401 3.400 0.425 3.299 0.453 3.200 0.482 3.109 0.506 3.000 0.527 2.800 0.552 2.600 0.568 2.400 0.580 2.200 0.592 2.000 0.602 1.800 0.611 1.600 0.619 1.400 0.629

0.1575 10.434 0.1659 10.282 0.1750 10.127 0.1850 9.969 0.1962 9.809 0.2091 9.646 0.2244 9.479 0.2424 9.308 0.2630 9.136 0.2860 8.963 0.3118 8.790 0.3409 8.617 0.3727 8.441 0.4030 8.268 0.4292 8.097 0.4528 7.927 0.4746 7.758 0.4945 7.591 0.5129 7.425 0.5301 7.260 0.5464 7.095 0.5624 6.927 0.5781 6.758 0.5937 6.587 0.6093 6.413 0.6249 6.236 0.6407 6.053 0.6566 5.860 0.6721 5.663 0.6868 5.464 0.7007 5.267 0.7141 5.073 0.7260 4.879 0.7314 4.783 0.7366 4.685 0.7414 4.588 0.7459 4.491 0.7502 4.393 0.7544 4.296 0.7582 4.198 0.7618 4.100 0.7649 4.002 0.7678 3.903 0.7704 3.803 0.7726 3.704 0.7746 3.598 0.7761 3.502 0.7776 3.389 0.7786 3.293 0.7796 3.183 0.7804 3.071 0.7811 2.968 0.7816 2.847 0.7824 2.633 0.7831 2.423 0.7836 2.217 0.7841 2.010 0.7845 1.805 0.7848 1.599 0.7851 1.394 0.7853 1.188

3.5826 5.198 3.5876 5.179 3.5926 5.160 3.5974 5.141 3.6021 5.121 3.6065 5.101 3.6106 5.081 3.6144 5.062 3.6181 5.043 3.6219 5.026 3.6257 5.009 3.6295 4.994 3.6332 4.977 3.6374 4.958 3.6422 4.937 3.6475 4.913 3.6532 4.889 3.6596 4.865 3.6669 4.844 3.6750 4.825 3.6838 4.807 3.6932 4.790 3.7030 4.773 3.7131 4.757 3.7235 4.740 3.7339 4.722 3.7443 4.701 3.7546 4.676 3.7643 4.646 3.7731 4.611 3.7809 4.572 3.7880 4.531 3.7949 4.488 3.7981 4.466 3.8011 4.442 3.8039 4.417 3.8065 4.391 3.8089 4.364 3.8111 4.337 3.8129 4.307 3.8143 4.275 3.8152 4.242 3.8152 4.204 3.8143 4.161 3.8122 4.115 3.8082 4.057 3.8028 3.998 3.7944 3.920 3.7847 3.844 3.7720 3.750 3.7582 3.650 3.7483 3.569 3.7411 3.492 3.7343 3.380 3.7301 3.280 3.7272 3.186 3.7245 3.093 3.7221 3.001 3.7196 2.909 3.7172 2.818 3.7145 2.725

3.0147 3.3634 3.0281 3.3656 3.0448 3.3706 3.0656 3.3793 3.0953 3.3961 3.1356 3.4225 3.1785 3.4501 3.2115 3.4664 3.2254 3.4627 3.2380 3.4571 3.2535 3.4538 3.2628 3.4438 3.2385 3.4005 3.1541 3.2993 3.0701 3.2013 3.0087 3.1282 2.9520 3.0613 2.8963 2.9966 2.8466 2.9390 2.8075 2.8927 2.7793 2.8579 2.7568 2.8291 2.7406 2.8070 2.7284 2.7889 2.7173 2.7722 2.7072 2.7566 2.7041 2.7481 2.6887 2.7274 2.6615 2.6952 2.6270 2.6559 2.5848 2.6093 2.5360 2.5565 2.4840 2.5009

2.4301 2.4438

2.3795 2.3904

2.3329 2.3414

2.2532 2.2596

2.1576 2.1623

2.0433 2.0466

1.8998 1.9022

1.7545 1.7561

1.6288 1.6300

1.4057 1.4065 1.2776 1.2781 1.1994 1.1998 1.1333 1.1335 1.0672 1.0673 1.0000 1.0000 0.9315 0.9314 0.8632 0.8630 0.7954 0.7951

3.7122 4.0610 3.7031 4.0408 3.6966 4.0226 3.6931 4.0069 3.6970 3.9980 3.7095 3.9966 3.7218 3.9936 3.7214 3.9765 3.7001 3.9375 3.6763 3.8956 3.6542 3.8547 3.6249 3.8060 3.5626 3.7248 3.4446 3.5898 3.3327 3.4640 3.2478 3.3675 3.1707 3.2801 3.0970 3.1974 3.0315 3.1239 2.9780 3.0633 2.9365 3.0151 2.9015 2.9738 2.8733 2.9397 2.8495 2.9101 2.8271 2.8821 2.8061 2.8555 2.7921 2.8361 2.7661 2.8048 2.7288 2.7625 2.6849 2.7138 2.6339 2.6585 2.5770 2.5975 2.5178 2.5347

2.4575 2.4712

2.4014 2.4124

2.3499 2.3584

2.2661 2.2725

2.1670 2.1717

2.0500 2.0533

1.9045 1.9069

1.7578 1.7594

1.6311 1.6322

1.4073 1.4081 1.2787 1.2793 1.2002 1.2005 1.1338 1.1340 1.0674 1.0675 1.0000 1.0000 0.9313 0.9312 0.8629 0.8627 0.7949 0.7946

4.4100 4.7591 4.3785 4.7164 4.3486 4.6748 4.3209 4.6349 4.2991 4.6002 4.2837 4.5710 4.2654 4.5374 4.2317 4.4869 4.1751 4.4128 4.1149 4.3344 4.0552 4.2559 3.9873 4.1686 3.8870 4.0493 3.7352 3.8806 3.5954 3.7269 3.4871 3.6068 3.3895 3.4989 3.2979 3.3983 3.2164 3.3089 3.1485 3.2338 3.0937 3.1724 3.0462 3.1186 3.0061 3.0725 2.9707 3.0312 2.9370 2.9920 2.9049 2.9544 2.8802 2.9242 2.8435 2.8822 2.7962 2.8299 2.7428 2.7718 2.6831 2.7078 2.6180 2.6385 2.5515 2.5684

2.4850 2.4987

2.4233 2.4343

2.3670 2.3755

2.2789 2.2853

2.1764 2.1811

2.0567 2.0600

1.9092 1.9116

1.7611 1.7627

1.6334 1.6345

1.4089 1.4097 1.2798 1.2804 1.2009 1.2013 1.1342 1.1345 1.0676 1.0677 1.0000 1.0000 0.9311 0.9310 0.8625 0.8623 0.7944 0.7942


TABLE 4—Continued

Mv B-V Mass Mbol lo%Teff logg x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.600 -2.716 -2.732

11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.701 4.600 4.500 4.400 4.301 4.200 4.100

0.639 0.651 0.664 0.678 0.695 0.713 0.733 0.755 0.779 0.805 0.835 0.867 0.902 0.941 0.984 1.032 1.087 1.149 1.222 1.306 1.360 1.368

1.536 1.498 1.460 1.423 1.387 1.354 1.323 1.298 1.273 1.249 1.225 1.202 1.178 1.152 1.123 1.091 1.056 1.019 0.978 0.933 0.886 0.841 0.797 0.753 0.707 0.661 0.616 0.576 0.541 0.511 0.485 0.463 0.442 0.422 0.413 0.405 0.397 0.390 0.383 0.377 0.372 0.369 0.367

0.7856 0.7857 0.7859 0.7860 0.7861 0.7862 0.7863 0.7864 0.7865 0.7866 0.7866 0.7866 0.7867 0.7867 0.7867 0.7867 0.7868 0.7868 0.7868 0.7868 0.7868 0.7868

0.1567 0.1646 0.1733 0.1828 0.1934 0.2055 0.2195 0.2362 0.2553 0.2767 0.3010 0.3290 0.3596 0.3895 0.4166 0.4409 0.4629 0.4830 0.5014 0.5185 0.5348 0.5506 0.5661 0.5814 0.5968 0.6122 0.6276 0.6431 0.6588 0.6742 0.6889 0.7028 0.7163 0.7284 0.7339 0.7391 0.7439 0.7486 0.7530 0.7572 0.7611 0.7646 0.7677

0.982 0.775 0.568 0.360 0.150

- 0.059 - 0.270 * 0.482 - 0.695 -0.909 -1.126 - 1.345 - 1.565 - 1.788 - 2.015 - 2.247 - 2.486 - 2.732 - 2.986 - 3.252 - 3.414 - 3.437

3.7118 3.7089 3.7059 3.7029 3.6997 3.6963 3.6927 3.6890 3.6853 3.6814 3.6773 3.6731 3.6687 3.6641 3.6592 3.6541 3.6487 3.6430 3.6368 3.6302 3.6261 3.6255

2.632 2.537 2.442 2.347 2.251 2.153 2.055 1.955 1.855 1.754 1.651 1.546 1.441 1.333 1.223 1.110 0.993 0.871 0.745 0.612 0.531 0.520

0.7277 0.6605 0.5923 0.5254 0.4588 0.3970 0.3528 0.3624 0.2920 0.1495 0.0554

-0.0129 -0.0766 -0.1366 -0.1940 -0.2484 -0.3041 -0.3579 -0.4080 -0.4451 -0.3960

0.7274 0.6601 0.5919 0.5250 0.4583 0.3965 0.3523 0.3619 0.2914 0.1489 0.0548

-0.0136 -0.0773 -0.1372 -0.1947 -0.2490 -0.3048 -0.3586 -0.4086 -0.4458 -0.3967

0.7271 0.6598 0.5915 0.5245 0.4578 0.3960 0.3518 0.3613 0.2909 0.1484 0.0542

-0.0142 -0.0779 -0.1378 -0.1953 -0.2497 -0.3054 -0.3592 -0.4093 -0.4464 -0.3973

[Fe/H] = -2.03 [O/Fe] = +0.70 Y = 0.2350

10.520 10.374 10.224 10.071 9.915 9.756 9.594 9.427 9.258 9.088 8.917 8.744 8.571 8.399 8.230 8.061 7.893 7.727 7.564 7.402 7.240 7.077 6.912 6.745 6.575 6.404 6.229 6.048 5.858 5.664 5.467 5.271 5.076 4.882 4.785 4.687 4.590 4.492 4.395 4.297 4.199 4.100 4.002

3.5746 3.5796 3.5845 3.5894 3.5941 3.5987 3.6029 3.6068 3.6106 3.6143 3.6181 3.6218 3.6255 3.6295 3.6340 3.6389 3.6442 3.6502 3.6570 3.6647 3.6732 3.6823 3.6919 3.7019 3.7122 3.7226 3.7331 3.7435 3.7537 3.7632 3.7719 3.7795 3.7865 3.7930 3.7961 3.7990 3.8017 3.8042 3.8064 3.8084 3.8100 3.8110 3.8114

5.198 5.180 5.163 5.144 5.125 5.106 5.087 5.067 5.049 5.031 5.014 4.998 4.982 4.965 4.944 4.921 4.896 4.872 4.850 4.831 4.813 4.797 4.781 4.766 4.751 4.735 4.718 4.698 4.673 4.644 4.609 4.570 4.528 4.484 4.460 4.436 4.411 4.384 4.357 4.328 4.297 4.264 4.228

3.0087 3.0236 3.0399 3.0602 3.0871 3.1234 3.1636 3.2003 3.2200 3.2351 3.2590 3.2747 3.2519 3.1886 3.1097 3.0399 2.9786 2.9207 2.8689 2.8281 2.7964 2.7731 2.7559 2.7417 2.7324 2.7216 2.7121 2.7069 2.6941 2.6694 2.6388 2.6006 2.5521 2.5002

2.4475

2.4015

2.3488

2.2610

3.3593 3.3634 3.3685 3.3771 3.3917 3.4147 3.4405 3.4614 3.4644 3.4620 3.4675 3.4641 3.4223 3.3417 3.2481 3.1659 3.0940 3.0268 2.9669 2.9188 2.8803 2.8507 2.8274 2.8074 2.7924 2.7761 2.7611 2.7507 2.7327 2.7030 2.6677 2.6252 2.5725 2.5170

2.4611

2.4123

2.3572

2.2672

3.7099 3.7032 3.6971 3.6941 3.6964 3.7062 3.7175 3.7227 3.7089 3.6889 3.6761 3.6535 3.5927 3.4948 3.3865 3.2920 3.2094 3.1329 3.0649 3.0094 2.9642 2.9283 2.8990 2.8731 2.8525 2.8306 2.8102 2.7945 2.7712 2.7366 2.6966 2.6497 2.5929 2.5338

2.4747

2.4231

2.3655

2.2734

0.7268 0.6594 0.5911 0.5241 0.4574 0.3955 0.3513 0.3608 0.2903 0.1478 0.0536

-0.0148 -0.0785 -0.1384 -0.1959 -0.2503 -0.3060 -0.3598 -0.4099 -0.4471 -0.3980

4.0607 4.0432 4.0258 4.0112 4.0012 3.9977 3.9946 3.9841 3.9534 3.9159 3.8848 3.8431 3.7632 3.6480 3.5250 3.4181 3.3249 3.2391 3.1629 3.1001 3.0481 3.0058 2.9705 2.9388 2.9125 2.8851 2.8593 2.8383 2.8098 2.7702 2.7255 2.6742 2.6133 2.5505

2.4883

2.4339

2.3738

2.2797

0.7265 0.6591 0.5907 0.5237 0.4569 0.3950 0.3508 0.3602 0.2897 0.1472 0.0530

-0.0154 -0.0791 -0.1390 -0.1965 -0.2509 -0.3067 -0.3605 -0.4106 -0.4477 -0.3987

4.4116 4.3832 4.3547 4.3283 4.3060 4.2893 4.2718 4.2455 4.1980 4.1430 4.0936 4.0327 3.9338 3.8013 3.6635 3.5442 3.4403 3.3453 3.2609 3.1907 3.1320 3.0834 3.0420 3.0046 2.9726 2.9396 2.9085 2.8821 2.8484 2.8038 2.7545 2.6988 2.6337 2.5673

2.5019

2.4447

2.3822

2.2859

0.7262 0.6587 0.5903 0.5232 0.4564 0.3946 0.3502 0.3597 0.2892 0.1466 0.0524

-0.0160 -0.0797 -0.1397 -0.1972 -0.2516 -0.3073 -0.3611 -0.4112 -0.4484 -0.3993

4.7625 4.7234 4.6836 4.6456 4.6109 4.5810 4.5490 4.5070 4.4427 4.3702 4.3025 4.2224 4.1044 3.9546 3.8021 3.6703 3.5558 3.4515 3.3589 3.2814 3.2159 3.1611 3.1136 3.0703 3.0327 2.9942 2.9576 2.9259 2.8870 2.8374 2.7834 2.7233 2.6541 2.5841

2.5155

2.4555

2.3905

2.2921

200


PQ oo KO TABLE A—Continued

00 Mv B-V Mass Mioi logTcyy x — 0.0 37 = 0.5 x = 1.0 x = 1.5 x = 2.0

4.000 3.898 3.800 3.695 3.600 3.494 3.400 3.300 3.200 3.108 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.589 -2.678

11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000

0.368 0.371 0.378 0.390 0.405 0.430 0.457 0.487 0.518 0.537 0.553 0.576 0.590 0.601 0.611 0.621 0.629 0.638 0.648 0.659 0.671 0.685 0.700 0.716 0.736 0.757 0.779 0.805 0.833 0.865 0.900 0.938 0.981 1.029 1.083 1.145 1.218 1.303 1.396 1.443

1.566 1.534 1.501 1.467 1.433 1.402 1.372 1.345 1.320 1.296 1.272 1.249 1.227 1.203 1.176 1.145 1.112 1.078 1.040 0.999 0.953 0.906 0.860 0.814 0.769

0.7706 0.7731 0.7752 0.7771 0.7786 0.7800 0.7810 0.7820 0.7829 0.7834 0.7839 0.7847 0.7853 0.7858 0.7863 0.7867 0.7870 0.7873 0.7875 0.7877 0.7879 0.7881 0.7882 0.7883 0.7884 0.7885 0.7886 0.7887 0.7887 0.7888 0.7888 0.7888 0.7889 0.7889 0.7889 0.7889 0.7890 0.7890 0.7890 0.7890

0.1564 0.1641 0.1723 0.1813 0.1914 0.2029 0.2163 0.2319 0.2499 0.2701 0.2929 0.3192 0.3490 0.3792 0.4064 0.4303 0.4523 0.4728 0.4918 0.5093 0.5256 0.5413 0.5565 0.5715 0.5865

3.903 3.802 3.704 3.597 3.501 3.391 3.290 3.176 3.060 2.957 2.840 2.627 2.419 2.212 2.006 1.801 1.596 1.390 1.184 0.977 0.770 0.562 0.353 0.144

-0.067 - 0.279 - 0.491 - 0.705 0.922

- 1.141 1.361

- 1.585 - 1.812 2.046

- 2.287 - 2.535 - 2.794 -3.068 - 3.342 - 3.478

3.8109 3.8093 3.8064 3.8016 3.7957 3.7861 3.7753 3.7612 3.7489 3.7422 3.7375 3.7316 3.7280 3.7254 3.7228 3.7205 3.7181 3.7156 3.7128 3.7101 3.7071 3.7042 3.7011 3.6978 3.6942 3.6905 3.6868 3.6828 3.6786 3.6742 3.6696 3.6647 3.6595 3.6541 3.6482 3.6419 3.6351 3.6277 3.6199 3.6160

4.188 4.142 4.093 4.032 3.971 3.889 3.806 3.705 3.610 3.542 3.477 3.368 3.271 3.178 3.086 2.995 2.903 2.811 2.717 2.624 2.529 2.434 2.339 2.242 2.143 2.044 1.944 1.842 1.739 1.634 1.527 1.418 1.307 1.191 1.071 0.947 0.816 0.677 0.536 0.466

2.1633

2.0417

1.8976

1.7713

2.1678

2.0450

1.8999

1.7728

2.1724

2.0482

1.9022

1.7744

2.1769

2.0514

1.9044

1.7760

1.6019 1.6029 1.6040 1.6051

1.3802 1.2752 1.2022 1.1355 1.0692 1.0000 0.9360 0.8666 0.7986 0.7306 0.6632 0.5946 0.5292 0.4656 0.4149 0.4119 0.3888 0.2440 0.1317 0.0574

-0.0073 -0.0682 -0.1263 -0.1808 -0.2375 -0.2911 -0.3397 -0.3836 -0.4093

1.3810 1.2758 1.2026 1.1358 1.0693 1.0000 0.9359 0.8665 0.7984 0.7303 0.6629 0.5942 0.5288 0.4652 0.4144 0.4113 0.3882 0.2434 0.1311 0.0568

-0.0079 -0.0688 -0.1269 -0.1814 -0.2381 -0.2918 -0.3403 -0.3843 -0.4100

1.3818 1.2763 1.2030 1.1360 1.0694 1.0000 0.9358 0.8663 0.7981 0.7300 0.6625 0.5938 0.5284 0.4647 0.4139 0.4108 0.3877 0.2428 0.1306 0.0562

-0.0084 -0.0694 -0.1275 -0.1820 -0.2387 -0.2924 -0.3410 -0.3849 -0.4106

[Fe/H] = -1.78 [O/Fe] = +0.66 Y = 0.2351

10.592 10.451 10.308 10.161 10.010 9.855 9.696 9.533 9.367 9.200 9.032 8.862 8.690 8.519 8.351 8.186 8.022 7.856 7.693 7.533 7.374 7.215 7.055 6.893 6.728

3.5667 3.5716 3.5765 3.5814 3.5861 3.5907 3.5949 3.5989 3.6026 3.6064 3.6101 3.6138 3.6173 3.6211 3.6255 3.6303 3.6355 3.6409 3.6471 3.6541 3.6621 3.6708 3.6801 3.6899 3.7001

5.194 5.178 5.162 5.144 5.127 5.108 5.089 5.070 5.051 5.033 5.016 5.000 4.984 4.967 4.948 4.926 4.902 4.877 4.854 4.833 4.815 4.799 4.784 4.770 4.756

3.0059 3.0188 3.0339 3.0546 3.0819 3.1174 3.1594 3.1963 3.2181 3.2307 3.2540 3.2815 3.2751 3.2174 3.1305 3.0580 3.0061 2.9560 2.9024 2.8523 2.8164 2.7884 2.7675 2.7530 2.7417

3.3579 3.3604 3.3648 3.3743 3.3899 3.4127 3.4408 3.4626 3.4682 3.4638 3.4695 3.4784 3.4529 3.3775 3.2754 3.1904 3.1277 3.0678 3.0057 2.9480 2.9052 2.8708 2.8439 2.8235 2.8066

3.7100 3.7021 3.6957 3.6941 3.6979 3.7080 3.7222 3.7289 3.7183 3.6971 3.6852 3.6754 3.6308 3.5376 3.4204 3.3228 3.2492 3.1797 3.1090 3.0437 2.9939 2.9532 2.9202 2.8941 2.8715

1.3825 1.2769 1.2033 1.1362 1.0695 1.0000 0.9357 0.8661 0.7979 0.7297 0.6622 0.5935 0.5280 0.4643 0.4134 0.4103 0.3872 0.2423 0.1300 0.0556

-0.0090 -0.0700 -0.1281 -0.1827 -0.2393 -0.2930 -0.3416 -0.3855 -0.4113

4.0622 4.0438 4.0268 4.0140 4.0059 4.0034 4.0038 3.9953 3.9685 3.9304 3.9009 3.8725 3.8088 3.6978 3.5655 3.4553 3.3708 3.2916 3.2124 3.1394 3.0828 3.0356 2.9966 2.9646 2.9364

2.1814

2.0546

1.9067

1.7776

1.6062

1.3833 1.2774 1.2037 1.1365 1.0696 1.0000 0.9356 0.8660 0.7977 0.7294 0.6618 0.5931 0.5275 0.4638 0.4129 0.4098 0.3866 0.2417 0.1294 0.0550

-0.0096 -0.0706 -0.1287 -0.1833 -0.2400 -0.2937 -0.3422 -0.3862 -0.4119

4.4145 4.3857 4.3579 4.3339 4.3141 4.2988 4.2854 4.2618 4.2188 4.1638 4.1167 4.0697 3.9869 3.8581 3.7106 3.5878 3.4924 3.4036 3.3157 3.2352 3.1716 3.1180 3.0730 3.0352 3.0013

201

x = 2.5

2.1860

2.0579

1.9090

1.7792

1.6073

1.3841 1.2780 1.2041 1.1367 1.0697 1.0000 0.9355 0.8658 0.7974 0.7291 0.6615 0.5927 0.5271 0.4633 0.4124 0.4093 0.3861 0.2412 0.1289 0.0545

-0.0102 -0.0712 -0.1293 -0.1839 -0.2406 -0.2943 -0.3429 -0.3868 -0.4125

4.7669 4.7277 4.6891 4.6540 4.6223 4.5944 4.5671 4.5283 4.4692 4.3973 4.3326 4.2669 4.1650 4.0184 3.8558 3.7203 3.6140 3.5155 3.4191 3.3309 3.2604 3.2005 3.1494 3.1058 3.0663



oo My B-V Mass Mboi logTejf logs x = 0.0 x = 0.5 x - 1.0 x = 1.5 x = 2.0

6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.900 4.800 4.700 4.600 4.501 4.400 4.301 4.200 4.100 4.000 3.897 3.800 3.691 3.600 3.493 3.400 3.317 3.200 3.105 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.541 -2.581

0.724 0.679 0.635 0.593 0.558 0.528 0.502 0.479 0.457 0.438 0.429 0.421 0.413 0.406 0.400 0.395 0.391 0.389 0.389 0.391 0.396 0.405 0.421 0.440 0.471 0.503 0.533 0.559 0.575 0.588 0.604 0.616 0.626 0.635 0.643 0.652 0.662 0.673 0.684 0.697 0.711 0.727 0.746 0.768 0.790 0.815 0.842 0.873 0.908 0.946 0.989 1.037 1.092 1.154 1.227 1.314 1.416 1.497 1.521

0.6016 0.6167 0.6319 0.6471 0.6625 0.6777 0.6925 0.7068 0.7204 0.7325 0.7381 0.7434 0.7483 0.7531 0.7576 0.7619 0.7657 0.7693 0.7724 0.7752 0.7777 0.7797 0.7816 0.7830 0.7844 0.7855 0.7863 0.7871 0.7876 0.7881 0.7888 0.7894 0.7899 0.7904 0.7907 0.7910 0.7913 0.7916 0.7918 0.7919 0.7921 0.7922 0.7923 0.7924 0.7925 0.7926 0.7927 0.7927 0.7928 0.7928 0.7929 0.7929 0.7929 0.7929 0.7930 0.7930 0.7930 0.7930 0.7930

6.561 6.391 6.219 6.041 5.855 5.664 5.470 5.275 5.080 4.885 4.788 4.689 4.592 4.494 4.396 4.298 4.200 4.101 4.002 3.903 3.801 3.703 3.593 3.499 3.385 3.277 3.178 3.045 2.941 2.828 2.618 2.411 2.205 2.000 1.795 1.589 1.383 1.176 0.969 0.761 0.552 0.343 0.132

-0.081 -0.293 -0.508 -0.725 -0.944 -1.165 -1.390 -1.619 -1.856 -2.099 -2.352 -2.618 -2.902 -3.208 -3.444 -3.517

3.7105 3.7210 3.7313 3.7414 3.7514 3.7608 3.7695 3.7775 3.7843 3.7905 3.7933 3.7960 3.7985 3.8007 3.8027 3.8043 3.8055 3.8060 3.8058 3.8047 3.8024 3.7989 3.7930 3.7856 3.7737 3.7603 3.7486 3.7401 3.7358 3.7323 3.7281 3.7251 3.7227 3.7203 3.7181 3.7157 3.7130 3.7101 3.7074 3.7043 3.7013 3.6981 3.6945 3.6905 3.6867 3.6827 3.6783 3.6737 3.6689 3.6637 3.6583 3.6523 3.6460 3.6391 3.6316 3.6232 3.6137 3.6062 3.6038

4.742 4.727 4.710 4.689 4.665 4.636 4.603 4.565 4.523 4.477 4.453 4.427 4.401 4.374 4.345 4.314 4.282 4.247 4.208 4.166 4.117 4.065 3.999 3.932 3.840 3.743 3.658 3.571 3.512 3.453 3.353 3.258 3.167 3.075 2.985 2.893 2.800 2.706 2.612 2.517 2.421 2.325 2.226 2.125 2.025 1.923 1.819 1.713 1.605 1.494 1.381 1.263 1.140 1.011 0.875 0.727 0.567 0.443 0.404

2.7338 2.7246 2.7140 2.7086 2.6979 2.6785 2.6532 2.6182 2.5701 2.5187

2.4668

2.4264

2.3582

2.2686

2.0399

1.9060

1.7954

1.5243

1.3643 1.2772 1.2037 1.1363 1.0685 1.0000 0.9358 0.8660 0.7982 0.7291 0.6627 0.5953 0.5323 0.4786 0.4666 0.4779 0.3383 0.2070 0.1258 0.0601

-0.0007 -0.0583 -0.1134 -0.1712 -0.2242 -0.2697 -0.3152 -0.3524 -0.3378

2.7932 2.7786 2.7628 2.7521 2.7364 2.7121 2.6820 2.6426 2.5904 2.5353

2.4803

2.4370

2.3663

2.8527 2.8326 2.8115 2.7957 2.7748 2.7456 2.7109 2.6670 2.6107 2.5520

2.9121 2.8866 2.8603 2.8392 2.8133 2.7792 2.7399 2.6915 2.6310 2.5686

2.4937 2.5072

2.4476

2.3744

2.4582

2.3826

2.0429

1.9082

1.7969

2.0460

1.9103

1.7984

1.5253 1.5263

1.3651 1.2777 1.2041 1.1365 1.0686 1.0000 0.9357 0.8659 0.7980 0.7288 0.6624 0.5950 0.5319 0.4781 0.4661 0.4774 0.3377 0.2065 0.1252 0.0595

-0.0013 -0.0589 -0.1140 -0.1718 -0.2248 -0.2703 -0.3158 -0.3530 -0.3385

1.3658 1.2782 1.2045 1.1367 1.0688 1.0000 0.9356 0.8657 0.7977 0.7285 0.6621 0.5946 0.5314 0.4777 0.4657 0.4769 0.3372 0.2060 0.1247 0.0589

-0.0019 -0.0595 -0.1146 -0.1724 -0.2254 -0.2709 -0.3164 -0.3537 -0.3391

2.9715 2.9407 2.9090 2.8828 2.8518 2.8127 2.7688 2.7159 2.6513 2.5853

2.5206

2.4689

2.3907

2.2746 2.2807 2.2867 2.2927

2.1667 2.1711 2.1754 2.1798 2.1841

2.0491

1.9125

1.7999

1.5273

1.3666 1.2788 1.2048 1.1370 1.0689 1.0000 0.9355 0.8655 0.7975 0.7282 0.6617 0.5942 0.5310 0.4773 0.4652 0.4764 0.3367 0.2054 0.1241 0.0584

-0.0025 -0.0600 -0.1152 -0.1730 -0.2260 -0.2715 -0.3170 -0.3543 -0.3397

2.0522

1.9147

1.8013

1.5283

1.3673 1.2793 1.2052 1.1372 1.0690 1.0000 0.9354 0.8654 0.7973 0.7279 0.6614 0.5938 0.5306 0.4768 0.4647 0.4759 0.3362 0.2049 0.1236 0.0578

-0.0030 -0.0606 -0.1158 -0.1736 -0.2266 -0.2721 -0.3176 -0.3549 -0.3403

202

x = 2.5

3.0310 2.9947 2.9578 2.9264 2.8903 2.8463 2.7977 2.7403 2.6716 2.6020

2.5341

2.4795

2.3988

2.2988

2.1885

2.0553

1.9168

1.8028

1.5293

1.3680 1.2798 1.2056 1.1374 1.0691 1.0000 0.9353 0.8652 0.7970 0.7277 0.6611 0.5935 0.5302 0.4764 0.4643 0.4755 0.3356 0.2043 0.1230 0.0572

-0.0036 -0.0612 -0.1164 -0.1742 -0.2272 -0.2728 -0.3182 -0.3555 -0.3410


1 992

ApJ

S . .

1.81

TABLE 4—Continued

Mv B-V Mass Mhoi logrc// logg x = 0.0 x = 0.5 x - 1.0 x - 1.5 x = 2.0 x - 2.5

[Fe/H] = —1.66 [O/Fe] = +0.63 Y = 0.2352

11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.000 4.901 4.800 4.701 4.600 4.501 4.400 4.301 4.200 4.100 4.000 3.896 3.800 3.691 3.600 3.492 3.400 3.316 3.200 3.108 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000

1.565 1.534 1.502 1.470 1.439 1.409 1.381 1.356 1.332 1.308 1.285 1.263 1.240 1.215 1.187 1.156 1.124 1.090 1.052 1.010 0.964 0.916 0.869 0.823 0.778 0.733 0.689 0.644 0.603 0.567 0.537 0.510 0.487 0.465 0.446 0.438 0.429 0.422 0.415 0.410 0.405 0.401 0.400 0.400 0.403 0.410 0.420 0.438 0.461 0.495 0.531 0.558 0.579 0.595 0.606 0.619 0.630 0.639 0.648 0.656 0.665 0.675 0.686 0.698 0.712

0.1600 0.1679 0.1764 0.1858 0.1963 0.2083 0.2224 0.2389 0.2577 0.2787 0.3024 0.3295 0.3591 0.3880 0.4140 0.4372 0.4586 0.4786 0.4969 0.5137 0.5296 0.5449 0.5599 0.5748 0.5896 0.6046 0.6197 0.6348 0.6499 0.6652 0.6803 0.6949 0.7095 0.7231 0.7352 0.7408 0.7461 0.7510 0.7559 0.7605 0.7648 0.7686 0.7722 0.7754 0.7782 0.7806 0.7826 0.7846 0.7859 0.7874 0.7885 0.7892 0.7900 0.7904 0.7908 0.7915 0.7921 0.7926 0.7931 0.7934 0.7938 0.7940 0.7943 0.7945 0.7946

10.557 10.416 10.273 10.127 9.977 9.822 9.663 9.499 9.334 9.168 9.001 8.832 8.662 8.494 8.328 8.164 7.999 7.836 7.674 7.517 7.360 7.203 7.044 6.883 6.720 6.553 6.384 6.213 6.037 5.853 5.664 5.471 5.276 5.082 4.886 4.789 4.691 4.593 4.495 4.397 4.298 4.200 4.101 4.002 3.903 3.800 3.703 3.592 3.497 3.377 3.266 3.167 3.037 2.935 2.821 2.612 2.406 2.200 1.995 1.790 1.584 1.377 1.170 0.963 0.754

3.5652 3.5701 3.5749 3.5797 3.5843 3.5887 3.5928 3.5966 3.6003 3.6040 3.6077 3.6114 3.6150 3.6190 3.6235 3.6284 3.6334 3.6389 3.6452 3.6525 3.6606 3.6695 3.6789 3.6888 3.6990 3.7094 3.7199 3.7302 3.7403 3.7502 3.7595 3.7681 3.7760 3.7831 3.7891 3.7918 3.7943 3.7967 3.7988 3.8006 3.8021 3.8030 3.8033 3.8027 3.8015 3.7988 3.7950 3.7880 3.7798 3.7658 3.7521 3.7430 3.7367 3.7324 3.7295 3.7260 3.7232 3.7209 3.7187 3.7165 3.7138 3.7112 3.7083 3.7055 3.7024

5.184 5.168 5.152 5.135 5.117 5.099 5.080 5.061 5.042 5.025 5.008 4.992 4.976 4.959 4.938 4.916 4.891 4.866 4.843 4.824 4.807 4.791 4.777 4.764 4.751 4.737 4.722 4.705 4.685 4.661 4.633 4.599 4.562 4.521 4.473 4.449 4.423 4.396 4.368 4.338 4.307 4.274 4.238 4.198 4.154 4.104 4.051 3.980 3.910 3.807 3.708 3.632 3.556 3.498 3.441 3.344 3.250 3.159 3.069 2.978 2.885 2.792 2.698 2.604 2.508

3.0133 3.0253 3.0415 3.0655 3.0970 3.1358 3.1758 3.2101 3.2257 3.2403 3.2638 3.2781 3.2564 3.1924 3.1113 3.0462 2.9948 2.9415 2.8871 2.8398 2.8073 2.7831 2.7647 2.7528 2.7427 2.7354 2.7265 2.7152 2.7083 2.6985 2.6803 2.6564 2.6216 2.5749 2.5241

2.4356

2.3593

2.2708

2.1669

2.0411

1.9202

1.7787

1.4978

1.3483 1.2708 1.2031 1.1340 1.0680 1.0000 0.9325 0.8664 0.7989 0.7312 0.6651

3.3610 3.3626 3.3681 3.3807 3.4003 3.4260 3.4518 3.4706 3.4699 3.4675 3.4732 3.4690 3.4289 3.3482 3.2529 3.1759 3.1140 3.0515 2.9888 2.9344 2.8952 2.8647 2.8405 2.8228 2.8072 2.7944 2.7802 2.7636 2.7516 2.7369 2.7138 2.6853 2.6460 2.5951 2.5407

3.7087 3.6999 3.6947 3.6961 3.7036 3.7163 3.7280 3.7313 3.7141 3.6947 3.6826 3.6599 3.6015 3.5040 3.3946 3.3056 3.2333 3.1615 3.0907 3.0289 2.9831 2.9464 2.9163 2.8929 2.8717 2.8535 2.8339 2.8121 2.7950 2.7752 2.7473 2.7141 2.6703 2.6154 2.5573

4.0566 4.0374 4.0214 4.0115 4.0070 4.0067 4.0041 3.9920 3.9585 3.9220 3.8922 3.8510 3.7741 3.6599 3.5363 3.4354 3.3525 3.2715 3.1925 3.1234 3.0710 3.0281 2.9921 2.9630 2.9362 2.9126 2.8876 2.8606 2.8384 2.8135 2.7808 2.7430 2.6947 2.6356 2.5740

4.4045 4.3749 4.3481 4.3270 4.3105 4.2972 4.2804 4.2528 4.2029 4.1494 4.1018 4.0421 3.9468 3.8159 3.6781 3.5651 3.4719 3.3815 3.2943 3.2180 3.1590 3.1098 3.0679 3.0331 3.0008 2.9716 2.9413 2.9091 2.8818 2.8519 2.8143 2.7718 2.7190 2.6558 2.5906

2.4461

2.3673

2.2768

2.1712

2.0441

1.9223

1.7801

1.4988

1.3490 1.2713 1.2035 1.1343 1.0681 1.0000 0.9324 0.8662 0.7987 0.7309 0.6647

2.0472 2.0502

1.9244 1.9265

1.7815 1.7829

1.4997 1.5007

1.3497 1.2719 1.2039 1.1345 1.0682 1.0000 0.9323 0.8661 0.7985 0.7306 0.6644

1.3504 1.2724 1.2042 1.1347 1.0683 1.0000 0.9322 0.8659 0.7982 0.7303 0.6641

2.0532

1.9286

1.7843

1.5017

1.3511 1.2729 1.2046 1.1349 1.0684 1.0000 0.9321 0.8657 0.7980 0.7301 0.6637

4.7525 4.7125 4.6750 4.6425 4.6140 4.5878 4.5568 4.5137 4.4474 4.3769 4.3116 4.2333 4.1196 3.9719 3.8199 3.6950 3.5912 3.4916 3.3962 3.3126 3.2469 3.1916 3.1438 3.1032 3.0653 3.0307 2.9951 2.9576 2.9252 2.8903 2.8478 2.8007 2.7434 2.6761 2.6072

2.4744 2.4878 2.5012 2.5146 2.5280 2.5414

2.4567 2.4673 2.4778 2.4884

2.3754 2.3834 2.3915 2.3995

2.2827 2.2887 2.2946 2.3006

2.1755 2.1797 2.1840 2.1883

2.0562

1.9307

1.7857

1.5026

1.3519 1.2734 1.2049 1.1352 1.0685 1.0000 0.9321 0.8656 0.7978 0.7298 0.6634

203


1 992

ApJ

S . J .

81IJ

. 163

B

TABLE 4—Continued

My B-V Mass Mboi logTe// logp x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0 x = 2.5

0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.400 -2.508 -2.517

12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.101 5.000 4.901 4.800 4.701 4.600 4.500 4.400 4.300 4.200

0.726 0.743 0.764 0.786 0.809 0.835 0.864 0.896 0.933 0.973 1.018 1.070 1.128 1.196 1.276 1.371 1.484 1.552 1.557

1.596 1.566 1.536 1.506 1.477 1.449 1.422 1.397 1.374 1.351 1.329 1.307 1.285 1.261 1.235 1.207 1.177 1.145 1.109 1.069 1.026 0.980 0.933 0.885 0.839 0.793 0.748 0.704 0.659 0.617 0.581 0.550 0.524 0.501 0.479 0.469 0.459 0.451 0.443 0.436 0.430 0.425 0.420 0.418 0.417

0.7948 0.7949 0.7950 0.7951 0.7952 0.7953 0.7954 0.7954 0.7955 0.7955 0.7956 0.7956 0.7956 0.7956 0.7957 0.7957 0.7957 0.7957 0.7957

0.1590 0.1667 0.1750 0.1841 0.1941 0.2055 0.2186 0.2339 0.2515 0.2713 0.2936 0.3193 0.3477 0.3760 0.4027 0.4271 0.4493 0.4694 0.4878 0.5049 0.5210 0.5364 0.5514 0.5661 0.5808 0.5955 0.6103 0.6252 0.6402 0.6551 0.6702 0.6852 0.6999 0.7147 0.7283 0.7345 0.7405 0.7461 0.7515 0.7566 0.7617 0.7663 0.7705 0.7744 0.7779

0.545 0.335 0.123

- 0.090 - 0.304 - 0.519 ■0.738 - 0.958 - 1.182 ■ 1.409

1.643 - 1.885 - 2.135 2.397

- 2.677 • 2.978 3.315 3.520 3.536

3.6994 3.6960 3.6922 3.6881 3.6842 3.6800 3.6754 3.6706 3.6655 3.6601 3.6542 3.6479 3.6410 3.6335 3.6251 3.6157 3.6046 3.5976 3.5970

2.412 2.315 2.215 2.113 2.012 1.909 1.804 1.696 1.586 1.474 1.356 1.234 1.107 0.972 0.827 0.668 0.490 0.379 0.371

0.5975 0.5374 0.4912 0.5100 0.4751 0.3064 0.1976 0.1255 0.0629 0.0041

-0.0514 -0.1095 -0.1648 -0.2128 -0.2578 -0.2995 -0.3150 -0.2593

0.5971 0.5370 0.4907 0.5095 0.4746 0.3059 0.1971 0.1250 0.0624 0.0035

-0.0520 -0.1101 -0.1654 -0.2134 -0.2584 -0.3001 -0.3156 -0.2600

0.5968 0.5366 0.4903 0.5090 0.4741 0.3054 0.1966 0.1244 0.0618 0.0030

-0.0526 -0.1107 -0.1660 -0.2140 -0.2590 -0.3007 -0.3162 -0.2606

0.5964 0.5362 0.4899 0.5086 0.4736 0.3049 0.1960 0.1239 0.0612 0.0024

-0.0532 -0.1113 -0.1665 -0.2146 -0.2596 -0.3013 -0.3168 -0.2612

0.5960 0.5358 0.4894 0.5081 0.4731 0.3044 0.1955 0.1233 0.0607 0.0018

-0.0538 -0.1119 -0.1671 -0.2152 -0.2602 -0.3019 -0.3174 -0.2618

0.5957 0.5354 0.4890 0.5076 0.4726 0.3039 0.1950 0.1228 0.0601 0.0013

-0.0543 -0.1124 -0.1677 -0.2158 -0.2608 -0.3025 -0.3181 -0.2624

[Fe/H] = -1.48 [O/Fe] = +0.60 Y = 0.2354

x = —0.5 x = 0.0 x = 0.5 x — 1.0 x = 1.5 x — 2.0

10.632 10.494 10.354 10.211 10.066 9.916 9.762 9.603 9.441 9.277 9.113 8.946 8.779 8.614 8.449 8.285 8.122 7.961 7.802 7.646 7.491 7.337 7.182 7.025 6.866 6.704 6.540 6.373 6.203 6.030 5.849 5.662 5.471 5.278 5.084 4.987 4.888 4.791 4.692 4.595 4.496 4.398 4.299 4.201 4.102

3.5575 3.5623 3.5671 3.5718 3.5763 3.5807 3.5849 3.5888 3.5925 3.5962 3.5999 3.6035 3.6071 3.6110 3.6153 3.6197 3.6245 3.6297 3.6357 3.6424 3.6500 3.6582 3.6671 3.6767 3.6866 3.6970 3.7075 3.7180 3.7284 3.7385 3.7483 3.7575 3.7659 3.7735 3.7806 3.7838 3.7867 3.7892 3.7916 3.7938 3.7957 3.7971 3.7984 3.7990 3.7989

5.180 5.165 5.149 5.133 5.116 5.098 5.080 5.062 5.043 5.026 5.009 4.993 4.977 4.961 4.942 4.920 4.895 4.871 4.848 4.827 4.809 4.793 4.779 4.766 4.753 4.741 4.728 4.714 4.698 4.678 4.655 4.627 4.593 4.556 4.515 4.492 4.468 4.443 4.415 4.388 4.359 4.329 4.296 4.262 4.224

2.6653 2.6873 2.7134 2.7429 2.7801 2.8281 2.8803 2.9301 2.9687 3.0013 3.0420 3.0819 3.0848 3.0504 3.0027 2.9494 2.8955 2.8452 2.8022 2.7647 2.7342 2.7133 2.6985 2.6873 2.6823 2.6791 2.6772 2.6734 2.6679 2.6645 2.6630 2.6520 2.6362 2.6066 2.5661

2.5206

2.4791

2.4405

2.3599

2.2731

3.0157 3.0275 3.0430 3.0615 3.0871 3.1228 3.1614 3.1965 3.2195 3.2356 3.2591 3.2809 3.2656 3.2143 3.1517 3.0855 3.0206 2.9609 2.9094 2.8644 2.8270 2.7998 2.7790 2.7621 2.7515 2.7428 2.7356 2.7265 2.7159 2.7075 2.7011 2.6853 2.6649 2.6307 2.5862

2.5371

2.4923

2.4508

2.3678

2.2789

3.3663 3.3678 3.3727 3.3802 3.3943 3.4175 3.4427 3.4631 3.4703 3.4700 3.4763 3.4800 3.4464 3.3782 3.3008 3.2217 3.1458 3.0765 3.0166 2.9641 2.9199 2.8863 2.8595 2.8369 2.8207 2.8066 2.7941 2.7797 2.7640 2.7506 2.7393 2.7187 2.6936 2.6549 2.6062

2.5536

2.5056

2.4612

2.3756

2.2847

3.7169 3.7081 3.7025 3.6989 3.7015 3.7123 3.7240 3.7297 3.7212 3.7045 3.6936 3.6791 3.6273 3.5422 3.4499 3.3580 3.2710 3.1921 3.1238 3.0638 3.0128 2.9729 2.9401 2.9116 2.8900 2.8704 2.8525 2.8329 2.8121 2.7937 2.7774 2.7520 2.7223 2.6791 2.6263

2.5700

2.5188

2.4715

2.3834

2.2905

4.0675 4.0486 4.0324 4.0178 4.0087 4.0072 4.0053 3.9964 3.9722 3.9391 3.9109 3.8784 3.8083 3.7063 3.5990 3.4943 3.3963 3.3078 3.2311 3.1635 3.1057 3.0594 3.0206 2.9864 2.9592 2.9342 2.9110 2.8862 2.8602 2.8367 2.8156 2.7853 2.7510 2.7033 2.6464

2.5865

2.5320

2.4819

2.3913

2.2962

4.4183 4.3891 4.3623 4.3367 4.3161 4.3021 4.2868 4.2632 4.2233 4.1737 4.1284 4.0777 3.9894 3.8704 3.7482 3.6306 3.5215 3.4235 3.3384 3.2633 3.1986 3.1460 3.1012 3.0613 3.0285 2.9980 2.9695 2.9394 2.9083 2.8798 2.8538 2.8187 2.7797 2.7275 2.6665

2.6029

2.5453

2.4922

2.3991

2.3020

204



My B-V Mass Mbol l°g^c// logfl' x — —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0

4.099 4.000 3.893 3.800 3.688 3.600 3.502 3.400 3.304 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -2.000 -2.200 -2.387 -2.474

12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200

0.419 0.423 0.432 0.446 0.469 0.496 0.535 0.574 0.593 0.611 0.631 0.642 0.652 0.660 0.668 0.678 0.687 0.697 0.709 0.722 0.736 0.752 0.772 0.793 0.816 0.841 0.868 0.898 0.932 0.969 1.011 1.058 1.111 1.171 1.242 1.324 1.421 1.526 1.577

1.627 1.597 1.568 1.538 1.510 1.482 1.456 1.433 1.411 1.389 1.369 1.349 1.330 1.308 1.284 1.258 1.229 1.198 1.165 1.129 1.089 1.047 1.002 0.956 0.909 0.861

0.7810 0.7838 0.7863 0.7882 0.7902 0.7916 0.7930 0.7941 0.7947 0.7953 0.7961 0.7968 0.7974 0.7979 0.7983 0.7986 0.7990 0.7992 0.7994 0.7996 0.7998 0.8000 0.8001 0.8002 0.8004 0.8005 0.8006 0.8006 0.8007 0.8007 0.8008 0.8008 0.8008 0.8009 0.8009 0.8009 0.8009 0.8010 0.8010

0.1594 0.1671 0.1753 0.1843 0.1942 0.2052 0.2177 0.2322 0.2489 0.2678 0.2892 0.3139 0.3413 0.3694 0.3960 0.4203 0.4423 0.4629 0.4819 0.4996 0.5162 0.5319 0.5470 0.5616 0.5760 0.5904

4.002 3.904 3.796 3.703 3.587 3.490 3.372 3.247 3.138 3.023 2.810 2.603 2.397 2.192 1.987 1.781 1.574 1.367 1.159 0.951 0.742 0.532 0.320 0.107

- 0.107 - 0.323 - 0.540 -0.760 - 0.982 - 1.209 - 1.441 - 1.680 - 1.926 - 2.182 - 2.454 - 2.744 -3.060 -3.396 - 3.565

3.7980 3.7963 3.7928 3.7876 3.7793 3.7689 3.7542 3.7414 3.7358 3.7310 3.7258 3.7227 3.7202 3.7180 3.7158 3.7133 3.7106 3.7080 3.7050 3.7022 3.6990 3.6957 3.6918 3.6880 3.6839 3.6797 3.6753 3.6706 3.6656 3.6603 3.6547 3.6485 3.6420 3.6348 3.6269 3.6181 3.6080 3.5968 3.5910

4.182 4.137 4.082 4.024 3.946 3.866 3.761 3.660 3.595 3.530 3.425 3.330 3.237 3.147 3.056 2.964 2.871 2.778 2.683 2.588 2.492 2.395 2.295 2.194 2.092 1.990 1.885 1.778 1.669 1.558 1.442 1.322 1.197 1.066 0.926 0.775 0.608 0.429 0.338

2.1687 2.1728 2.1769 2.1811 2.1852 2.1893

2.0468 2.0497 2.0526 2.0555

1.9510

1.7079

1.4642 1.3434 1.2716 1.2005 1.1323 1.0689 1.0000 0.9304 0.8648 0.7966 0.7277 0.6628 0.6027 0.5480 0.5542 0.5693 0.4002 0.2700 0.1903 0.1254 0.0654 0.0093

-0.0503 -0.1078 -0.1592 -0.2066 -0.2543 -0.2863 -0.2984

1.9530

1.7092

1.4652 1.3441 1.2721 1.2008 1.1325 1.0690 1.0000 0.9303 0.8647 0.7964 0.7274 0.6625 0.6023 0.5476 0.5538 0.5688 0.3997 0.2695 0.1898 0.1248 0.0649 0.0087

-0.0509 -0.1084 -0.1598 -0.2072 -0.2549 -0.2869 -0.2991

1.9549

1.7105

1.4661 1.3448 1.2726 1.2012 1.1327 1.0691 1.0000 0.9302 0.8645 0.7962 0.7271 0.6622 0.6020 0.5472 0.5534 0.5683 0.3992 0.2689 0.1892 0.1243 0.0643 0.0081

-0.0515 -0.1090 -0.1604 -0.2079 -0.2555 -0.2875 -0.2997

[Fe/H] = —1.26 [O/Fe] =+0.55 Y — 0.2358

10.689 10.555 10.418 10.278 10.136 9.990 9.841 9.687 9.530 9.370 9.207 9.043 8.879 8.716 8.554 8.394 8.234 8.074 7.916 7.761 7.608 7.456 7.304 7.152 6.998 6.842

3.5497 3.5544 3.5590 3.5636 3.5681 3.5725 3.5767 3.5806 3.5844 3.5880 3.5916 3.5951 3.5986 3.6024 3.6065 3.6109 3.6156 3.6205 3.6260 3.6320 3.6388 3.6464 3.6547 3.6636 3.6732 3.6833

5.173 5.158 5.143 5.127 5.111 5.094 5.077 5.060 5.042 5.024 5.007 4.991 4.976 4.960 4.942 4.921 4.898 4.874 4.850 4.828 4.808 4.790 4.775 4.761 4.749 4.737

2.6751 2.6969 2.7224 2.7513 2.7846 2.8253 2.8723 2.9197 2.9632 3.0007 3.0415 3.0804 3.0930 3.0674 3.0176 2.9628 2.9163 2.8747 2.8330 2.7943 2.7622 2.7351 2.7124 2.6980 2.6883 2.6845

3.0277 3.0393 3.0544 3.0725 3.0944 3.1231 3.1571 3.1905 3.2190 3.2405 3.2646 3.2859 3.2805 3.2379 3.1731 3.1052 3.0476 2.9961 2.9456 2.8990 2.8598 2.8262 2.7974 2.7773 2.7621 2.7529

3.3804 3.3819 3.3865 3.3937 3.4042 3.4209 3.4419 3.4614 3.4749 3.4805 3.4878 3.4914 3.4681 3.4084 3.3285 3.2477 3.1789 3.1175 3.0582 3.0038 2.9575 2.9173 2.8824 2.8565 2.8358 2.8213

1.9569

1.7118

1.4670 1.3455 1.2731 1.2015 1.1330 1.0692 1.0000 0.9301 0.8644 0.7959 0.7269 0.6618 0.6016 0.5468 0.5529 0.5679 0.3987 0.2684 0.1887 0.1237 0.0637 0.0076

-0.0521 -0.1096 -0.1610 -0.2085 -0.2562 -0.2882 -0.3003

3.7331 3.7245 3.7187 3.7150 3.7141 3.7187 3.7268 3.7323 3.7308 3.7205 3.7110 3.6970 3.6557 3.5790 3.4840 3.3902 3.3102 3.2390 3.1708 3.1086 3.0551 3.0085 2.9675 2.9358 2.9096 2.8897

2.0584 2.0613

1.9588 1.9608

1.7131

1.4679 1.3461 1.2736 1.2019 1.1332 1.0693 1.0000 0.9300 0.8642 0.7957 0.7266 0.6615 0.6012 0.5464 0.5525 0.5674 0.3982 0.2679 0.1881 0.1232 0.0632 0.0070

-0.0527 -0.1102 -0.1616 -0.2091 -0.2568 -0.2888 -0.3010

4.0860 4.0672 4.0509 4.0363 4.0241 4.0167 4.0118 4.0034 3.9868 3.9606 3.9344 3.9027 3.8434 3.7496 3.6396 3.5328 3.4415 3.3604 3.2835 3.2134 3.1528 3.0996 3.0525 3.0151 2.9834 2.9581

1.7144

1.4689 1.3468 1.2741 1.2022 1.1334 1.0694 1.0000 0.9299 0.8640 0.7955 0.7263 0.6612 0.6009 0.5460 0.5521 0.5669 0.3977 0.2674 0.1876 0.1226 0.0626 0.0064

-0.0533 -0.1108 -0.1623 -0.2097 -0.2574 -0.2894 -0.3016

4.4389 4.4100 4.3833 4.3578 4.3342 4.3147 4.2969 4.2745 4.2429 4.2008 4.1578 4.1085 4.0312 3.9204 3.7952 3.6754 3.5729 3.4819 3.3962 3.3182 3.2505 3.1908 3.1376 3.0945 3.0572 3.0266

205


PQ oo ^ TABLE 4—Continued

My B-V Mass Mbol logoff \ogg x = -0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5 x = 2.0

^ 7.000 0.814 ^ 6.800 0.769 << 6.600 0.725 S 6.400 0.681 2 6.200 0.638

6.000 0.600 5.800 0.569 5.600 0.543 5.400 0.520 5.200 0.499 5.100 0.489 5.000 0.480 4.901 0.471 4.800 0.462 4.701 0.455 4.600 0.449 4.501 0.445 4.400 0.442 4.300 0.440 4.200 0.441 4.097 0.444 4.000 0.452 3.893 0.465 3.800 0.482 3.683 0.519 3.600 0.559 3.516 0.595 3.400 0.626 3.200 0.652 3.000 0.666 2.800 0.675 2.600 0.684 2.400 0.692 2.200 0.701 2.000 0.710 1.800 0.720 1.600 0.731 1.400 0.743 1.200 0.757 1.000 0.775 0.800 0.795 0.600 0.817 0.400 0.840 0.200 0.865 0.000 0.893

—0.200 0.924 -0.400 0.958 -0.600 0.996 -0.800 1.039 -1.000 1.087 -1.200 1.142 -1.400 1.205 -1.600 1.278 -1.800 1.365 -2.000 1.470 -2.182 1.582 -2.263 1.646

0.6049 6.683 0.6196 6.521 0.6343 6.357 0.6491 6.189 0.6639 6.018 0.6788 5.841 0.6938 5.658 0.7089 5.470 0.7237 5.279 0.7373 5.086 0.7436 4.989 0.7497 4.891 0.7553 4.793 0.7609 4.695 0.7662 4.597 0.7713 4.498 0.7759 4.400 0.7803 4.301 0.7841 4.202 0.7876 4.103 0.7908 4.001 0.7935 3.904 0.7960 3.796 0.7979 3.700 0.8002 3.568 0.8018 3.463 0.8030 3.357 0.8040 3.220 0.8052 3.001 0.8061 2.792 0.8068 2.586 0.8075 2.380 0.8080 2.175 0.8085 1.969 0.8089 1.763 0.8092 1.556 0.8095 1.348 0.8098 1.140 0.8100 0.930 0.8102 0.719 0.8103 0.506 0.8105 0.292 0.8106 0.077 0.8108 -0.141 0.8109 -0.361 0.8109 -0.582 0.8110 -0.807 0.8111 -1.038 0.8111 -1.275 0.8111 -1.519 0.8112 -1.773 0.8112 -2.042 0.8112 -2.329 0.8113 -2.640 0.8113 -2.998 0.8113 -3.373 0.8113 -3.598

3.6937 4.726 3.7043 4.714 3.7150 4.701 3.7254 4.686 3.7356 4.668 3.7453 4.645 3.7545 4.618 3.7627 4.585 3.7699 4.547 3.7767 4.505 3.7798 4.482 3.7826 4.458 3.7853 4.433 3.7877 4.406 3.7897 4.378 3.7914 4.348 3.7926 4.317 3.7934 4.282 3.7936 4.246 3.7930 4.206 3.7915 4.161 3.7887 4.112 3.7839 4.051 3.7779 3.990 3.7642 3.884 3.7502 3.787 3.7393 3.701 3.7307 3.612 3.7235 3.497 3.7199 3.399 3.7173 3.307 3.7149 3.215 3.7126 3.124 3.7103 3.033 3.7078 2.941 3.7051 2.847 3.7024 2.754 3.6994 2.658 3.6963 2.562 3.6926 2.463 3.6886 2.361 3.6845 2.260 3.6804 2.157 3.6760 2.053 3.6713 1.946 3.6663 1.838 3.6610 1.727 3.6554 1.612 3.6492 1.492 3.6426 1.368 3.6354 1.238 3.6275 1.098 3.6186 0.948 3.6085 0.783 3.5963 0.591 3.5828 0.387 3.5744 0.264

2.6837 2.7468 2.6826 2.7405 2.6791 2.7319 2.6744 2.7222 2.6701 2.7130 2.6707 2.7088 2.6633 2.6967 2.6498 2.6785 2.6203 2.6445 2.5830 2.6032

2.5409 2.5575

2.5078 2.5211

2.4596 2.4700

2.3787 2.3865

2.2917 2.2976

2.1873 2.1916

2.0851 2.0881

1.9585 1.9605

1.6067 1.6080 1.4319 1.4329 1.3356 1.3364 1.2703 1.2709 1.2034 1.2038 1.1352 1.1355 1.0688 1.0689 1.0000 1.0000 0.9309 0.9308 0.8645 0.8643 0.7955 0.7952 0.7337 0.7334 0.6702 0.6698 0.6166 0.6162 0.6160 0.6156 0.6554 0.6549 0.4809 0.4804 0.3385 0.3380 0.2559 0.2553 0.1925 0.1920 0.1337 0.1331 0.0737 0.0731 0.0142 0.0135

-0.0403 -0.0410 -0.0901 -0.0907 -0.1416 -0.1423 -0.1772 -0.1779 -0.2101 -0.2107 -0.1780 -0.1786

2.8099 2.8730 2.7985 2.8564 2.7847 2.8375 2.7700 2.8178 2.7559 2.7989 2.7469 2.7850 2.7301 2.7635 2.7071 2.7358 2.6687 2.6929 2.6234 2.6435

2.5740 2.5906

2.5344 2.5477

2.4804 2.4908

2.3944 2.4023

2.3034 2.3092

2.1958 2.2000

2.0911 2.0941

1.9625 1.9645

1.6093 1.6107 1.4339 1.4349 1.3371 1.3379 1.2714 1.2720 1.2042 1.2045 1.1357 1.1359 1.0690 1.0692 1.0000 1.0000 0.9307 0.9306 0.8642 0.8640 0.7950 0.7948 0.7331 0.7328 0.6695 0.6691 0.6158 0.6154 0.6151 0.6147 0.6544 0.6539 0.4799 0.4794 0.3374 0.3369 0.2548 0.2542 0.1914 0.1908 0.1325 0.1319 0.0725 0.0719 0.0129 0.0123

-0.0416 -0.0422 -0.0913 -0.0920 -0.1429 -0.1435 -0.1785 -0.1792 -0.2114 -0.2120 -0.1793 -0.1799

2.9362 2.9994 2.9143 2.9723 2.8904 2.9432 2.8656 2.9135 2.8418 2.8848 2.8231 2.8612 2.7969 2.8303 2.7645 2.7932 2.7172 2.7414 2.6637 2.6839

2.6071 2.6237

2.5611 2.5744

2.5011 2.5115

2.4102 2.4181

2.3151 2.3209

2.2042 2.2085

2.0970 2.1000

1.9665 1.9685

1.6120 1.6133 1.4359 1.4369 1.3386 1.3394 1.2725 1.2731 1.2049 1.2053 1.1362 1.1364 1.0693 1.0694 1.0000 1.0000 0.9305 0.9304 0.8638 0.8637 0.7945 0.7943 0.7325 0.7322 0.6688 0.6684 0.6150 0.6147 0.6143 0.6138 0.6535 0.6530 0.4789 0.4783 0.3363 0.3358 0.2537 0.2531 0.1903 0.1897 0.1313 0.1307 0.0713 0.0707 0.0117 0.0111

-0.0428 -0.0434 -0.0926 -0.0932 -0.1442 -0.1448 -0.1798 -0.1805 -0.2127 -0.2133 -0.1806 -0.1812

206


PQ oo KO TABLE A—Continued

oo Mv B — V Mass Mbol logTeff logg x = —0.5 x = 0.0 x = 0.5 a: = 1.0 07 = 1.5

ft [Fe/H] = —1.03 [O/Fe] =+0.50 Y = 0.2368

12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.101 5.000 4.900 4.800 4.701 4.600 4.501 4.400 4.300 4.200 4.096 4.000 3.884 3.800 3.741 3.678 3.600 3.512 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800

1.690 1.662 1.633 1.604 1.575 1.546 1.519 1.493 1.469 1.446 1.426 1.406 1.388 1.370 1.350 1.330 1.307 1.282 1.254 1.223 1.189 1.151 1.112 1.069 1.025 0.980 0.934 0.888 0.841 0.796 0.753 0.712 0.669 0.627 0.594 0.567 0.542 0.521 0.512 0.504 0.495 0.488 0.481 0.475 0.471 0.469 0.470 0.472 0.477 0.485 0.508 0.535 0.573 0.610 0.647 0.667 0.681 0.697 0.707 0.716 0.723 0.732 0.740 0.750 0.760

0.1560 0.1629 0.1702 0.1784 0.1872 0.1971 0.2081 0.2208 0.2354 0.2519 0.2701 0.2907 0.3143 0.3408 0.3679 0.3937 0.4176 0.4399 0.4606 0.4800 0.4980 0.5147 0.5306 0.5458 0.5606 0.5751 0.5896 0.6040 0.6186 0.6332 0.6479 0.6625 0.6772 0.6919 0.7071 0.7223 0.7369 0.7504 0.7567 0.7629 0.7687 0.7744 0.7800 0.7852 0.7899 0.7943 0.7982 0.8019 0.8055 0.8085 0.8118 0.8139 0.8156 0.8169 0.8180 0.8187 0.8195 0.8205 0.8214 0.8221 0.8227 0.8232 0.8236 0.8240 0.8244

10.839 10.714 10.587 10.456 10.321 10.182 10.040 9.893 9.742 9.588 9.434 9.277 9.118 8.958 8.798 8.641 8.485 8.328 8.172 8.016 7.863 7.714 7.565 7.417 7.268 7.119 6.966 6.812 6.655 6.495 6.333 6.167 5.999 5.827 5.648 5.464 5.276 5.085 4.990 4.892 4.795 4.696 4.599 4.500 4.402 4.302 4.203 4.104 4.000 3.903 3.780 3.684 3.604 3.516 3.412 3.309 3.186 2.974 2.766 2.560 2.355 2.150 1.944 1.737 1.529

3.5363 3.5409 3.5455 3.5500 3.5545 3.5589 3.5632 3.5673 3.5711 3.5748 3.5785 3.5822 3.5858 3.5893 3.5930 3.5971 3.6014 3.6059 3.6106 3.6157 3.6214 3.6277 3.6348 3.6425 3.6508 3.6597 3.6691 3.6790 3.6892 3.6997 3.7101 3.7205 3.7306 3.7404 3.7496 3.7579 3.7656 3.7721 3.7750 3.7776 3.7800 3.7822 3.7840 3.7855 3.7864 3.7867 3.7862 3.7852 3.7833 3.7800 3.7720 3.7624 3.7501 3.7388 3.7289 3.7234 3.7194 3.7150 3.7120 3.7096 3.7075 3.7052 3.7030 3.7005 3.6978

5.170 5.157 5.144 5.130 5.115 5.099 5.083 5.066 5.049 5.032 5.015 4.999 4.984 4.969 4.953 4.936 4.917 4.895 4.871 4.847 4.824 4.804 4.786 4.770 4.755 4.742 4.730 4.718 4.706 4.694 4.681 4.666 4.649 4.629 4.603 4.572 4.537 4.494 4.471 4.446 4.420 4.393 4.364 4.333 4.300 4.264 4.224 4.183 4.136 4.085 4.006 3.930 3.850 3.770 3.689 3.627 3.562 3.460 3.365 3.274 3.184 3.093 3.001 2.909 2.815

2.6591 2.6801 2.7019 2.7288 2.7615 2.8001 2.8446 2.8907 2.9344 2.9680 2.9993 3.0391 3.0823 3.0963 3.0706 3.0279 2.9809 2.9391 2.9003 2.8599 2.8194 2.7839 2.7579 2.7371 2.7193 2.7094 2.7035 2.6992 2.6983 2.6934 2.6896 2.6843 2.6804 2.6796 2.6766 2.6603 2.6367 2.6024

2.5647

2.5400

2.4780

2.4048

2.3190

2.2239

2.1688

1.8118

1.5292 1.4224 1.3442 1.2727 1.2026 1.1382 1.0670 1.0000 0.9326

3.0206 3.0321 3.0442 3.0611 3.0832 3.1107 3.1432 3.1764 3.2063 3.2253 3.2414 3.2652 3.2914 3.2882 3.2459 3.1885 3.1288 3.0756 3.0267 2.9774 2.9289 2.8862 2.8536 2.8266 2.8030 2.7875 2.7763 2.7667 2.7606 2.7506 2.7419 2.7317 2.7230 2.7176 2.7098 2.6889 2.6610 2.6228

2.5815

2.5535

2.4885

2.4129

2.3250

2.2281

2.1715

1.8134

1.5304 1.4234 1.3449 1.2732 1.2029 1.1384 1.0671 1.0000 0.9325

3.3822 3.3842 3.3865 3.3934 3.4049 3.4213 3.4419 3.4622 3.4783 3.4827 3.4835 3.4913 3.5007 3.4801 3.4214 3.3492 3.2766 3.2122 3.1532 3.0949 3.0385 2.9885 2.9493 2.9162 2.8867 2.8657 2.8490 2.8342 2.8229 2.8079 2.7941 2.7791 2.7657 2.7556 2.7431 2.7175 2.6853 2.6431

2.5983

2.5670

2.4991

2.4209

2.3310

2.2323

2.1742

1.8151

1.5316 1.4243 1.3456 1.2738 1.2033 1.1387 1.0672 1.0000 0.9324

3.7439 3.7364 3.7290 3.7258 3.7268 3.7320 3.7406 3.7481 3.7504 3.7401 3.7257 3.7176 3.7100 3.6721 3.5969 3.5100 3.4245 3.3487 3.2798 3.2125 3.1480 3.0908 3.0450 3.0057 2.9704 2.9438 2.9218 2.9017 2.8853 2.8651 2.8464 2.8266 2.8083 2.7935 2.7764 2.7462 2.7096 2.6635

2.6150

2.5805

2.5096

2.4289

2.3369

2.2364

2.1768

4.1057 4.0887 4.0715 4.0582 4.0487 4.0427 4.0395 4.0340 4.0225 3.9976 3.9679 3.9438 3.9194 3.8641 3.7724 3.6708 3.5724 3.4853 3.4063 3.3301 3.2576 3.1932 3.1407 3.0952 3.0541 3.0220 2.9945 2.9692 2.9476 2.9224 2.8987 2.8740 2.8510 2.8315 2.8097 2.7748 2.7339 2.6839

2.6318

2.5940

2.5202

2.4370

2.3429

2.2406

2.1795

1.8168 1.8185

1.5328 1.4252 1.3463 1.2743 1.2037 1.1389 1.0673 1.0000 0.9323

1.5341 1.4262 1.3470 1.2748 1.2040 1.1391 1.0674 1.0000 0.9323

207

x= 2.0

4.4677 4.4410 4.4141 4.3907 4.3707 4.3536 4.3383 4.3201 4.2947 4.2552 4.2103 4.1702 4.1289 4.0562 3.9480 3.8317 3.7203 3.6220 3.5329 3.4477 3.3671 3.2955 3.2365 3.1848 3.1379 3.1002 3.0673 3.0367 3.0099 2.9796 2.9510 2.9214 2.8937 2.8695 2.8430 2.8035 2.7583 2.7042

2.6486

2.6075

2.5307

2.4450

2.3488

2.2448

2.1822

1.8202

1.5353 1.4271 1.3477 1.2753 1.2044 1.1393 1.0676 1.0000 0.9322



oo My B-V Mass Mboi logTe/y log# x = -0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.800 -1.971 -2.043

13.000 12.800 12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800 8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.200 5.101 5.000 4.901 4.800

0.774 0.790 0.808 0.828 0.850 0.873 0.900 0.928 0.960 0.994 1.032 1.074 1.122 1.177 1.239 1.310 1.396 1.498 1.616 1.691

1.729 1.705 1.681 1.656 1.631 1.605 1.580 1.555 1.530 1.507 1.485 1.464 1.443 1.425 1.408 1.391 1.372 1.353 1.333 1.311 1.286 1.256 1.223 1.186 1.147 1.104 1.058 1.013 0.968 0.923 0.877 0.831 0.787 0.745 0.703 0.663 0.627 0.598 0.573 0.552 0.542 0.534 0.526 0.519

0.8246 0.8249 0.8251 0.8253 0.8254 0.8256 0.8258 0.8259 0.8260 0.8260 0.8261 0.8262 0.8262 0.8262 0.8263 0.8263 0.8263 0.8264 0.8264 0.8264

0.1539 0.1602 0.1672 0.1746 0.1825 0.1912 0.2010 0.2122 0.2250 0.2394 0.2559 0.2741 0.2946 0.3180 0.3439 0.3700 0.3951 0.4189 0.4411 0.4618 0.4812 0.4994 0.5167 0.5330 0.5486 0.5636 0.5782 0.5925 0.6067 0.6210 0.6353 0.6498 0.6644 0.6791 0.6939 0.7087 0.7236 0.7384 0.7531 0.7674 0.7741 0.7806 0.7868 0.7930

1.319 1.108 0.896 0.682 0.466 0.248 0.028

■ 0.194 ■ 0.419 ■0.648 0.884 1.125 1.375 1.639 1.917 2.214 2.547 2.919 3.348 3.635

3.6945 3.6909 3.6871 3.6831 3.6789 3.6746 3.6699 3.6649 3.6597 3.6541 3.6481 3.6417 3.6349 3.6273 3.6191 3.6098 3.5991 3.5864 3.5711 3.5605

2.718 2.620 2.519 2.418 2.315 2.211 2.104 1.995 1.884 1.770 1.652 1.530 1.403 1.267 1.123 0.967 0.791 0.591 0.359 0.202

0.8663 0.8008 0.7371 0.6857 0.7036 0.7472 0.5398 0.4026 0.3237 0.2618 0.1983 0.1364 0.0798 0.0253

-0.0324 -0.0788 -0.1189 -0.1467 -0.0239

0.8662 0.8006 0.7368 0.6854 0.7032 0.7468 0.5393 0.4022 0.3232 0.2613 0.1977 0.1359 0.0792 0.0247

-0.0330 -0.0794 -0.1195 -0.1473 -0.0245

0.8660 0.8004 0.7365 0.6851 0.7028 0.7463 0.5389 0.4017 0.3227 0.2608 0.1972 0.1353 0.0786 0.0241

-0.0336 -0.0800 -0.1201 -0.1479 -0.0252

10.959 10.842 10.724 10.603 10.479 10.351 10.218 10.080 9.937 9.789 9.639 9.487 9.333 9.178 9.021 8.866 8.713 8.559 8.405 8.252 8.101 7.952 7.803 7.656 7.512 7.367 7.222 7.077 6.929 6.778 6.625 6.468 6.309 6.146 5.981 5.810 5.635 5.454 5.269 5.080 4.985 4.888 4.792 4.695

3.5243 3.5286 3.5329 3.5371 3.5414 3.5456 3.5498 3.5539 3.5579 3.5617 3.5653 3.5690 3.5726 3.5760 3.5796 3.5834 3.5875 3.5918 3.5961 3.6008 3.6057 3.6111 3.6170 3.6234 3.6304 3.6380 3.6463 3.6551 3.6644 3.6742 3.6842 3.6946 3.7050 3.7155 3.7257 3.7355 3.7448 3.7531 3.7605 3.7669 3.7697 3.7722 3.7744 3.7764

5.164 5.152 5.140 5.128 5.114 5.101 5.086 5.071 5.054 5.038 5.021 5.005 4.989 4.974 4.959 4.945 4.928 4.909 4.887 4.865 4.842 4.820 4.799 4.779 4.762 4.746 4.733 4.720 4.708 4.697 4.686 4.674 4.662 4.649 4.633 4.613 4.589 4.559 4.523 4.481 4.458 4.433 4.407 4.379

2.2814 2.3051 2.3316 2.3666 2.4049 2.4489 2.5004 2.5569 2.6159 2.6717 2.7194 2.7674 2.8226 2.8776 2.9012 2.8907 2.8700 2.8437 2.8136 2.7825 2.7550 2.7306 2.7074 2.6849 2.6642 2.6507 2.6412 2.6353 2.6363 2.6361 2.6402 2.6446 2.6470 2.6511 2.6517 2.6538 2.6535 2.6512 2.6411 2.6131

2.5860

2.5601

2.6506 2.6654 2.6827 2.7084 2.7369 2.7706 2.8112 2.8561 2.9024 2.9447 2.9781 3.0110 3.0505 3.0890 3.0959 3.0696 3.0346 2.9956 2.9542 2.9131 2.8767 2.8443 2.8137 2.7844 2.7574 2.7380 2.7230 2.7118 2.7076 2.7024 2.7015 2.7010 2.6985 2.6979 2.6938 2.6914 2.6866 2.6799 2.6655 2.6334

2.6026

2.5733

3.0198 3.0257 3.0339 3.0502 3.0689 3.0925 3.1222 3.1553 3.1890 3.2177 3.2367 3.2548 3.2785, 3.3004" 3.2906 3.2485 3.1993 3.1476 3.0949 3.0439 2.9985 2.9580 2.9200 2.8839 2.8506 2.8254 2.8048 2.7883 2.7789 2.7686 2.7628 2.7574 2.7501 2.7448 2.7360 2.7290 2.7196 2.7086 2.6899 2.6537

2.6192

2.5865

0.8659 0.8001 0.7363 0.6847 0.7024 0.7459 0.5384 0.4012 0.3222 0.2602 0.1966 0.1347 0.0780 0.0235

-0.0342 -0.0806 -0.1207 -0.1486 -0.0258

0.8657 0.7999 0.7360 0.6844 0.7021 0.7455 0.5379 0.4007 0.3216 0.2597 0.1961 0.1342 0.0775 0.0229

-0.0348 -0.0812 -0.1213 -0.1492 -0.0264

[Fe/H] = -0.78 [O/Fe] = +0.39 Y = 0.2391

x = —1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0

3.3892 3.3861 3.3852 3.3921 3.4011 3.4144 3.4332 3.4546 3.4757 3.4908 3.4955 3.4985 3.5066 3.5120 3.4853 3.4274 3.3640 3.2996 3.2357 3.1746 3.1203 3.0717 3.0263 2.9834 2.9439 2.9128 2.8867 2.8648 2.8502 2.8349 2.8242 2.8138 2.8017 2.7916 2.7782 2.7665 2.7527 2.7372 2.7143 2.6741

2.6358

2.5997

3.7587 3.7466 3.7366 3.7341 3.7333 3.7363 3.7442 3.7540 3.7624 3.7639 3.7543 3.7424 3.7347 3.7236 3.6802 3.6064 3.5287 3.4516 3.3764 3.3054 3.2421 3.1854 3.1326 3.0829 3.0371 3.0001 2.9685 2.9413 2.9216 2.9012 2.8855 2.8703 2.8534 2.8385 2.8203 2.8041 2.7858 2.7659 2.7387 2.6944

2.6525

2.6129

208

x = 2.0

0.8655 0.7997 0.7357 0.6841 0.7017 0.7451 0.5375 0.4002 0.3211 0.2592 0.1955 0.1336 0.0769 0.0223

-0.0354 -0.0818 -0.1219 -0.1498 -0.0270

x = 1.5

4.1283 4.1072 4.0881 4.0762 4.0656 4.0584 4.0554 4.0534 4.0492 4.0372 4.0132 3.9863 3.9630 3.9353 3.8751 3.7855 3.6935 3.6037 3.5172 3.4361 3.3640 3.2991 3.2389 3.1824 3.1304 3.0875 3.0503 3.0178 2.9929 2.9675 2.9468 2.9267 2.9050 2.8853 2.8625 2.8417 2.8189 2.7946 2.7631 2.7147

2.6691

2.6261



My B-V Mass Mboi logTe// logp x = -1.0 x = -0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

4.701 4.600 4.500 4.400 4.299 4.200 4.088 4.000 3.914 3.870 3.838 3.800 3.726 3.600 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.600 -1.721 -1.743

13.200 13.000 12.800 12.600 12.400 12.200 12.000 11.800 11.600 11.400 11.200 11.000 10.800 10.600 10.400 10.200 10.000 9.800 9.600 9.400 9.200 9.000 8.800

0.513 0.509 0.506 0.505 0.506 0.510 0.519 0.535 0.566 0.601 0.636 0.671 0.704 0.729 0.750 0.760 0.769 0.776 0.784 0.793 0.804 0.816 0.831 0.848 0.866 0.888 0.912 0.936 0.963 0.993 1.025 1.061 1.101 1.146 1.196 1.253 1.317 1.393 1.479 1.591 1.690 1.744

1.744 1.721 1.699 1.676 1.652 1.629 1.605 1.582 1.559 1.537 1.515 1.493 1.473 1.453 1.434 1.417 1.400 1.382 1.364 1.345 1.324 1.301 1.273

0.7989 0.8043 0.8094 0.8142 0.8185 0.8223 0.8261 0.8289 0.8317 0.8333 0.8344 0.8354 0.8364 0.8374 0.8385 0.8394 0.8401 0.8408 0.8413 0.8418 0.8422 0.8425 0.8428 0.8430 0.8433 0.8434 0.8436 0.8439 0.8440 0.8441 0.8442 0.8443 0.8443 0.8444 0.8444 0.8445 0.8445 0.8446 0.8446 0.8446 0.8446 0.8446

0.1537 0.1599 0.1666 0.1737 0.1813 0.1896 0.1988 0.2093 0.2213 0.2350 0.2505 0.2678 0.2869 0.3084 0.3324 0.3583 0.3846 0.4094 0.4319 0.4531 0.4732 0.4921 0.5101

4.598 4.499 4.401 4.301 4.201 4.102 3.988 3.893 3.792 3.728 3.671 3.607 3.508 3.361 3.145 2.937 2.731 2.525 2.320 2.113 1.905 1.695 1.484 1.272 1.058 0.840 0.620 0.399 0.175

- 0.054 -0.286 - 0.523 - 0.767 -1.020 -1.285 - 1.561 -1.857 - 2.183 - 2.543 -2.999 - 3.417 - 3.662

3.7781 3.7793 3.7798 3.7796 3.7790 3.7774 3.7740 3.7683 3.7581 3.7474 3.7373 3.7278 3.7192 3.7124 3.7068 3.7039 3.7015 3.6994 3.6974 3.6950 3.6923 3.6893 3.6859 3.6823 3.6785 3.6741 3.6694 3.6647 3.6596 3.6543 3.6487 3.6427 3.6364 3.6296 3.6222 3.6143 3.6054 3.5953 3.5837 3.5682 3.5534 3.5444

4.350 4.318 4.284 4.246 4.206 4.161 4.104 4.046 3.966 3.898 3.835 3.772 3.699 3.613 3.505 3.411 3.319 3.229 3.138 3.047 2.953 2.857 2.759 2.660 2.559 2.455 2.348 2.241 2.131 2.018 1.903 1.784 1.662 1.533 1.398 1.255 1.102 0.931 0.740 0.496 0.270 0.136

2.4935

2.4210

2.3419

2.2891

2.5037

2.4285

2.3472

2.2926

2.5138

2.4360

2.3525

2.2961

2.5239

2.4435

2.3579

2.2997

2.5340

2.4510

2.3632

2.3032

2.5442

2.4585

2.3685

2.3067

2.1425 2.1446 2.1468 2.1489 2.1510 2.1531

1.6370 1.4928 1.4086 1.3378 1.2663 1.2028 1.1339 1.0676 1.0000 0.9333 0.8644 0.8051 0.7646 0.8310 0.8178 0.5786 0.4650 0.3907 0.3259 0.2639 0.2042 0.1408 0.0814 0.0326

-0.0205 -0.0561 -0.0197

0.3546

1.6384 1.4939 1.4094 1.3384 1.2667 1.2032 1.1341 1.0677 1.0000 0.9332 0.8642 0.8049 0.7643 0.8307 0.8175 0.5782 0.4646 0.3903 0.3254 0.2634 0.2037 0.1403 0.0809 0.0321

-0.0210 -0.0567 -0.0203

0.3541

1.6397 1.4949 1.4102 1.3390 1.2672 1.2035 1.1342 1.0678 1.0000 0.9332 0.8641 0.8047 0.7641 0.8304 0.8171 0.5778 0.4642 0.3898 0.3250 0.2629 0.2032 0.1398 0.0804 0.0315

-0.0215 -0.0572 -0.0208

0.3535

[Fe/H] = -0.65 [O/Fe] = +0.30 Y = 0.2413

11.002 10.889 10.775 10.659 10.540 10.418 10.291 10.159 10.021 9.878 9.732 9.583 9.433 9.280 9.124 8.969 8.818 8.667 8.516 8.364 8.213 8.064 7.917

3.5186 3.5228 3.5270 3.5311 3.5352 3.5393 3.5433 3.5473 3.5512 3.5549 3.5586 3.5623 3.5659 3.5694 3.5728 3.5764 3.5804 3.5846 3.5889 3.5935 3.5982 3.6032 3.6087

5.158 5.147 5.136 5.124 5.111 5.098 5.085 5.070 5.054 5.038 5.022 5.006 4.991 4.975 4.959 4.944 4.930 4.914 4.894 4.872 4.849 4.827 4.805

2.2789 2.2993 2.3218 2.3548 2.3889 2.4302 2.4802 2.5369 2.5952 2.6526 2.7021 2.7470 2.7947 2.8446 2.8864 2.9092 2.8983 2.8602 2.8263 2.8019 2.7782 2.7528 2.7296

2.6512 2.6629 2.6766 2.7005 2.7252 2.7567 2.7963 2.8419 2.8881 2.9325 2.9682 2.9986 3.0313 3.0655 3.0911 3.0978 3.0717 3.0201 2.9745 2.9396 2.9064 2.8726 2.8415

3.0237 3.0266 3.0314 3.0463 3.0616 3.0833 3.1125 3.1469 3.1811 3.2125 3.2343 3.2503 3.2680 3.2865 3.2959 3.2865 3.2451 3.1800 3.1226 3.0773 3.0347 2.9923 2.9535

1.6410 1.4959 1.4110 1.3396 1.2676 1.2038 1.1344 1.0679 1.0000 0.9331 0.8639 0.8045 0.7638 0.8301 0.8168 0.5774 0.4638 0.3894 0.3245 0.2625 0.2027 0.1393 0.0799 0.0310

-0.0220 -0.0577 -0.0214

0.3530

3.3962 3.3903 3.3863 3.3921 3.3981 3.4100 3.4288 3.4520 3.4741 3.4926 3.5005 3.5021 3.5047 3.5076 3.5008 3.4752 3.4186 3.3399 3.2708 3.2151 3.1630 3.1121 3.0655

1.6424 1.4970 1.4118 1.3402 1.2681 1.2041 1.1346 1.0679 1.0000 0.9330 0.8638 0.8043 0.7636 0.8298 0.8164 0.5770 0.4633 0.3890 0.3241 0.2620 0.2023 0.1388 0.0794 0.0305

-0.0226 -0.0583 -0.0219

0.3524

3.7689 3.7541 3.7413 3.7380 3.7346 3.7367 3.7452 3.7572 3.7672 3.7727 3.7668 3.7539 3.7415 3.7287 3.7058 3.6640 3.5922 3.4999 3.4190 3.3529 3.2914 3.2319 3.1775

1.6437 1.4980 1.4126 1.3409 1.2685 1.2044 1.1348 1.0680 1.0000 0.9329 0.8637 0.8041 0.7634 0.8295 0.8161 0.5766 0.4629 0.3885 0.3236 0.2615 0.2018 0.1383 0.0789 0.0300

-0.0231 -0.0588 -0.0225

0.3519

4.1416 4.1180 4.0963 4.0840 4.0712 4.0635 4.0616 4.0625 4.0604 4.0529 4.0332 4.0058 3.9784 3.9499 3.9108 3.8528 3.7658 3.6599 3.5673 3.4907 3.4197 3.3517 3.2895

209


19 9

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.81U

.163

B

TABLE 4—Continued

Mv B-V Mass Mfjol logTeff logg x =—1.0 X = -0.5 or = 0.0 x = 0.5 x = 1.0 x = 1.5

8.600 8.400 8.200 8.000 7.800 7.600 7.400 7.200 7.000 6.800 6.600 6.400 6.200 6.000 5.800 5.600 5.400 5.301 5.200 5.101 5.000 4.901 4.800 4.701 4.600 4.500 4.400 4.298 4.200 4.085 4.000 3.940 3.910 3.880 3.800 3.711 3.600 3.400 3.200 3.000 2.800 2.600 2.400 2.200 2.000 1.800 1.600 1.400 1.200 1.000 0.800 0.600 0.400 0.200 0.000

-0.200 -0.400 -0.600 -0.800 -1.000 -1.200 -1.400 -1.543 -1.587

1.241 1.205 1.165 1.122 1.076 1.030 0.986 0.942 0.897 0.851 0.807 0.765 0.725 0.685 0.649 0.618 0.592 0.580 0.570 0.560 0.551 0.544 0.537 0.531 0.527 0.524 0.524 0.526 0.531 0.548 0.571 0.612 0.654 0.696 0.736 0.756 0.771 0.787 0.795 0.804 0.812 0.821 0.831 0.844 0.858 0.874 0.893 0.914 0.936 0.961 0.986 1.014 1.045 1.080 1.118 1.162 1.210 1.264 1.326 1.396 1.477 1.578 1.677 1.764

0.5271 0.5432 0.5586 0.5733 0.5879 0.6022 0.6164 0.6308 0.6452 0.6598 0.6745 0.6893 0.7041 0.7190 0.7340 0.7488 0.7639 0.7711 0.7782 0.7849 0.7915 0.7979 0.8042 0.8101 0.8155 0.8207 0.8254 0.8298 0.8336 0.8378 0.8407 0.8431 0.8446 0.8458 0.8469 0.8477 0.8484 0.8495 0.8504 0.8512 0.8519 0.8525 0.8530 0.8534 0.8538 0.8541 0.8544 0.8546 0.8548 0.8551 0.8553 0.8555 0.8556 0.8557 0.8557 0.8558 0.8559 0.8559 0.8560 0.8560 0.8560 0.8561 0.8561 0.8561

7.771 7.626 7.483 7.342 7.199 7.054 6.908 6.759 6.607 6.452 6.294 6.132 5.967 5.798 5.624 5.446 5.262 5.170 5.075 4.981 4.885 4.789 4.692 4.596 4.497 4.399 4.300 4.198 4.099 3.977 3.882 3.798 3.738 3.675 3.563 3.458 3.335 3.122 2.915 2.709 2.502 2.295 2.088 1.878 1.668 1.455 1.239 1.021 0.801 0.578 0.353 0.123

-0.110 -0.348 -0.593 -0.848 -1.113 -1.389 -1.685 -2.009 -2.366 -2.804 -3.247 -3.658

3.6146 3.6211 3.6282 3.6359 3.6442 3.6529 3.6620 3.6715 3.6814 3.6916 3.7018 3.7121 3.7221 3.7319 3.7411 3.7497 3.7572 3.7606 3.7637 3.7665 3.7691 3.7713 3.7731 3.7746 3.7757 3.7762 3.7759 3.7751 3.7731 3.7672 3.7597 3.7473 3.7353 3.7240 3.7137 3.7085 3.7045 3.7002 3.6978 3.6955 3.6933 3.6910 3.6885 3.6856 3.6824 3.6789 3.6750 3.6706 3.6660 3.6612 3.6562 3.6510 3.6454 3,6396 3.6333 3.6266 3.6193 3.6115 3.6028 3.5929 3.5815 3.5670 3.5516 3.5367

4.785 4.766 4.750 4.735 4.722 4.709 4.697 4.686 4.674 4.662 4.650 4.636 4.619 4.600 4.576 4.548 4.513 4.494 4.472 4.450 4.425 4.399 4.371 4.342 4.309 4.275 4.237 4.195 4.149 4.079 4.012 3.931 3.859 3.789 3.704 3.642 3.577 3.475 3.383 3.292 3.201 3.109 3.016 2.921 2.825 2.725 2.624 2.519 2.412 2.304 2.194 2.082 1.966 1.848 1.725 1.596 1.461 1.319 1.166 0.997 0.808 0.575 0.337 0.112

2.7066 2.6847 2.6645 2.6531 2.6464 2.6415 2.6433 2.6446 2.6489 2.6538 2.6558 2.6594 2.6599 2.6618 2.6606 2.6593 2.6444

2.6189

2.5960

2.5666

2.5000

2.4359

2.3684

2.3970

1.5951 1.4801 1.4058 1.3367 1.2678 1.1986 1.1337 1.0672 1.0000 0.9342 0.8707 0.8101 0.7931 0.9230 0.7241 0.5442 0.4564 0.3898 0.3284 0.2662 0.1992 0.1399 0.0888 0.0323

-0.0050 -0.0049 0.3036

2.8115 2.7829 2.7567 2.7396 2.7275 2.7173 2.7140 2.7104 2.7097 2.7098 2.7070 2.7059 2.7017 2.6992 2.6935 2.6878 2.6685

2.6391

2.6125

2.5797

2.5101

2.4433

2.3736

2.4002

2.9163 2.8812 2.8489 2.8261 2.8086 2.7931 2.7848 2.7761 2.7705 2.7658 2.7582 2.7524 2.7436 2.7365 2.7264 2.7163 2.6927

2.6592

2.6290

2.5927

2.5201

2.4507

2.3788

2.4034

3.0211 2.9795 2.9411 2.9126 2.8897 2.8690 2.8556 2.8419 2.8314 2.8218 2.8095 2.7989 2.7855 2.7738 2.7592 2.7448 2.7169

2.6794

2.6454

2.6058

2.5301

2.4581

2.3841

2.4067

3.1260 3.0778 3.0334 2.9991 2.9708 2.9448 2.9263 2.9077 2.8922 2.8779 2.8607 2.8454 2.8274 2.8111 2.7921 2.7733 2.7411

2.6619

2.6188

2.5401

2.4655

2.3893

2.4099

1.5964 1.4812 1.4067 1.3374 1.2682 1.1989 1.1339 1.0673 1.0000 0.9341 0.8706 0.8099 0.7929 0.9226 0.7237 0.5437 0.4559 0.3893 0.3279 0.2657 0.1987 0.1393 0.0882 0.0318

-0.0056 -0.0054 0.3030

1.5978 1.4823 1.4076 1.3380 1.2687 1.1993 1.1341 1.0674 1.0000 0.9340 0.8704 0.8097 0.7926 0.9223 0.7233 0.5433 0.4554 0.3888 0.3274 0.2652 0.1981 0.1388 0.0877 0.0312

-0.0062 -0.0060 0.3024

1.5992 1.4834 1.4085 1.3387 1.2692 1.1996 1.1343 1.0675 1.0000 0.9339 0.8703 0.8095 0.7923 0.9220 0.7229 0.5429 0.4550 0.3884 0.3269 0.2646 0.1976 0.1382 0.0871 0.0306

-0.0068 -0.0066 0.3018

1.6005 1.4845 1.4093 1.3393 1.2697 1.1999 1.1346 1.0676 1.0000 0.9338 0.8701 0.8093 0.7921 0.9216 0.7225 0.5424 0.4545 0.3879 0.3264 0.2641 0.1971 0.1377 0.0866 0.0301

-0.0073 -0.0072 0.3012

3.2309 3.1761 3.1256 3.0857 3.0519 3.0207 2.9971 2.9735 2.9531 2.9339 2.9119 2.8920 2.8693 2.8485 2.8250 2.8018 2.7653

2.6996 2.7197

2.6784

2.6319

2.5501

2.4729

2.3945

2.4131

1.9318 1.9337 1.9355 1.9374 1.9393 1.9411

1.6019 1.4856 1.4102 1.3400 1.2702 1.2003 1.1348 1.0677 1.0000 0.9337 0.8700 0.8091 0.7918 0.9213 0.7222 0.5420 0.4541 0.3874 0.3259 0.2636 0.1965 0.1371 0.0860 0.0295

-0.0079 -0.0078 0.3006

210


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63B

TABLE 4—Continued

My B — V Mass A^boi log log51 x = —1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

[Fe/H] = -0.47 [O/Fe] = +0.23 Y =

13.400 1.752 13.200 1.731 13.000 1.710 12.800 1.689 12.600 1.668 12.400 1.647 12.200 1.626 12.000 1.606 11.800 1.586 11.600 1.566 11.400 1.546 11.200 1.526 11.000 1.507 10.800 1.488 10.600 1.469 10.400 1.450 10.200 1.431 10.000 1.413 9.800 1.396 9.600 1.379 9.400 1.362 9.200 1.343 9.000 1.322 8.800 1.297 8.600 1.267 8.400 1.232 8.200 1.193 8.000 1.151 7.800 1.106 7.600 1.059 7.400 1.015 7.200 0.972 7.000 0.929 6.800 0.884 6.600 0.839 6.400 0.797 6.200 0.757 6.000 0.718 5.800 0.681 5.600 0.651 5.400 0.624 5.301 0.612 5.200 0.601 5.101 0.590 5.000 0.581 4.901 0.573 4.800 0.566 4.701 0.561 4.600 0.558 4.500 0.556 4.400 0.557 4.295 0.562 4.200 0.572 4.073 0.607 4.030 0.651 4.022 0.695 4.000 0.740 3.941 0.780 3.800 0.810 3.600 0.829 3.400 0.840 3.200 0.849 3.000 0.857 2.800 0.866 2.600 0.876

0.1559 11.017 0.1622 10.905 0.1688 10.794 0.1759 10.681 0.1834 10.567 0.1914 10.451 0.2004 10.330 0.2106 10.204 0.2224 10.072 0.2359 9.934 0.2510 9.792 0.2678 9.648 0.2865 9.502 0.3075 9.352 0.3313 9.201 0.3567 9.050 0.3819 8.901 0.4061 8.753 0.4292 8.604 0.4510 8.454 0.4716 8.305 0.4910 8.157 0.5095 8.010 0.5270 7.866 0.5436 7.724 0.5595 7.583 0.5747 7.443 0.5895 7.303 0.6040 7.162 0.6185 7.019 0.6329 6.875 0.6474 6.728 0.6620 6.578 0.6768 6.426 0.6916 6.270 0.7065 6.111 0.7215 5.948 0.7365 5.781 0.7514 5.609 0.7671 5.432 0.7822 5.250 0.7894 5.159 0.7964 5.066 0.8031 4.973 0.8098 4.878 0.8164 4.784 0.8228 4.686 0.8287 4.590 0.8343 4.492 0.8395 4.393 0.8443 4.294 0.8489 4.187 0.8530 4.088 0.8586 3.943 0.8614 3.872 0.8630 3.830 0.8643 3.771 0.8656 3.679 0.8670 3.512 0.8684 3.296 0.8695 3.087 0.8704 2.879 0.8712 2.674 0.8719 2.466 0.8724 2.258

3.5125 5.146 3.5167 5.135 3.5208 5.124 3.5248 5.113 3.5287 5.101 3.5326 5.089 3.5364 5.076 3.5401 5.062 3.5438 5.047 3.5473 5.032 3.5508 5.016 3.5543 5.000 3.5578 4.985 3.5614 4.971 3.5648 4.956 3.5684 4.942 3.5723 4.928 3.5763 4.911 3.5805 4.892 3.5848 4.871 3.5895 4.850 3.5944 4.828 3.5996 4.806 3.6052 4.785 3.6113 4.766 3.6179 4.749 3.6251 4.733 3.6327 4.718 3.6407 4.705 3.6492 4.692 3.6581 4.680 3.6674 4.668 3.6770 4.656 3.6869 4.645 3.6970 4.632 3.7070 4.618 3.7170 4.602 3.7267 4.582 3.7360 4.560 3.7441 4.530 3.7515 4.496 3.7549 4.477 3.7581 4.456 3.7610 4.434 3.7637 4.411 3.7659 4.385 3.7677 4.357 3.7690 4.327 3.7697 4.293 3.7698 4.257 3.7693 4.218 3.7676 4.170 3.7641 4.119 3.7531 4.020 3.7405 3.942 3.7285 3.878 3.7170 3.809 3.7069 3.733 3.6992 3.636 3.6941 3.530 3.6911 3.435 3.6887 3.343 3.6867 3.253 3.6844 3.161 3.6821 3.069

2.2945 2.6687 2.3109 2.6764 2.3318 2.6887 2.3572 2.7052 2.3923 2.7312 2.4320 2.7615 2.4810 2.8004 2.5380 2.8466 2.5982 2.8951 2.6570 2.9412 2.7037 2.9744 2.7463 3.0029 2.7953 3.0372 2.8518 3.0783 2.8950 3.1054 2.9048 3.0994 2.8929 3.0727 2.8735 3.0400 2.8509 3.0054 2.8255 2.9692 2.8005 2.9345 2.7773 2.9026 2.7540 2.8712 2.7314 2.8413 2.7105 2.8136 2.6905 2.7874 2.6747 2.7657 2.6651 2.7505 2.6607 2.7408 2.6581 2.7331 2.6586 2.7286 2.6634 2.7285 2.6658 2.7260 2.6707 2.7262 2.6724 2.7231 2.6736 2.7198 2.6745 2.7161 2.6747 2.7118 2.6751 2.7078 2.6719 2.7002 2.6561 2.6801

2.6349 2.6550

2.6228 2.6393

2.5882 2.6012

2.5266 2.5367

2.4694 2.4769

2.4238 2.4290

2.4209 2.4239

1.7063 1.7080 1.5644 1.5657 1.4779 1.4789 1.4036 1.4044 1.3378 1.3384 1.2652 1.2657 1.1998 1.2001

0.2454

3.0430 3.4174 3.0420 3.4077 3.0456 3.4026 3.0533 3.4014 3.0702 3.4092 3.0910 3.4206 3.1199 3.4394 3.1552 3.4640 3.1920 3.4891 3.2255 3.5098 3.2451 3.5159 3.2596 3.5163 3.2792 3.5213 3.3049 3.5316 3.3160 3.5266 3.2941 3.4888 3.2526 3.4326 3.2066 3.3732 3.1599 3.3145 3.1130 3.2568 3.0686 3.2026 3.0278 3.1531 2.9884 3.1057 2.9512 3.0610 2.9167 3.0199 2.8842 2.9811 2.8567 2.9477 2.8360 2.9215 2.8210 2.9012 2.8082 2.8832 2.7986 2.8687 2.7936 2.8587 2.7863 2.8466 2.7817 2.8371 2.7739 2.8247 2.7659 2.8120 2.7577 2.7993 2.7489 2.7861 2.7405 2.7732 2.7285 2.7567 2.7042 2.7282

2.6752 2.6953

2.6558 2.6723

2.6143 2.6274

2.5467 2.5568

2.4844 2.4918

2.4342 2.4395

2.4269 2.4299

1.7097 1.7114 1.5670 1.5683 1.4800 1.4810 1.4052 1.4061 1.3390 1.3396 1.2661 1.2666 1.2004 1.2007

3.7919 4.1665 3.7735 4.1393 3.7596 4.1167 3.7497 4.0980 3.7484 4.0876 3.7503 4.0800 3.7590 4.0787 3.7728 4.0817 3.7861 4.0833 3.7941 4.0786 3.7868 4.0577 3.7731 4.0299 3.7635 4.0057 3.7583 3.9851 3.7373 3.9480 3.6836 3.8785 3.6126 3.7927 3.5398 3.7065 3.4691 3.6237 3.4006 3.5444 3.3367 3.4708 3.2784 3.4037 3.2229 3.3402 3.1710 3.2809 3.1230 3.2262 3.0780 3.1749 3.0387 3.1298 3.0070 3.0926 2.9814 3.0616 2.9583 3.0334 2.9387 3.0088 2.9239 2.9890 2.9068 2.9671 2.8926 2.9481 2.8755 2.9263 2.8582 2.9043 2.8409 2.8825 2.8232 2.8603 2.8060 2.8387 2.7850 2.8133 2.7523 2.7764

2.7155 2.7356

2.6888 2.7053

2.6405 2.6536

2.5668 2.5769

2.4993 2.5068

2.4447 2.4499

2.4329 2.4359

1.7130 1.7147 1.5697 1.5710 1.4820 1.4831 1.4069 1.4077 1.3402 1.3409 1.2670 1.2675 1.2010 1.2013

211


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TABLE 4—Continued

My B — V Mass Mbol logTe// log^f x = -1.0 x = —0.5 x = 0.0 x = 0.5 x = 1.0 x = 1.5

2.400 0.888 2.200 0.902 2.000 0.919 1.800 0.937 1.600 0.958 1.400 0.981 1.200 1.004 1.000 1.029 0.800 1.056 0.600 1.085 0.400 1.119 0.200 1.158 0.000 1.201

-0.200 1.249 -0.400 1.303 -0.600 1.365 -0.800 1.435 -1.000 1.519 -1.200 1.625 -1.320 1.742 -1.328 1.807

0.8729 2.048 0.8733 1.836 0.8737 1.622 0.8740 1.405 0.8743 1.185 0.8745 0.962 0.8748 0.738 0.8751 0.510 0.8752 0.279 0.8754 0.044 0.8755 -0.198 0.8755 -0.449 0.8756 -0.709 0.8757 -0.979 0.8757 -1.265 0.8758 -1.576 0.8758 -1.914 0.8759 -2.307 0.8759 -2.801 0.8759 -3.372 0.8760 -3.700

3.6793 2.974 3.6762 2.877 3.6726 2.777 3.6687 2.674 3.6643 2.569 3.6596 2.461 3.6549 2.353 3.6500 2.242 3.6448 2.129 3.6393 2.013 3.6333 1.893 3.6269 1.767 3.6201 1.635 3.6126 1.497 3.6044 1.350 3.5951 1.189 3.5846 1.011 3.5717 0.803 3.5547 0.537 3.5338 0.225 3.5212 0.044

1.1324 1.1326 1.0671 1.0672 1.0000 1.0000 0.9328 0.9328 0.8784 0.8782 0.8766 0.8764 1.0159 1.0156 0.7664 0.7660 0.6022 0.6018 0.5196 0.5191 0.4552 0.4548 0.3916 0.3911 0.3239 0.3234 0.2593 0.2588 0.2029 0.2024 0.1447 0.1441 0.0939 0.0934 0.0623 0.0617 0.1440 0.1435 0.4961 0.4955

1.1328 1.1330 1.0673 1.0674 1.0000 1.0000 0.9327 0.9326 0.8781 0.8780 0.8762 0.8760 1.0153 1.0151 0.7657 0.7653 0.6014 0.6010 0.5187 0.5183 0.4543 0.4539 0.3907 0.3902 0.3229 0.3224 0.2583 0.2578 0.2019 0.2014 0.1436 0.1431 0.0929 0.0923 0.0612 0.0606 0.1429 0.1424 0.4950 0.4944

1.1332 1.1334 1.0675 1.0676 1.0000 1.0000 0.9325 0.9325 0.8778 0.8777 0.8758 0.8756 1.0148 1.0145 0.7650 0.7647 0.6006 0.6002 0.5179 0.5175 0.4535 0.4530 0.3897 0.3893 0.3219 0.3214 0.2573 0.2568 0.2009 0.2004 0.1426 0.1420 0.0918 0.0913 0.0601 0.0595 0.1418 0.1412 0.4938 0.4933

point in equally old, but more metal rich systems to be significantly displaced below the maximum luminosity that is reached by giant stars. That is, the upper RGB should look like a downward-facing arc. In fact, such has been observed in NGC 6553 (Ortolani, Barbuy, & Bica 1990), which has an estimated [Fe/H] = -0.29 (see ArmandrofF 1989). Although we have not yet computed the models to allow a detailed fit of these data, we anticipate that reasonably good agreement will be obtained. Certainly such observations will provide a power- ful constaint on stellar temperatures and bolometric corrections.

The second point concerns the prediction that the lower main sequences for different [ Fe/ H ] ’s should come together at Mv ^ 12 ( see Fig. 8 ). Since this is not apparent on the theoretical plane (Fig. 7), this confluence is due solely to the adopted color-temperature relations and BCF scale (see the discussion in Paper I). The only evidence that we can offer in favor of this prediction is the existence of extremely metal deficient subdwarfs like LHS 489, which has MF ^ 11.7 and (B - V) = 1.71 (see Ake & Greenstein 1980; Dawson 1984; Hartwick, Cowley, & Mould 1984). Granted, the distances of such stars are based on uncertain photometric parallaxes, but it is more their very red colors than their Mv's which suggest that, at sufficiently faint luminosities, the main-sequence for very metal poor stars can become redder than that for more metal rich ones. Further work to check this prediction would be extremely interesting and valuable.

3.2. Luminosity Function Considerations

Representative examples of our computed luminosity functions (LFs) are shown in Figures 10-12 to demonstrate their sensitivity to variations in x, age, and [Fe/H]. The first of these plots illustrates the well-known result that the mass function has essentially no effect on an LF above the turnoff {Mv ^ 4.2 in these particular cases) but a profound influence at fainter magnitudes. This is truly quite fortunate since it

means that the brighter part of an LF can be used to say something about the evolutionary properties of cluster stars, independent of any knowledge about their mass spectrum. Specifi- cally, it gives a direct measure of their relative lifetimes as a function of MF, which can be readily tested by comparisons with observations. As Renzini & Fusi Pecci ( 1988) have emphasized, such comparisons provide a much more fundamental check of stellar structure theory than the fitting of CMDs.

At My ^ 7, on the other hand, the LF has essentially no age-dependence since low-mass stars require much more than a Hubble time to evolve appreciably. (What the theory must provide is accurate mass-luminosity relations—see Paper I for some discussion of this aspect of the problem.) Clearly, the fainter the observations, the easier it is to define jc, if indeed a power law is found to be a reasonable description of the stellar distribution, and if dynamical effects are unimportant. In fact, it now seems that the latter assumption is unrealistic. As Richer et al. ( 1991 ) have recently reported, derived mass functions for the GCs seem to display a wide range of slopes without a clear correlation with either metal abundance or concen- tration class. They find that the strongest correlation is between x and the estimated time for the cluster to disrupt and suggest that dynamical evolution may have been responsible for producing very different present-day mass functions from what were originally very similar IMFs.

One potentially important prediction from the present calculations is that there should be a distinct change in the slope of an observed LF at faint magnitudes, if not an actual turn- over (see Fig. 10). This is predicted to occur at Mv ^ 9.0,9.8, and 10.5 when [Fe/H] = -2.26, -1.26, and -0.47 respectively, and corresponds to the transition from a relatively flat mass-luminosity relation to one that is becoming more steeply sloped (in the direction of increasing Mv). The models predict that this should occur near a mass of ^0.3^© (see Paper I). As shown in Figure 11, the luminosity at which this morphological change takes place is independent of age—just as one would expect at such faint magnitudes. Consequently, this fea-


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Fig. 7.—Comparison on the theoretical plane of the entire set of 14 Gyr isochrones that have been computed in this investigation (for [Fe/H] values ranging from -0.47 to —2.26, in the direction indicated) with the fiducial sequences derived by Frogel et al. ( 1981 ) for M92, Ml3, and 47 Tue and with the properties of Groombridge 1830.

Fig. 8.—Similar to the previous figure except that the comparison is made on the {Mv, B - F)-plane. Apparent distance moduli equal to 14.7, 14.4, and 13.4 and reddenings of 0.02, 0.02, and 0.04 mag have been assumed for M92, M13, and 47 Tue, respectively. The sources of the cluster fiducial sequences and the subdwarf data are given in the text.

ture could be used (at least in principle) as a “standard candle” to determine cluster distances. But incredibly precise and accurate photometry would be required to detect this changeover, if it manages to survive those dynamical processes that tend to remove low-mass stars ( a major complication! ). Furthermore, a concensus has yet to be reached on the predicted location of zero-age main-sequence stars for a given mass and chemical composition (e.g., see Dorman, Nelson, & Chau 1989; Burrows, Hubbard, & Lunine 1989). Hence, while it is worth keeping in mind, the prediction of structure in the lower main- sequence LF will probably not prove to be of any practical value in constraining the cluster distance scale.

Both Figures 10 and 11 show that the shape of a luminosity function in the tumoff-to-subgiant branch region depends sen- sitively on the metal abundance, as does the location of the “bump” on the RGB. The latter arises during the normal course of events when the hydrogen-burning shell contacts the composition discontinuity left behind by the deepest penetra- tion of the envelope convection zone: until the shell source readjusts to the composition change, the ascent of a star up the giant branch is effectively stalled (see Sweigart & Gross 1978). This “bump” feature could also help to refine cluster distances, except that it depends so critically on our understanding of convection. If any overshooting were to occur, for instance, then the predicted location of the “bump” would be displaced to fainter magnitudes. As a result, this characteristic is argu-

Fig. 9.—Comparison of 14 Gyr isochrones for the indicated [Fe/H] values with a number of the trigonometric-parallax subdwarfs given by Laird et al. ( 1988). Filled circles, squares, and triangles identify, in turn, those stars having [Fe/H] < -1.5, -1.5 ^ [Fe/H] < -1.2 and —0.9 < [Fe/H] < -0.5. The mean metallicities of the 3, 6, and 3 stars in each group are, respectively, -2.1, -1.4, and -0.6. Vertical error bars reflect the current parallax uncertainties.


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Fig. 10.—Plot of the computed luminosity functions for the three indicated [Fe/H] values assuming, in each case, an age of 14 Gyr and three values of x (given to the immediate right of each curve), which character- ize the adopted power-law mass function. The different loci for each metal abundance are normalized to have identical log 0 values at Mv = 2.

ably of greater value in assisting our determination of the depth of convection in giants than in its use as a “standard candle.” (Paper I does, however, quantify the relations between “bump” Mk, [Fe/H], and age for this grid of models.)

At first sight, one might surmise that the region of an LF

Fig. 11.—Similar to Fig. 10; in this case, LFs are plotted for the fixed value of jc = 1.0 and three different ages, as indicated.

Fig. 12.—Similar to the Figs. 10-11 ; in this case, LFs for three different [Fe/H] values but the same jc, age, and normalization at Mv = 2 are intercompared.

marking the transition between the RGB and the main sequence—occurring at 3 ^ Mv ^ 4 in the examples given in Figure 11—could be used to deduce cluster ages. There may be some hope here, though the matching of the location (i.e., Mv) of this transition suffers from the same ambiguities that the turnoff point of an isochrone does in CMD fits. Both require an independent estimate of the distance. Rather, it is the detailed shape of the changeover that may help to constrain absolute ages. There are clearly some morphological differences between the loci corresponding to 10, 14, and 18 Gyr, though they may be too small to be detected with any reliability. (We return to this point below.) Certainly, the most careful photometric study of the largest possible sample of turnoff and subgiant branch stars would be needed to see whether absolute ages can be obtained simply by matching the shapes of predicted and observed LFs in the vicinity of the turnoff. We reiterate that the advantage of this approach is that it is independent of the distance, which could (instead) be inferred once the age has been determined.

The final permutation of the three parameters we have been considering is examined in Figure 12. This shows a superposi- tion of computed luminosity functions for a fixed x and age, but for different [Fe/H]’s. The morphological differences in the turnoff region and the metallicity dependence of the RGB “bump” are especially conspicuous in this figure. However, the main point of this plot is to illustrate two other aspects of LFs. First, the slope of red giant segment is independent of [ Fe/ H ] ( as well as age—see Fig. 11). And second, the numbers of stars fainter than Mv ^ 10.5 is nearly identical for all [Fe/ H] values—when normalized at some point on the giant branch—if the same mass-function exponent is assumed. (Al- though not plotted, our calculations indicate that this result holds true for other choices of x besides the one indicated in Fig. 12.)

But how well do our theoretical LFs match those that have been observed? To respond to this question, we will consider some of the available data for M92 and 47 Tucanae, whose


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metallicities encompass those of the majority of the Galactic GCs. The upper panel of Figure 13 contains a composite LF for M92 based on photographic data by Hartwick ( 1970) and CCD observations by Stetson & Harris ( 1988). The ordinate values reflect the actual numbers of stars in the Hartwick data set, which is by far the largest one yet obtained for M92. (Note that the horizontal branch and asymptotic giant branch contributions are not included in this plot.) An adjustment of ô log </> = 0.76 was added to the Stetson & Harris LF in order have reasonable agreement in the region of overlap. In addition, 1 <7 error bars, specifying where n is the actual number of observed stars in a given bin, have been attached to a few of the points to give one an impression of the associated uncertainty.

We have combined photographic data by Hesser & Hart- wick (1977) and by King, Da Costa, & Demarque (1985) with the CCD observations by Hesser et al. ( 1987) to produce the composite LF for 47 Tue in the lower panel of Figure 13. In this case, the ordinate reflects the actual numbers of stars that were counted by King et al., while <5 log $ = 0.65 and 1.57 were added to the Hesser & Hartwick and the Hesser et al. data, respectively, to obtain continuity between the results of the three studies. Possible contamination from the horizontal branch and asymptotic giant branch has been avoided in part, by excluding the upper RGB where the first and second ascent giant branches are not easily distinguished ( see King et al.). As in the upper panel, uncertainty estimates (±1\fñ) are given for a

Fig. 13.—Composite luminosity functions for M92 ( upper panel) and 47 Tue ( lower panel) based on observations reported in the indicated references (see the text).

Fig. 14.—Comparison of the composite M92 luminosity function given in Fig. 13 with theoretical curves for [Fe/H] = -2.26 and -1.78, assuming, in each case, an age of 14 Gyr and x = 0.0,0.5, and 1.0. Stetson & Harris ( 1988 ) actually give three different estimates of the true M92 LF, depending on the number of detections in each frame and the x statistic (see their Table XIV). Whereas the filled circles reproduce their results for X < 1.5 (here and in previous figure), the open triangles give their results when no restriction is placed on x* ( The third estimate lies between the two that have been plotted.) To achieve the fits shown, distances corresponding to ( w - M)v = 14.78 and 14.66 and normalizations of3096 stars and 28.2 stars at Mv = 2 were assumed for the [Fe/H] = -2.26 and -1.78 cases, respectively. Note the discrepancy between theory and observation at M/s between 4 and 6.

few of the observations. On close inspection, the joining of the Hesser et al. and Hesser & Hartwick data sets may seem to be faulty—the former appears to be slightly too high relative to the latter—but Hesser et al.’s estimate of the LF along the lower giant branch has also been taken into account in the adopted fit. Certainly, there is considerable subjectivity in- volved in these decisions: every effort should be made to obtain observed LFs that span, at the very least, the region from somewhat below the turnoff to significantly above the base of the RGB, since it is so critical for meaningful comparisons with the theory.

Figure 14 shows how well theoretical LFs for 14 Gyr and two [Fe/H] values, on the assumption of x = 0.0, 0.5, and 1.0 in each case, match the M92 observations. Distance moduli have been chosen by requiring the respective isochrones to match the observed CMD as accurately as possible in the vicinity of the turnoff. These fits are illustrated in Figure 15, which reveal that there is some discrepancy in the predicted and observed locations of the giant branch. Indeed, had we chosen to fit the data to the 16 Gyr loci, the agreement would have been exceed-


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Fig. 15.—Demonstration that the turnoff luminosity of the Stetson & Harris (1988) fiducial for M92 (filled circles) is identical to those predicted by 14 Gyr isochrones for [Fe/H] = -2.26 and -1.78, if the indicated distance moduli are assumed. Arbitrary horizontal adjustments were applied to the M92 locus in order to match the main-sequence positions of the two sets of isochrones.

ingly good (in both cases). However, as emphasized by Van- denBerg ( 1991 ) and others, the prediction of the giant branch position relative to the turnoff is subject to great uncertainty. While it may be that the correct conclusion to be drawn from Figure 15 is that M92 is older than 14 Gyr, it is equally proba- ble that 14 Gyr (or less) is the correct age of M92, and that the discrepancy is no more than an indication that our understanding of convection, low-temperature opacities, etc., is lacking in some way.

Interestingly, when the theoretical and observed LFs are normalized so that both contain the same number of stars in a bin centered on Mv = 2 (as in Fig. 14), too many stars are predicted in the magnitude range 4.5 ^ Mv ^ 6.0. On the other hand, if agreement is forced at Mv — 4.5, then the fit along the giant branch becomes especially problematical (see Fig. 16). Bergbusch (1990) has already commented on this difficulty in his discussion of all existing data for M92. This is potentially a very serious problem. Clearly variations in the mass function cannot be the explanation since this has a significant effect only at fainter magnitudes.6 So, if the observations are correct, then they must be saying that something is missing in canonical evolutionary theory. Even more interestingly, preliminary calculations which allow for a small central isothermal core in the centers of evolving stars—such as might be expected if weakly interacting massive particles (WIMPs) exist (see Faulkner & Swenson 1991)—appear to yield a much more satisfactory match of the data (see Stetson 1991 and Vanden- Berg & Stetson 1991). However, it is entirely possible that

6 It is possible that the assumption of a power law ( or any smooth) mass spectrum is not correct for M92. However, a rather large fluctuation in the IMF (over £0.1^o, centered at ^Q.lJtQ) would be required to explain the cluster observations. A further (even more compelling) argument against this hypothesis is Bolte’s ( 1991 ) discovery of exactly the same behavior in the M30 LF. An explanation in terms of binary stars also seems unlikely given that the principal sequences of the two clusters are extremely tight on the CM plane (see Stetson & Harris 1988; Boite 1987).

another explanation can be found for the discrepancy, which certainly seems to be real.

One encouraging aspect of the comparisons shown in Fig- ures 14 and 16 is that the predicted location of the “bump” feature on the RGB LF is within ^0.2 mag of that observed. This seems to have been detected at about the 3 a level in the Hartwick ( 1970) data (see Fig. 13) and clearly provides some support for the adopted distances (and ages) as well as the assumed treatment of convection (see Fusi Pecci et al. 1990). The brightest giant observed by Hartwick appears to be slightly more luminous than the predicted RGB tip luminosity, which may be an indication that this star is actually on the asymptotic giant branch or that the adopted distances are too large or that the present models suffer from somé deficiency. As far as the lower main sequence data are concerned, our comparisons support the conclusion reached by Stetson & Harris (1988) that the LF data cannot be fitted by a single power-law mass function. But one does have the impression (see Fig. 16) that the value of jc decreases with increasing Mv\ i.e., the data seem to be consistent with a relatively high value of x near the turnoff but progressively lower values at fainter magnitudes. This could be an indication that the initial mass function of M92 was steeply sloped but that it has been greatly modified by the evaporation of low-mass stars over the lifetime of the cluster ( see Richer et al. 1991).

The 0.5 < Mv < 6.5 region of the [Fe/H] = -2.26, x= 1.0, 14 Gyr comparison in Figure 14 is magnified in Figure 17. Superposed on this are additional theoretical loci for 12 and 16 Gyr, after suitable horizontal and vertical adjustments were made to compensate for differences in the turnoff magnitudes and to ensure identical normalizations at Mv = 2. The point of this diagram is to demonstrate that the predicted LFs for different ages are morphologically distinct in the region connecting

Fig. 16.—Similar to the [Fe/H] = -2.26 comparison shown in Fig. 14 except that a small vertical shift has been applied to the theoretical curves in order to match the M92 observations at Mv ~ 5, instead of Mv = 2. This causes the predicted and observed giant branch LFs to disagree.


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No. 1. 1992 ISOCHRONES AND LUMINOSITY FUNCTIONS 217

the RGB and lower main sequence segments (see Simoda & Iben 1970). Granted, the differences are quite small—possibly too small to be a good age discriminant—but an exceedingly well-defined LF for M92 should certainly provide some con- straint on the absolute cluster age, even if it does no more than set a firm upper or lower bound. Of greater urgency perhaps is the need to clarify whether or not the apparent discrepancy at Mv > 4 is real. If it is, then there may well be major imphca- tions for our understanding of the evolution of globular cluster stars and the ages of these stellar systems.

Another way of intercomparing theory and observation is through the use of the logarithm of the integrated luminosity function. Rood & Crocker ( 1985) have, for instance, argued that it provides the best means of determining the location of the RGB “bump” in actual cluster data. In addition, the shape of the integrated LF may allow a reasonably precise determination of the helium flash luminosity (and, from it, the cluster distance—e.g., see YandenBerg & Durrell 1990), provided that the asymptotic giant branch and horizontal branch contributions can be separated out. Figure 18 shows that Hartwick’s ( 1970) M92 data can be matched reasonably well by the integrated LF derived from a 14 Gyr, [Fe/H] = -2.26 isochrone. To be sure, the agreement is far from perfect at the bright end, but in view of the small numbers of luminous giants that were observed, the discrepancy is probably not statistically significant. (Although not shown, it was not possible to obtain any better agreement by assuming different distances, ages, or chemical compositions.) As found by Rood & Crocker, the log 2( 0 ) versus Mv relation has a definite change in character at the position of the RGB “bump” (where the dashed straight line deviates from the solid curve at Mv æ -0.25 ). According to the present calculations, the change in slope at this point is predicted to be much smaller than that observed in M92. How- ever, the latter may be a statistical fluctuation: a much more extensive survey of the numbers of bright giants in M92 is clearly needed.

Mv

Fig. 17.—A magnified view of the [Fe/H] = -2.26 comparison shown in Fig. 14 over the region 0.5 < Mv < 6.5. Theoretical loci for ages of 12 and 16 Gyr have been added to the plot to show that there are distinct, albeit subtle, morphological differences near Mv = 3.

Mv

Fig. 18.—Comparison of the logarithm of the integrated luminosity function for the giant branch of M92 (open circles) with that predicted for a 14 Gyr, [Fe/H] = -2.26 isochrone. The dashed curve gives a straight- fine fit to the solid curve between Mv « 0 and Mv » 2.5.

The M92 comparison just described did raise the concern that there might be an unsuspected problem with our calculations. So, to be very sure that the giant-branch LFs produced by our code were not appreciably different from the predictions of other workers, we compared some of them with those given by Green et al. (1987). Figure 19 illustrates one such comparison and, although there are small variations presumably arising from differences in Y, the assumed opacities, etc., the agreement is rather good.7 We believe that the bump at Mv ^ 2.4 in the Yale locus {toppanel) is a numerical artifact produced when Green et al. matched up the main-sequence tracks by Mengel et al. ( 1979) with the RGBs by Sweigart & Gross ( 1978 ) : it is to their credit that this very difficult task was done so successfully. Although subsequent work has demonstrated that the reff scale of the Yale isochrones is not consistent with predictions based on the mixing-length theory of convection (see Pedersen et al. 1990)—and hence cannot be reproduced using an independent code—temperature uncertainties have little impact on computed luminosity functions, except through the bolometric corrections. As a result, the Green et al. LFs should be especially useful in comparisons with observations and certainly provide a valuable complement to the present work.

Figure 20 shows a fit of our computed LFs, assuming [Fe/H] = -0.65, an age of 14 Gyr, and the three indicated values of x, to the composite LF for 47 Tue first presented in Figure 13. As was found in the case of M92, the slope of the red giant segment is matched exceedingly well by the theory. In contrast, the lower main-sequence data are not reproduced

7 YandenBerg ( 1992b) shows, in a comparison of University of Victoria and Yale LFs for the same age, Y, and Z, that the deviations between the two remain quite small down to Mv ~ 7.


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Mv

Fig. 19.—Comparison between the differential and integrated luminosity functions ( upper and lower panels, respectively) computed in this study with those calculated by Green et al. ( 1987 ) for the indicated parameters.

particularly well by a single theoretical locus, although the error bars on the star counts are such (see Fig. 13) that the discrepancy is generally less than 2 g. (Given that a value of .x = 0.0 ± 0.5 does encompass most of the data—see Hesser et al. 1987—it is possible that future work will show that a single power-law mass function is applicable to this particular clus-

Fig. 20.—Comparison of the composite 47 Tue luminosity function given in Fig. 13 with theoretical curves for [Fe/H] = -0.65, 14 Gyr, and values of x = —0.5, 0.0, and 0.5.

ter.) The upturn at the faint end does provide some support for the choice of [Fe/H] = -0.65 for 47 Tue (as well as the adopted distance). On the other hand, the predicted location of the RGB “bump” seems to be too bright, which might be an indication that the cluster is actually further away (which would imply a younger age ). It is also possible that the discrepancy should be viewed as evidence that convection extends deeper into the interiors of cluster giants during their first ascent of the RGB than canonical models predict. While the giant branch LF appears to be well observed, much can still be done to improve the main-sequence observations of 47 Tue. In particular, the bridging between the RGB and the lower main- sequence segments needs to be established much more reli- ably. It is possible, for instance, that the numbers of turnoff stars relative to the giants is not consistent with theoretical predictions, as seems to be the case in M92. Once again, further work in this critical region is urgently needed.

We finish this section with a few brief comments concerning Ml3. A few years ago, Drukier et al. ( 1988) presented a very deep luminosity function for this globular cluster and made use of a preliminary theoretical LF to interpret the data. As the latter has also been used elsewhere (e.g., see Richer et al. 1991 ), we feel that it is worthwhile to alleviate any concerns that the use of the present calculations would significantly alter the conclusions reached in those papers. Figure 21 presents a completely analogous plot to that given by Drukier et al., except that the theoretical loci are derived from the present paper. The assumed chemical composition is slightly difierent —which simply serves to confirm the claim made by Drukier et al. that such variations are inconsequential—but the resultant comparison between theory and observation is virtually identical to that originally reported (see their Fig. 2). Given that only two points (those between Mv = 8 and 10) deviate noticeably from a theoretical curve for x ^ 1 and that their uncertainty estimates are large, it seems to us that it remains an open question whether or not a single power-law mass function can be fitted to the Ml3 data. (Although we have given a considerable emphasis to the power-law form for the mass function in this investigation, this has mainly been for the sake of simpheity. Because of comphcations arising from dynami-

Fig. 21.—Comparison of the Drukier et al. ( 1988 ) luminosity function for the lower main-sequence of Ml 3 (filled circles) with theoretical curves for 14 Gyr, [Fe/H] = -1.48, and x = 0.5, 1.5, and 2.5.


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cal processes that cause mass segregation and the preferential evaporation of lower mass stars, it is not at all clear whether a power law provides an accurate description of either the IMF or the PMF of real stellar populations.)

4. CONCLUDING REMARKS

In this investigation we have presented an extensive grid of isochrones and luminosity functions for iron abundances in the range -2.26 < [Fe/H] < -0.47, current best estimates of the helium and oxygen contents, and ages from 5-8 Gyr (depending on the [Fe/H] value) to 18 Gyr. A considerable effort has been made to satisfy all available observational constraints, especially insofar as the slope of the giant branch and the location of the lower main-sequence (as set by the subdwarfs) are concerned. Indeed, even if there are major revi- sions to stellar physics (e.g., to opacities or model-atmosphere derived boundary conditions ), we believe that any future models which incorporate these new data must still satisfy the same observational constraints that we have used here. That is, it is our opinion that it will be difficult to improve upon the CMD aspect of the present work until the observational constraints themselves are refined. Current distance and chemical composition uncertainties continue to be the limiting factor: only after they are reduced will further substantial progress be possible in predicting stellar reff’s and colors.

Unfortunately, the [O/Fe] value appropriate to a given [Fe/H] is completely up in the air at the present time. Al- though our choices seem to be a credible compromise of the available data (see Paper I), it is entirely possible that they are incorrect. However, it is a reasonable rule of thumb that the age at a given turnoff luminosity decreases by about 8 percent for each increase in [O/Fe] of 0.3 dex (e.g., see Fahlman, Richer, & VandenBerg 1985; VandenBerg 1985b). This can be used to adjust the ages derived from the present isochrones should it become clear that our assumptions concerning [O/Fe] are inappropriate. Work to assess the impact of variations in the abundances of the a-nuclei elements is also needed. However, they should influence the stellar structure only through the opacity; consequently [a/Fe] enhancements will presumably require some renormalization of the computed reff’s in order to satisfy subdwarf and RGB constraints. One can also expect some revision of age-luminosity relations, but the effects should be small, especially for the most metal poor compositions where the free-free opacity sources are the dominant ones in the stellar interiors.

We regard the main contribution of this paper to be the theoretical luminosity functions contained herein. These have been derived using a new (fully described) interpolation code that seems to work extremely well, judging from the smooth-

ness of the results and the fine agreement that we have found with the Green et al. ( 1987 ) computations. Since they span the entire magnitude range from Mv 3 to Mv ^ 12, the LFs should provide particularly useful input into models of stellar populations as well as the means to advance our understanding of the Galactic GCs. However, as far as the latter are concerned, more accurate observations are urgently needed in order for meaningful progress to be made. At the present time, it is not possible to say, for instance, whether or not LFs can be used to further refine current estimates of cluster ages. Indeed, our examination of the available M92 LF (and possibly of that for 47 Tue) suggests that canonical models may not even be representative of evolving cluster stars. If confirmed, this could have major ramifications for models of galactic evolution and for the limits that the globulars place on the age of the universe. Even the giant branch component of cluster LFs is open to question. As Kraft (1989) has noted, the available M3 and Ml3 luminosity functions for stars brighter than Mv ~ 4 do not agree well with those for M92 and 47 Tue, when all have been similarly normalized in a region just below the turnoff. Are these differences real? One would surmise that they are not—since the effects of modest changes in chemical composition and age are predicted to be quite small ( recall Figs. 11-12) —but obviously this must be checked.

While we await improved observations, we intend to carry out further theoretical work to explore the effects of variations in [O/Fe] and Y, at a fixed [Fe/H], to complement this work and the study by Proffitt & VandenBerg (1991), which investi- gated the consequences of helium diffusion. One can anticipate that the intercomparison of predicted and observed LFs will lead to some important new revelations in the coming years.

D.A.V. is especially grateful for the support of an E.W.R. Steacie Memorial Fellowship (and a substantial operating grant) from the Natural Sciences and Engineering Research Council of Canada. This work was also supported by a grant for educational leave to P.A.B. from the University of Regina. We would like to thank Alan Irwin for helpful comments concerning interpolation methods, Gary Da Costa for providing the actual star count data that were discussed in the King et al. ( 1985) investigation of 47 Tucanae, Peter Dawson for useful information concerning Population II subdwarfs, and Bob Kraft and Greg Fahlman for their comments on the manu- script. The enthusiasm and encouragement expressed by Allan Sandage, Bob Kraft, Roger Bell, Judith Cohen, David Hart- wick, Jim Hesser, Peter Stetson, Harvey Richer, Greg Fahl- man, René Racine, and Bill Harris (among others) has also been most appreciated.

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