THE ASTROPHYSICAL JOURNAL, 479 :408È415, 1997 April 101997. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

PHOTOSPHERIC HEATING IN COLLIDING-WIND BINARIES

DOUGLAS R. WILLIAM G. AND LAURA R.GIES, BAGNUOLO, JR., PENNY1Center for High Angular Resolution Astronomy, and Department of Physics and Astronomy, Georgia State University,

Atlanta, GA 30303 ; gies=chara.gsu.edu, bagnuolo=chara.gsu.edu, penny=chara.gsu.eduReceived 1996 February 29 ; accepted 1996 October 22

ABSTRACTThe spectra of many massive binaries show secondary line depths that are deeper when the secondary

is approaching, a phenomenon we refer to as the Struve-Sahade e†ect. Such systems are expected tocontain colliding stellar winds, and we show how the X-ray Ñux from the bow shock that wraps aroundthe secondary will preferentially heat one hemisphere of the secondary. If the bow shock su†ers anysigniÐcant Coriolis deÑection due to orbital motion, then the heated surface of the secondary will be bestseen during orbital phases of secondary approach. We present model calculations for the system AOCassiopeiae that illustrate how the secondaryÏs light curve appears brighter during these orbital phases(as observed). We Ðnd that the model proÐles of spectral lines that are insensitive to or that strengthenwith heating will appear deeper when the secondary is approaching, but the same heating e†ects may benulled or even reversed in lines that weaken with increased temperature. This di†ering response of linesto heating may be at odds with reports of systematic deepening of UV and optical lines, and thus theconnection between such heating and the Struve-Sahade e†ect needs further observational and theoreti-cal investigation.Subject headings : binaries : spectroscopic È stars : early-type È stars : individual (AO Cassiopeiae) È

stars : mass loss

1. INTRODUCTION

Spectroscopic studies of the fainter companion stars inmassive binaries have depended largely on observationsobtained at quadrature phases, when the stars generallyhave their largest radial velocity separation. Investigatorsbeginning with Maury andBailey (1896), (1920a, 1920b),

have noted that massive binaries often displayStruve (1937)variable secondary (fainter star) line depths. In suchsystems, the secondaryÏs lines usually appear deeper duringorbital phases of approach (see Struve 1950, Sahade 1962,and a phenomenon that we will refer to as theTable 1),““ Struve-Sahade e†ect ÏÏ et al. et(Howarth 1997). Howarthal. report that the Struve-Sahade e†ect is present in(1997)the UV spectra of eight of the 15 SB2 systems they exam-ined. The origin of the Struve-Sahade e†ect remains unclear

suggested that a gas stream(Struve 1950). Sahade (1959)exists from the primary to the secondary that sweeps pastthe trailing side of the secondary, and during phases ofsecondary recessional velocity, the secondary is obscured bythe gas stream. Ðnds that the signature ofStickland (1996)the secondary star in cross-correlation functions of IUEspectra obtained during receding velocities are both weakerand broader, which may be consistent with electron scat-tering by trailing gas. on the otherAbhyankhar (1959),hand, suggested that the line deepening during approachingphases is caused by enhanced density on the approachinghemisphere of the secondary star. Clearly, the origin of theStruve-Sahade e†ect must be understood in order to deter-mine which quadrature phase provides the most reliableinformation about the secondaryÏs physical parameters(Ñux, radius, etc.).

Massive stars have strong stellar winds, and there is nowa growing body of evidence suggesting that winds willcollide in binaries in a bow shock between the stars (see the

1 Current address : University of Montreal, Department of Physics, C.P.6128, Succ. Centre Ville, Montreal, PQ, Canada H3C 3J7.

theoretical study of Blondin, & Pollock andStevens, 1992the observational reviews of andGies 1995, St-Louis 1995,

The location of the bow shock dependsMarchenko 1995).on the momentum balance between the two stellar winds,and in cases where the primaryÏs wind momentum domi-nates, the bow shock could reach close to the photosphereof the secondary. The close proximity of the shock region tothe surface of the secondary could lead to local heating ofthe photosphere. Furthermore, if the ratio of wind speed tosecondary orbital velocity is not too large, then the bowshock will have a Coriolis deÑection that will shift the apexof maximal heating from a position on-axis to above theleading hemisphere of the secondary. This colliding-windÈinduced heating will increase the secondaryÏs contributionto the composite spectrum and yield both a brighter lightcurve and (potentially) deeper secondary lines when theheated (approaching) hemisphere is directed toward us.Here we explore this solution to the Struve-Sahade e†ect ina colliding-winds model for the O ] O binary, AO Cassio-peiae.

2. COLLIDING WINDS AND SECONDARY PHOTOSPHERIC

HEATING IN AO CAS

The close binary, AO Cas, has both a short period (3.52days) and luminous components (O9.5 III ] O8 V;

& Gies and so it is an excellent candidateBagnuolo 1991),for colliding winds & Wiggs Furthermore, the(Gies 1991).secondary lines display strengthening during approachingphases & Horak & Sahade(Struve 1949 ; Struve 1958 ;

et al. and so we have selec-Howarth 1997 ; Stickland 1996),ted AO Cas as a test case to calculate the e†ects of colliding-winds heating. Our goal is to match the observed V -bandlight curve and variable line depth ratio using a(Koch 1960)simple geometrical model. The secondary-to-primary linedepth ratio appears to change from 0.53 near orbital phase0.15 to 0.66 near phase 0.72 in the UV cross-correlationfunctions (CCFs) presented by & Wiggs seeGies (1991;

408

PHOTOSPHERIC HEATING IN COLLIDING-WIND BINARIES 409

TABLE 1

MASSIVE BINARIES DISPLAYING THE STRUVE-SAHADE EFFECT

Star Name References

HD 1337 . . . . . . . . AO Cas Struve & Horak 1949 ; Struve & Sahade 1958 ; Gies & Wiggs 1991 ; Howarth et al. 1997HD 47129 . . . . . . . PlaskettÏs star Struve 1948 ; Sahade 1962 ; Howarth et al. 1997HD 57060 . . . . . . . 29 UW CMa Sahade 1959 ; Bagnuolo et al. 1994 ; Howarth et al. 1997HD 65818 . . . . . . . V Pup Maury 1920bHD 93205 . . . . . . . . . . Howarth et al. 1997HD 97484 . . . . . . . EM Car Stickland, Lloyd, & Corcoran 1994 ; Stickland 1996HD 100213 . . . . . . TU Mus Stickland et al. 1995 ; Howarth et al. 1997 ; Stickland 1996HD 116658 . . . . . . a Vir Struve 1950HD 135240 . . . . . . d Cir Stickland et al. 1993a ; Stickland 1996HD 143018 . . . . . . n Sco Inglis 1956HD 144217 . . . . . . b Sco Struve 1937 ; Abhyankhar 1959HD 149404 . . . . . . V918 Sco Stickland & Koch 1996 ; Howarth et al. 1997HD 151890 . . . . . . k1 Sco Bailey 1896; Maury 1920a ; Stickland 1996 ; Stickland, Sahade, & Henrichs 1996HD 152248 . . . . . . . . . Struve 1944 ; Howarth et al. 1997HD 159176 . . . . . . . . . Conti, Cowley, & Johnson 1975 ; Stickland et al. 1993b ; Howarth et al. 1997HD 163181 . . . . . . V453 Sco Sahade & Frieboes-Conde 1965 ; Hutchings 1975HD 169515 . . . . . . RY Sct Cowley & Hutchings 1976HD 185507 . . . . . . p Aql Struve 1950HD 218066 . . . . . . CW Cep Stickland, Koch, & Pfei†er 1992 ; Stickland 1996

their Fig. 3), and so we will seek models that can reproducea line depth ratio increase of 24% between these phases(orbital phase 0.0 is deÐned by primary superiorconjunction). We Ðrst present a simple model for the dis-tribution of heating around the photosphere of the second-ary, and then we apply the heating model to producesynthetic light curves and line proÐles for the binary.

2.1. Colliding-W ind Geometry and HeatingThe presence of a colliding-winds bow shock close to the

photosphere of the secondary can lead to photosphericheating by a variety of means (X-ray irradiation from thehot plasma in the shock, or perhaps shock heating of thephotosphere directly if the primaryÏs wind overwhelms thesecondaryÏs). We consider Ðrst the heating due to back-scattering of photons in the high-density regions of the bowshock. & Hummer show how the dense windsAbbott (1985)of very luminous O stars act to backscatter the stellar radi-ation Ðeld in a process they refer to as ““ wind blanketing.ÏÏThey derive the e†ective bolometric albedo of the windmaterial and show how the returning photons alter thephotospheric structure. Their main conclusion is that thesurface temperature is increased by an amount

TblTun

DA1 ] A

B1 [ A

B

B1@4, (1)

where and are the wind-blanketed and unblanketedTbl Tunsurface temperatures, respectively, and is the wind bolo-ABmetric albedo. They present a model for the wind of the hot

O star, f Pup, and they Ðnd that the bolometric albedoreaches 0.34 for a mass-loss rate of 1.5 ] 10~5 yr~1M

_(and scales roughly as Here we suppose that similarM0 1@3).wind scattering can occur as photons encounter the sub-stantial decelerations and densities in the bow shock, andthat the backscattered photons will heat the photosphereaccording to the equation above.

We assume that backscattered Ñux (and thus the albedo)will vary as

ABP

1d2AL 1/L 2

r12] 1

r22Bp1@3 , (2)

where d is the radial distance between a point in the bowshock and the surface of the secondary, is the ratio ofL 1/L 2primary to secondary luminosity, and are the distancesr1 r2from the bow shock position to the centers of the primaryand secondary, respectively, and p is the mass surfacedensity in the bow shock. We then can associate a windalbedo for any position on the secondary with the value(from for a bow shock position directly above thateq. [2])point on the secondary. In fact, any given point on thesecondary will be illuminated by photons over a range inangle (not just those from directly above), and so theangular distribution we derive for secondary heating willprobably be much narrower than in actuality.

We chose to derive the heating of the secondary as afunction of the angle t between the apex of the bow shockand the secondary surface position as measured from thecenter of the secondary. We used an analytical bow shockmodel from & Willson to determine d,Girard (1987) r1, r2,and p as a function of angle t. We selected a model with amomentum balance parameter mw\ 10, which we showbelow is a reasonable approximation for AO Cas (Fig. 1).We also assumed a luminosity ratio and sec-(L 1/L 2\ 1.72)ondary radius (0.206 of the system separation) appropriateto the case of AO Cas. Note that the Girard & Willsonmodels are only applicable to winds with constant velocityand instantaneous cooling (so that the bow shock is asurface), but we expect they will serve as an adequate Ðrstapproximation. We then determined the bolometric albedo

and surface temperature deviation as a(eq. [2]) (eq. [1])function of t. The resulting distribution is dominated byterms in d and p, and the temperature deviation is wellmatched by a Gaussian with an e~1 half-width of *t\ 18¡from the bow shock apex. Again, we caution that the actualdistribution is probably broader since we have taken thealbedo to be that for a bow shock position directly over-head rather than integrating over all the solid angle. Theamplitude of the heating remains a free parameter in thissimple model because the constant of proportionality in thealbedo expression depends on the density and(eq. [2])velocity laws in the wind, and these laws are probably verydi†erent for colliding winds than for radiatively drivenwinds & Gayley(Owocki 1995 ; Gayley 1996).

-1.0 -0.5 0.0 0.5

-0.5

0.0

0.5

0.25

0.75

410 GIES, BAGNUOLO, & PENNY Vol. 479

FIG. 1.ÈA diagram of the stellar shapes in the orbital plane. Thearrows at the center of the primary (left) and secondary (right) show theorbital motion around the center of mass ( Ðlled circle). The thick arc showsthe location of the bow shock, and the line from the center of the secondaryto the shock locates the apex position (at h \ 30¡ to the axis joining thestars). The open circle shows the central location of the Ha emission. Thesecondary attains radial velocity minimum at orbital phase 0.75.

The Ðnal ingredient in this simple model is to introduce aCoriolis deÑection of the bow shock due to the orbitalmotion of the system. The angle will depend on the relativevalues of the wind and orbital velocities in the vicinity of theshock, and in close binary systems like AO Cas, theprimaryÏs wind will attain only a fraction of the terminalvelocity before striking the bow shock near its apex posi-tion, and so wind and orbital velocities may be comparable.This Coriolis deÑection will displace the apex of the shockby an angle h in the orbital plane toward the leading hemi-sphere of the secondary, and thus the heating e†ects will bemost apparent between primary inferior conjunction andthe next quadrature when the secondary attains itsmaximum approach velocity (Note that the intro-(Fig. 1).duction of a nonzero h strictly invalidates the albedoexpression since and p will no longer be func-[eq. (2)] r1tions of t alone ; nevertheless, since the dominant termdepends on the distance from the bow shock to the second-ary surface, d, we expect that albedo distribution based onh \ 0 will be approximately correct.)

Our assumptions about the colliding-wind geometry inAO Cas are based on the Ha emission results of &GiesWiggs They found that the residual emission has a(1991).radial velocity variation that places the emission near theleading hemisphere of the secondary if the variation isassumed to be entirely due to orbital motion. This place-ment centers the emission source just above the secondaryÏssurface in the equatorial plane (see the open circle in Fig. 1).We assume that this emission arises in the high gas densitiesfound near the bow shock apex, and thus we take theCoriolis deÑection to be h \ 30¡ so that the bow shock apexis aligned in the direction of the site of the Ha emission.Because the Ha emission is situated so close to the second-ary, we selected a colliding-wind model from the solutionsof & Willson with a stagnation pointGirard (1987)(momentum balance) on-axis that occurs just above the sec-ondaryÏs radius. We used the solution for mw\ 10, where

is the ratio of mass-loss rates, and ism\M0 1/M0 2 w\ v1/v2

the ratio of wind velocities. The radii and temperatures weadopt (below) lead to luminosities that imply a ratio ofmass-loss rates of m\ 2.5 according to the mass-lossformula of & Prinja thus, w\ 4.0 in ourHowarth (1989) ;simple model. The resulting bow shock geometry is illus-trated in Figure 1.

Our Ðnal expression for the secondary heating is

*TT

\ f expC[A t*tB2D

, (3)

where f is the fractional heating directly below the bowshock apex, t is the angle between a surface element and thebow shock apex measured from the center of the secondary,and *t ([18¡) controls the width of the heating distribu-tion. The heating expression was restricted to the hemi-sphere facing the bow shock apex (t\ 90¡). The bow shockapex position is placed in the orbital plane, displaced by anangle, h, from the axis to the leading hemisphere of thesecondary Although the expression was derived for(Fig. 1).heating by backscattering of the secondaryÏs Ñux, we notethat it will also serve reasonably well for X-ray heating sincethe X-ray Ñux incident on the secondaryÏs surface will alsovary approximately as p/d2.

2.2. L ight CurveThe heating due to colliding winds will increase the sec-

ondaryÏs contribution to the total system Ñux and alter thephotometric light curve, and here we calculate light-curvechanges predicted by this simple model. The light curvesand line proÐles (below) were calculated using the binarysurface integration code of & DoughtyMochnacki (1972),which we have altered to include the e†ects of radiationpressure and asynchronous rotation & Bolton(Gies 1986).We further modiÐed the code to adjust the secondaryÏssurface temperature according to equation (3).

Our set of input parameters for the system have beenmodiÐed from the light-curve solutions of & WiggsGies

according to the stellar spectral types (and inferred(1991)temperatures) derived from a Doppler tomographic recon-struction of the UV spectra by & GiesBagnuolo (1991).Thus, we take the polar temperatures and gravities to be (T ,log g) \ (32,000, 3.3) and (36,000, 3.9) for the primary andsecondary, respectively. Fluxes were taken from Kurucz

and quadratic limb-darkening laws from &(1979), WadeRucinski & Gies argue that the UV(1985). Bagnuolo (1991)Ñux ratio falls in the range A hotter sec-F2/F1\ 0.5È0.7.ondary yields a deeper secondary eclipse at phase 0.5 (notseen in the observations), and so the best Ðt of the lightcurve based on these parameters occurs with the smallestsecondary radius allowed by the UV intensity ratio (R2\0.206 in units of system separation). We also set the second-aryÏs rotational speed at 1.7 times the synchronous rate toprovide an approximate match to the observed ratio ofprojected rotational velocities.

The nominal, baseline model light curve (for an inclina-tion i \ 64¡ and no heating by colliding winds) is illustratedin (solid line), together with the ““ Interval III ÏÏFigure 2group of V -band photometric observations by Koch (1960).The Ðt is poor near phase 0.5 because the model predictsthat the hotter secondary should produce a deeper, grazingeclipse than is seen at phase 0.0. There is also a problem inthe brighter, rising part of the light curve observed betweenphases 0.5 and 0.8.

0.0 0.5 1.0ORBITAL PHASE

0.20

0.15

0.10

0.05

0.00

-0.05

V M

AG

NIT

UD

E D

IFF

ER

EN

CE

No. 1, 1997 PHOTOSPHERIC HEATING IN COLLIDING-WIND BINARIES 411

FIG. 2.ÈV -band light curves for AO Cas. The observations ( Ðlled circles ; are compared with three model Ðts : no wind heating (solid line),Koch 1960)secondary heating with maximum *T /T \ 15% (dashed line), and *T /T \ 62% (triple-dotÈdashed line).

We then calculated a series of light-curve models withcolliding-winds heating for a variety of choices for param-eters f and *t. We found that we could make a reasonablematch of the light curve for *t in the range 18¡È90¡, pro-vided the product, f*t, was approximately constant. Thedashed curve in shows the model light curve forFigure 2*t\ 45¡ and f\ 15%. The heating from colliding windsbrightens the light curve between phases 0.4 and 0.8, andproduces an essentially perfect match with the observations.Note that the phase range of brightening is set in the modelby the assumed Coriolis deÑection (h \ 30¡ from the Haobservations), and thus the good agreement between theobserved and model light curves o†ers independent supportfor the heating model.

2.3. L ine Depth VariationsColliding-winds heating of the secondary will increase the

secondaryÏs Ñux contribution to the observed, compositespectrum and make the secondaryÏs lines appear moreprominent. However, surface heating may in some casesreduce the spectral line strengths in the secondary spectrum,and so both competing e†ects must be considered in amodel of photospheric heating. We Ðrst consider a sche-matic approach to the problem, and then we present linetransfer calculations for two heating scenarios.

The observed residual line depth of a secondary line inthe composite spectrum (at an orbital phase when the line isfully resolved) is given by

r0\ r2F2

F1] F2, (4)

where is the line depth in the secondary spectrum alone,r2and and are the monochromatic Ñuxes of the primaryF1 F2and secondary, respectively. Let us suppose that the entire

secondary is then heated by an amount so that the*T2,fractional line depth change in the composite spectrumbecomes

*r0r0

\ *T2T2

Ad ln r2d ln T2

] F1F1] F2

d ln F2d ln T2

B. (5)

Furthermore, let us suppose that the monochromatic Ñuxcan be expressed as a Planck curve, so that ÑuxF2\ Bj,and temperature variations are related by

L ln BjL ln T

4 X , (6)

where X \ u/[1 [ exp ([u)] and u \ hc/(jkT ) (MihalasThen the fractional line depth change in the compos-1978).

ite spectrum becomes

*r0r0

\ X*T2T2

A d ln r2d ln F2

] F1F1] F2

B. (7)

The above expression also applies to the Ñux and lineproÐle from a given heated surface patch of the secondary.The expression shows that the relative variations will havegreater amplitude closer to the Wien peak (where X is large)and in cases where the primary is much brighter than thesecondary However, there are circumstances in(F1[ F2).which a given line will weaken with heating, so that the Ðrstterm in the parentheses will be negative, and, consequently,the Ðnal net increase or decrease in secondary line strengthin the composite spectrum will depend on which term inparentheses dominates.

The calculation of the intrinsic line depth changes withheating requires a stellar atmospheres code since the linestrength depends on a combination of factors, i.e., the indi-vidual line opacity, the continuum opacity, and the atmo-

-4 -2 0 2log MASS (gm cm-2 )

20

40

60

80

100

TE

MP

ER

AT

UR

E (

okK

)

36000

+WIND

38000

412 GIES, BAGNUOLO, & PENNY Vol. 479

spheric temperature gradient between depths where the lineand continuum attain optical depth unity (Mihalas 1978).We used the non-LTE atmospheres code TLUSTY

& Lanz to construct model atmospheres for(Hubeny 1995)two heating models for the secondary. The basic model forthe secondaryÏs atmosphere was calculated using Teff \39,000 K, log g \ 3.9, and a microturbulent velocity of 2 kms~1. Non-LTE populations were calculated explicitly for 10levels of hydrogen and 15 levels of helium. The resultingtemperature structure is shown as a function of columnmass in Note that temperature inversion in theFigure 3.upper atmosphere is the result of restricting the non-LTEcalculations to H and He; in more sophisticated modelsthat include iron, for example, the temperature decreasesoutward & Lanz We then used the model(Hubeny 1995).atmosphere with the spectrum synthesis code SYNSPEC

Lanz, & Je†ery and atomic line lists from(Hubeny, 1994)& Bell to make model spectra. We illustrateKurucz (1995)

sample results for a small section of the UV spectrum usedby & Wiggs in and for the He I j6678Gies (1991) Figure 4line in Figure 5.

We Ðrst constructed a heated model by including an arti-Ðcially high wind blanketing albedo in TLUSTY. We setthe albedo at a constant value of 0.25 except in the He II

Lyman continuum and lines, where we used a higher albedoof 0.60 (see & Hummer The resulting tem-Abbott 1985).perature structure dotted line) does show signiÐcant(Fig. 3,surface heating and a reduction in the temperature gradientin the line-forming region (the Rosseland optical depth isunity near log m\ 0). Both changes lead to a reduction inline strength in transitions that tend to decline in strengthwith increasing temperature (Fe IV and Ni IV lines in Fig. 4)but not in lines that strengthen with increasing temperature(Fe V). The is seen dramatically in where theFigure 5,

heating causes a large reduction in He I j6678 but nochange in He II j6683.

The colliding-winds shock front will probably be a sig-niÐcant source of hard X-rays et al. and so(Stevens 1992),heating by wind blanketing alone must greatly underesti-mate the actual heating in the photosphere. A usefulexample of X-ray illumination of a photosphere is the X-raybinary HZ Her \ Her X-1, in which an F dwarf has onehemisphere Ñooded by hard X-rays from an accretion disksurrounding a neutron star. McCray, & AuerLondon,

calculated the X-rayÈheating e†ect on the photo-(1981)sphere and found that X-ray heating penetrates deep intothe photosphere (well past optical depth unity). The result isthat a signiÐcant temperature gradient remains in the line-forming region, and strong absorption lines are formed thatwe observe when the X-rayÈilluminated atmosphere isoriented in our direction (when the spectrum resembles aB3ÈB6 type ; & Hutchings et al.Crampton 1974 ; Anderson

Since the important characteristics of X-ray heating1994).for photospheric line formation are a steep temperature gra-dient and a higher temperature in the line-forming region,we constructed a simple model atmosphere with a highere†ective temperature (38,000 K) to make an approximatemodel for deep X-ray heating. This model dashed(Fig. 3,line) has the requisite characteristics and leads to modelabsorption lines that are only slightly strengthened orweakened with heating (Figs. and dashed line).4 5,

The net line depth changes in the composite binary spec-trum are illustrated for a sample UV line, Fe V j1370.943, in

The proÐles were made using the GENSYNFigure 6.binary star disk integration code & Doughty(Mochnacki

described above. Intensity proÐles were generated1972)with SYNSPEC for 10 surface normal angles (k \ cosh \ 1.0È0.1) for this transition alone, for both primary and

FIG. 3.ÈThe temperature structure of the secondaryÏs atmosphere as a function of integrated column mass depth. The plots represent the modelatmosphere for K with no external heating (solid line), heating by exaggerated wind blanketing (dotted line), and deep heating (represented by aTeff \ 36,000

K model ; dashed line).Teff \ 38,000

1371.0 1371.2 1371.4 1371.6 1371.8WAVELENGTH (Angstroms)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

INT

EN

SIT

Y

Fe

V 1

370.

943

Fe

IV 1

371.

124

Fe

V 1

371.

215

O V

13

71.2

96

Ni I

V 1

371.

411

Fe

IV 1

371.

555

Ni I

V 1

371.

680

Ni I

V 1

371.

778

36000

+WIND

38000

6676 6678 6680 6682 6684WAVELENGTH (Angstroms)

0.4

0.6

0.8

1.0

1.2

1.4

INT

EN

SIT

Y

He

I 66

78.1

50

He

II 66

83.2

10

36000

+WIND

38000

No. 1, 1997 PHOTOSPHERIC HEATING IN COLLIDING-WIND BINARIES 413

FIG. 4.ÈSynthetic spectra for a small portion of the UV spectrum of the secondary star (with identiÐcations of the major lines). The various plots arebased on similarly marked atmospheres in Fig. 3.

secondary star atmospheric models. The continuum limb-darkening laws were also taken from these SYNSPECresults. The GENSYN code was then run (using the samesystem parameters used for the light-curve analysis) for thesame two orbital phases, 0.15 and 0.72, corresponding to

the UV quadrature observations presented by &GiesWiggs The approaching phase composite proÐle(1991).(phase 0.72) with no colliding-winds heating is shown in

as a solid line. Note that the secondary appearsFigure 6relatively stronger in this Fe V line than in the UV compos-

FIG. 5.ÈSynthetic spectra for He I j6678 and He II j6683 in the spectrum of the secondary star. The various plots are based on similarly markedatmospheres in Fig. 3.

-400 -200 0 200 400RADIAL VELOCITY (km s-1 )

0.990

0.995

1.000

INT

EN

SIT

Y

414 GIES, BAGNUOLO, & PENNY Vol. 479

FIG. 6.ÈModel Fe V j1370.943 proÐles for the combined spectrum of AO Cas at orbital phase 0.72 (near minimum velocity of the secondary). The solidline depicts the proÐle with no extra heating of the secondary by winds. The dashed line shows the result for a maximum heating of *T /T \ 24%. The dottedline illustrates the result again for *T /T \ 24% but with the equivalent width decreased artiÐcially at higher temperature.

ite CCFs shown in Gies & Wiggs because their CCFs arebased on a large sample of lines, many of which weaken (asopposed to Fe V, which strengthens) in the hotter second-ary.

We next investigated the inÑuence of colliding-windsheating on this line by calculating proÐles for several valuesof the heating parameter f (and using *t\ 45¡ and h \ 30¡from the light-curve analysis). We Ðrst assumed that theintrinsic line proÐle in the secondary spectrum remainedconstant with heating (a good assumption for Fe V

j1370.943 ; see These tests showed that the ratio ofFig. 4).secondary to primary line depth increased between phases0.15 and 0.72 (receding and approaching quadratures)directly with increases in heating parameter f, and a 24%increase in relative line depth is accomplished with f \ 0.24

dashed line). This value of f is larger than, but com-(Fig. 6,parable to, the estimate f \ 0.15 from the light-curve Ðt.Note that, as described in part of this increaseequation (7),results from a relative decrease in the strength of theprimaryÏs line because of dilution by the secondaryÏs contin-uum Ñux. The asymmetry in the red part of the secondaryproÐle at this phase occurs because the center of heating isapparently displaced toward the primary at this viewingorientation. The asymmetry becomes more pronouncedwith a narrower heating distribution (smaller *t), and sincesuch asymmetries have not been reported, we favor modelswith broader heating. The asymmetry is also reduced if alarger Coriolis deÑection is adopted.

The line depth variations in the CCFs presented by Gies& Wiggs are based on measurements in six spectral(1991)regions (see their Table 3), and these regions contain manylines that are much more sensitive to temperature changesthan Fe V j1370.943 (see We attempted to modelFig. 4).

these changes (predominantly in Fe IV lines) by calculatingsynthetic spectra for each UV region and for both nominal

K) and deeply heated K) model(Teff \ 36,000 (Teff \ 38,000atmospheres. We then compared how much more Ñux wasproduced by the hotter atmosphere with how much the linedepths changed on average. The line depth variations wereestimated by taking the average ratio of line depth in thehot and nominal atmospheres for all lines deeper than 10%of the continuum in unbroadened spectra. In each region,the average line depth decreased somewhat in the heatedmodel, and we estimate that the derivative d ln r2/d ln F2ranges from [0.33 in the 1359È1377 region to [1.54 inÓthe 1745È1766 region, with an average value of [0.86Ófrom all six regions. Then, if we use the average value

in with the UV Ñuxd ln r2/d ln F2\ [0.86 equation (7)ratio & Gies we Ðnd that theF2/F1\ 0.5 (Bagnuolo 1991),terms in the parentheses nearly cancel, so that we mightexpect the average UV line depths to actually decrease by asmall amount during the approaching phase.

The general line weakening with increased temperaturethat is apparently common in other UV lines was usedÐnally to reduce artiÐcially the line strength of Fe V

j1370.943 in the GENSYN code. We again assumed thatthe Ñux can represented as a Planck curve, and we esti-mated the fractional line depth change with heating (see eq.

by[6])

d ln r2d ln T2

\ d ln r2d ln F2

d ln F2d ln T2

\ Xd ln r2d ln F2

. (8)

The proÐles for heating ( f\ 0.24) with this line-strengthreduction included are shown in (dotted line), andFigure 6both secondary and primary line depths are reduced as

No. 1, 1997 PHOTOSPHERIC HEATING IN COLLIDING-WIND BINARIES 415

expected. Thus, it appears that colliding-winds heating canaccount for line strengthening during approach in lines likeFe V j1370.943, but the same heating e†ects may be nulledor even reversed in lines that weaken with increased tem-perature.

3. CONCLUSIONS

These exploratory calculations demonstrate that whenthe secondary star in a massive binary is preferentiallyheated under the apex of a colliding-winds bow shock, thesecondaryÏs Ñux and line proÐles will show variations withorbital phase. Our model for these variations in the massivebinary AO Cas can explain the otherwise mysterious, brightportion of the light curve seen when the heated hemisphereis oriented in our direction. The model also predicts thatspectral lines that are insensitive to, or that strengthen with,heating will appear deeper when the secondary is approach-ing, the observed phenomenon we refer to as the Struve-Sahade e†ect. However, an assessment of the line variationsin the UV lines, which show the Struve-Sahade e†ect in thecross-correlations functions for AO Cas presented by Gies& Wiggs indicates that many of those speciÐc UV(1991),lines probably decrease in strength with heating in the sec-ondary. Thus, the simple model is unable to account for ageneral deepening of these UV lines during approach.

The observational evidence from investigations of Ha(Gies the UV wind lines and X-ray1995, 1996), (Koch 1996),emission properties of binaries containing(Corcoran 1996)O-type stars strongly supports the presence of collidingwinds in some systems, and although the models we presenthere have mixed success, it is clear that the shocks fromcolliding winds can potentially alter the photospheres of the

weaker wind, secondary stars. We stress that our models arevery simple and may misrepresent several important pro-cesses, in particular the e†ects of X-ray heating on thephotosphere, radiative transfer through the bow shockitself, and the possibility that the shock occurs right in thephotosphere If photospheric heating of the(Gayley 1996).secondary by colliding winds does occur, then the heatingmodel predicts that lines that grow in strength with increas-ing temperature will display the largest deepening duringthe orbital phases between superior conjunction of the sec-ondary and the following quadrature. Thus, a direct test ofthe model is possible through measurements of the Struve-Sahade e†ect in high signal-to-noise ratio spectra of di†er-ent line species.

D. R. G. is grateful for the hospitality of Professor Sahadeand colleagues at the La Plata Observatory, Argentina, whosponsored a recent workshop on colliding-wind binarieswhere some of these ideas were developed. We thank IvanHubeny for making available his TLUSTY and SYNSPECcodes, and Dave Stickland, Steve Shore, and an anonymousreferee for many helpful comments on an early version ofthis paper. This work was supported in part by NASA grantNAG 5-2979. Institutional support has been provided fromthe GSU College of Arts and Sciences, and from the Chan-cellorÏs Initiative Fund from the Board of Regents of theUniversity System of Georgia administered through theGSU office of the Vice President for Research and Spon-sored Programs. We gratefully acknowledge all thissupport. This research has made use of the SIMBAD data-base, operated at CDS, Strasbourg, France.

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Note added in proof.ÈApproximate calculations by K. G. Gayley (private communication) suggest that the wind-windboundary occurs in the AO Cas system at a position just above the secondaryÏs photosphere because of radiative braking bythe secondaryÏs Ñux. Photons backscattered to the secondary from the boundary may be a signiÐcant source of heating.