THE ASTROPHYSICAL JOURNAL, 509 :848È855, 1998 December 201998. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

HYDROGEN-LIKE ION EMISSION IN THE SPECTRA OF LOW-MASS X-RAY BINARIES

M. A. T. R. AND L.BAUTISTA, KALLMAN, ANGELINI

Laboratory for High Energy Astrophysics, NASA Goddard Space Flight Center, Greenbelt, MD 20771

D. A. LIEDAHL

Department of Physics and Space Technology, Lawrence Livermore National Laboratory, P.O. Box 808, L-41, Livermore, CA 94550

AND

D. P. SMITS

HartRAO, P.O. Box 443, Krugersdorp 1740, South AfricaReceived 1998 February 4 ; accepted 1998 July 24

ABSTRACTWe study the emission from H-like ions, particularly oxygen and neon, observed in ASCA spectra of

low-mass X-ray binaries (LMXBs). The observed strengths of Lya emission lines relative to the recombi-nation continua di†er from the classical recombination model. This suggests a di†erent excitation mecha-nism for the lines. Various mechanisms are considered, which include three-body recombination,collisional excitation, recombination satellite line emission, and resonant Ñuorescent excitation. We Ðndthat the detection of Lyman recombination continuum implies that the plasma is photoionized, in agree-ment with previous studies by Hatchett, Bu†, & McCray and Liedahl & Paerels. Under collisional ion-ization conditions, on the other hand, the Lyman continuum should be negligible unless the temperaturewere greater than 3 ] 106 K. Otherwise, the enhancement of Lya emission with respect to the continuummay be due to (1) three-body recombination at electron densities greater than 1017 cm~3 and tem-peratures below 2 ] 105 K, (2) contributions to the recombination spectrum from collisional excitationof the H-like ionization stage, (3) contributions to recombination Lya emission from satellite lines due torecombination onto the He-like ionization stage, and (4) contributions to the recombination spectrumfrom resonant Ñuorescence excitation of the H-like ionization stage. Further observations of higher orderLyman series lines and lines from other ionization stages are suggested to discriminate between thevarious excitation mechanisms. In addition, the implications of the di†erent spectral formation mecha-nisms to the hydrodynamic accretion model of LMXBs are discussed.Subject headings : atomic processes È binaries : close È X-rays : stars

1. INTRODUCTION

Low-mass X-ray binaries (LMXBs) are thought to consistof a neutron star in orbit with a late-type star (see, e.g.,

Nagase, & Parmar Their energy spectra areWhite, 1995).dominated by X-rays, and the emission in other wavelengthbands is almost entirely due to reprocessing. Thus, anyattempt to derive properties of these objects from theirspectra must take into account the physics of reprocessing.

In the X-ray energy band the dominant process produc-ing the observable spectra, in addition to the bremsstrah-lung and inverse Compton continuum, is expected to berecombination. This is because in the absence of anyheating mechanism other than photoionization by a strongX-ray Ñux, the temperature of a gas will be too low to allowefficient excitation by collisions with thermal electrons (see,e.g., & McCray If so, the reprocessedKallman 1982).spectra will include both line emission due to cascades fol-lowing recombination and free-bound continuum radiationdue to radiative recombination. The X-ray band is wellsuited to searches for such features, since current instru-ments have sensitivity at energies including the strongestlines and the free-bound continua of several ions that areexpected to be astrophysically abundant, notably the H-likeand He-like ions of oxygen, neon, magnesium, silicon,sulfur, and iron (see, e.g., et al. &Angelini 1995 ; LiedahlPaerels Detailed models for reprocessing in photo-1996).ionized gases suggest that the strongest lines are likely to bethose of O VIII, Ne X, Mg XII, Si XIV, and S XVI et(Kallmanal. 1996).

Observations of most of the brightest LMXBs have beencarried out by the ASCA satellite (see, e.g., Kallman,White,& Angelini Some of the results of the analysis of six of1997).the brightest objects are as follows :

1. Most (four of six) objects conform to the expectationsby showing a predominance of emission that is consistentwith O VIII.

2. The remainder of the objects show spectra suggestiveof signiÐcant departures from solar abundances if classicalrecombination spectra for these objects are adopted. In onecase, 4U 1626[67, the Ne/O ratio seems enhanced by afactor of D5 relative to the solar values et al.(Angelini

similarly, the spectrum of Cyg X-2 implies an iron/1995) ;oxygen ratio greater than solar.

3. In all cases showing emission from H-like ions theratio of line emission to free-bound continuum emission issigniÐcantly greater than that expected from radiativerecombination. The best examples of this are 4U 1626[67,in which the Ne X Lya to Lyman continuum ratio is 3.6~1.1`0.8,and 4U 0614]09, in which the O VIII Lya to Lyman contin-uum ratio is D7.5. By contrast, the Lya to Lyman contin-uum ratios from radiative recombination are expected to beclose to unity.

In this paper we explore mechanisms that may accountfor the X-ray line/continuum ratios in LMXBs. Theseinclude three-body recombination electron impact(° 2),excitation recombination satellite lines and Ñuo-(° 3), (° 4),rescence For all of the objects considered, a deÐnitive(° 5).conclusion about the spectral formation mechanism will

848

4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2

−4.4

−4.2

−4

−3.8

−3.6

−3.4

log

(Ne

α3Bn=

2 / α

Rn=

2)

4.6 4.8 5 5.2 5.4 5.6 5.8 6 6.2

−1

−.5

0

.5

1

log (Te) [K]

log

(Ne

α3BT /

αRT)

HYDROGEN-LIKE ION EMISSION 849

have to wait for better quality spectra where other H-likelines and lines from other ionization stages are detected, asdiscussed in It is expected that by correct interpretation° 6.of the observed spectra one may determine the physicalconditions (temperature, density, and ionization structureof the plasma) of the emitting region that will constrain themodel of accretion onto a neutron star. This is discussedin ° 7.

2. THREE-BODY RECOMBINATION

Three-body or collisional recombination is a mechanismwhereby the energy liberated as the result of recombinationis carried away by an electron, rather than being radiated asa bound-free continuum photon. Thus, three-body recombi-nation provides a mechanism for populating excited levelswithout any continuum emission. Owing to the necessitythat two electrons participate, high densities are required.

In order to evaluate the efficiency of three-body recombi-nation we use the semiempirical formula for electron impactionization by & Zhang and detailedSampson (1988)balance relation to obtain the three-body recombinationcoefficients. One important characteristic of the &SampsonZhang formula is that it takes into account the so-(1988)called ““ continuum lowering ÏÏ e†ect (see The expression° 3).for the ionization rate coefficient of a level with principalquantum number n in an H-like ion of nuclear charge Z canbe written as (see eq. [35] of & ZhangSampson 1988)

Cn\ constant ]

CT

e1@2 n5

Z4 fn

Ay \ E

nkT

e

BD, (1)

where represents a function of n, y, e~y, and exponen-fn(y)

tial integral functions on y. From and detailedequation (1)balance the three-body recombination coefficients are

an3B(T

e, Z) \ constant ]

CT

e~1 n7

Z4 eyfn(y)D

. (2)

One can notice from that the three-bodyequation (2)recombination coefficients decrease with the nuclear chargeas

an3B(T

e, Z) \ Z~6a

n3BAT

eZ2 , 1

B. (3)

Also, by plotting versus n it is found that the three-bodyan3B

recombination coefficients increase with the principalquantum number roughly as n3. On the other hand, radi-ative recombination coefficients scale with Z as

an(T

e, Z)\ Za

ATe

Z2 , 1B

, (4)

and scale with the principal quantum number roughly asn~1. Therefore, the contribution of three-body recombi-nation to the total recombination process will shift towardhigher excitation states as the nuclear charge of the ionincreases. For example, under conditions of K andT

e\ 105

cm~3, three-body rates dominate over radiativeNe\ 1017

rates for direct recombination, not considering cascades, oflevels with n [ 8 for Z\ 6, n [ 11 for Z\ 8, and n [ 15 forZ\ 10.

In addition, three-body recombination rates increasewith respect to the radiative rates as decreases.T

eFigure 1

shows the ratio of direct three-body to radiative recombi-nation onto n \ 2 (Fig. 1, top), and the ratio of three-

FIG. 1.ÈRatios of three-body to radiative recombination rates onto then \ 2 levels (top) and summed from n \ 2 to n \ 50 (bottom) at N

e\ 1017

cm~3 as a function of the temperature.

body to radiative recombination summed from n \ 2 to 50(Fig. 1, bottom) as a function of for Z\ 8 and N \ 1017T

ecm~3. It can be seen that the direct recombination onto then \ 2 states, and all low-n states in general, is dominated byradiative recombination for any temperature unlessextremely high densities (greater than 1019 cm~3) werepresent in the plasma. However, the total recombinationrate onto the H-like ion and onto the n \ 2 states by meansof the cascades from higher states should be dominated bythree-body recombination at temperatures below approx-imately 3] 105 K for N \ 1017 cm~3. This will haveimportant implications for the ionization balance of theplasma and also for the emitted recombination spectrum.As three-body recombination occurs preferentially ontohighly excited levels, the line emission from these levelsshould be strongly enhanced. Lya emission is also enhanceddue to the cascades from high levels onto the n \ 2 statemultiplet.

The recombination spectra were calculated using anadapted version of the computer code developed by Smits

The recombination-collision-cascade problem is(1991).solved using the matrix condensation technique &(BurgessSummers All atomic rates for H-like ions are as1976).described in with the only exception being theSmits (1991),collisional ionization and three-body recombination coeffi-cients that were taken from & Zhang forSampson (1988)the present work. All lines, including the Lyman lines, aretaken to be optically thin. The main modiÐcations to the

model were in allowing for the lowering of theSmits (1991)continuum at very high densities. Our results agree within

16 16.5 17 17.5 18 18.5 191

2

3

4

I(Ly

α)w 3B

/ I(

Lyα)

w/o 3B

Z=8

Te = 5x104 K

105 K

2x105 K

16 16.5 17 17.5 18 18.5 191

2

3

4

log ( Ne ) [cm−3]

I(Ly

α)w 3B

/ I(

Lyα)

w/o 3B

Z=10

Te = 5x104 K

105 K

2x105 K

850 BAUTISTA ET AL. Vol. 509

2% with the results of & Storey andHummer (1987) Storey& Hummer for the species and range of conditions(1988)that they calculated.

The lowering of the continuum e†ect is very importantunder the high plasma densities considered here. This e†ectcomes about from cutting the high-n orbitals of ions due toparticle packing, Debye shielding, Stark broadening, andcollisional broadening. Under the conditions of interesthere, particle packing is the most important of these mecha-nisms. Particle packing occurs when the mean internuclearseparation in the plasma is smaller than the distance fromthe nucleus to the high-n ionic orbitals. By comparing themean internuclear separation in the plasma with the meansize of ionic orbitals of principal quantum number n, onecan deÐne a continuum level as (Hahn 1997)

nP\A1.8887] 108Z

N1@3B1@2

, (5)

where Z is the nuclear charge of the ion considered and N isthe nuclei density of the plasma in cm~3.

Debye shielding is the mechanism by which high-norbitals are shielded from the electrostatic attraction to thenucleus by a high density of free electrons. According to thismechanism, the continuum level is given by asHahn (1997)

nD

\ 2.6] 107Z2AT

eNB1@4

, (6)

where is in degrees kelvin.TeUnder a high concentration of singly charged ions in a

plasma, a microelectric Ðeld is formed that will lead to Starkbroadening of the atomic levels. Then, for sufficiently high-nnumbers, the atomic levels will merge with each other,which lowers the continuum. In this case the continuumlevel is given by & Teller(Inglis 1939)

nS\A1.814] 1026Z6

NB2@15

. (7)

For temperatures lower than 105 K (Z2/n), the electronscontribute to the broadening through the static Stark e†ect.Therefore the density N in the last equation should includeboth positive and negative charges. At higher temperaturesthe electrons contribute to the broadening by means of col-lisions, but this is smaller than the Stark e†ect of the sameelectrons at lower temperatures. At high temperatures onlypositive charges are considered for this equation.

Furthermore, one may deÐne as the minimum ofnC

NP,

and Then, only orbitals with may beNF, N

D, N

T. n \ n

Ctreated as bound, while orbitals with are mixed withn [ nCthe continuum and must be excluded from the calculation

of the recombination process. One can see that in the case ofoxygen, for example, under conditions of T \ 105 K andN \ 1016 cm~3, only levels with n ¹ 83 are bound, atN \ 1018 cm~3 only levels with n ¹ 38 are bound, andat N \ 1020 cm ~3 only levels with n ¹ 18 are bound.

shows ratios of Lya emissivities with andFigure 2without three-body recombination as functions of the elec-tron density for O VIII and Ne X It can be(Fig. 2a) (Fig. 2b).seen that the Lya emission can be enhanced by a factor ofseveral by three-body recombination at temperatures lowerthan approximately 2 ] 105 K and electron densitiesbetween 1017 and 1019 cm~3. On the other hand, the con-tinuum emission remains una†ected by this radiationlessrecombination process. For greater than about 1019N

e

FIG. 2.ÈRatio of Lya emissivities including three-body recombinationcontributions to those without three-body recombination[I(Lya)

w3B]as a function of the electron density. The upper panel corre-[I(Lya)w@o3B]sponds to the case of oxygen (Z\ 8), and the lower panel corresponds to

neon (Z\ 10).

cm~3, the multiplets n \ 2 in O VIII and Ne X are col-lisionally de-excited, and the Lya emissivity will no longerincrease with N

e.

3. COLLISIONAL EXCITATION AND IONIZATION

Excitation of the n \ 2 levels by electron impact excita-tion as opposed to recombination requires (1) sufficientlyenergetic electrons, and consequently high temperatures, tocross the large energy gap between the n \ 1 and n \ 2levels in H-like ions, and (2) a relatively high fraction of ionsin the H-like stage with respect to the fully stripped stage.We Ðnd, using collisional ionization rates of &SampsonZhang and radiative recombination coefficients for(1988)H-like ions from & Seaton that this lastBurgess (1960),condition is satisÐed for ions like O VIII and Ne X in col-lisionally ionized plasmas with temperatures up to severalmillion degrees (see also & RothenÑugArnaud 1985).

Both collisional excitation and ionization should scale inthe same way with the nuclear charge of the ion, which from

(see also eq. [12] of Sampson & Zhang) isequation (1)

Cnn{(T , Z) \ Z~3C

nn{A TZ2 , 1

B. (8)

Then, under collisional ionization conditions, the change inthe ratio of collisional to recombination emissivities with Zis balanced by the opposite change in ionization. By con-trast, in a photoionized plasma the ratio of collisional to

5.4 5.6 5.8 6 6.2−5

0

5

10

log

j(Lyα

) reco

mb

/ j(L

yα) co

ll (a)

5.4 5.6 5.8 6 6.2−12

−10

−8

−6

−4

−2

log ( Te ) [ K ]

log

I(Ly

α)re

com

b / I

(Lyα

) coll

(b)

16 16.5 17 17.5 18 18.5 194.6

4.8

5

5.2

5.4

5.6

5.8

6

6.2

6.4

log

(Te)

[K]

log (Ne) [cm−3]

Collisional excitation

Radiative Recomb.

Three−body Recomb.

Radiative+Three−body Recomb.

↑↓

No. 2, 1998 HYDROGEN-LIKE ION EMISSION 851

FIG. 3.È(a) Ratio of recombination to collisional Lya emissivities forO VIII as a function of the temperature. The dotted line represents the ratioof Lya to continuum recombination ratio. (b) Ratio of recombination tocollisional Lya intensities in a collisionally ionized plasma as a function ofthe temperature.

recombination excitation, assuming no changes in the ionicfractions, should drop with the nuclear charge roughly asZ~4, according to equations and(4) (5).

In order to study the collisional excitation mechanism ofLya in H-like ions, we construct a collisional-radiativemodel for these ions including all of the level up to n \ 5.The collisional excitation coefficients for energy-changingtransitions are as in and for angularJohnson (1972),momentumÈchanging transitions we use the impact-parameter method, but we include the modiÐcations sug-gested by & Storey Somewhat moreHummer (1987).accurate excitation coefficients may be used for selectedtransitions in some ions (see but that wouldCallaway 1994),not a†ect the general conclusions of the present work.

The solid curve in shows the ratio of recombi-Figure 3anation to collisional Lya line rate coefficients as a functionof for cm~3. This ratio is equivalent to the lineT

eN

e\ 1015

emissivities ratio for the case of equal ionic fractions forO`7 and O`8. The recombination to collisional Lya ratio isnearly independent of the electron density at low density(less than 1016 cm~3), since both line emissivities are lin-early dependent on One can see from this Ðgure that asN

e.

the temperature increases the recombination emissivitiesdecrease with respect to collisional excitation. Moreover,both emissivities become approximately equal at T

eD 1.1

] 106 K. Also in we show for reference the ratioFigure 3aof Lyman recombination continuum to collisional Lyaemissivity (dashed line).

FIG. 4.ÈO VIII Lya emissivity collisional-recombination phase diagramin the space. The radiative recombination-dominated regime is(N

e, T

e)

found in the region. The dotted line to the right separateslow-Ne, low-T

ethis regime from that where three-body recombination contributesbetween 10% and 50% of the total emissivity. The solid line limits the

regime dominated by three-body recombination. Thehigh-Ne, low-T

edashed curve at delimits the regime where collisionally excitedhigh-Teemissivities exceed the recombination ones.

In we plot the ratio of recombination to col-Figure 3blisional Lya emissivities as a function of for a collisionallyT

eionized plasma; that is, the ratio of line rate coefficientsmultiplied by the ratio of ionic fractions. This(Fig. 3a)

shows that despite the fact the recombination emissivitiesare greater than the collisional ones at low the lowT

e,

ionization of the plasma causes collisional excitation of theH-like stages to dominate the Lya emission. Moreover,because of the very small fraction of fully stripped ionsunder collisional ionization conditions, both Lya recombi-nation and the Lyman recombination continuum emissionshould be absent from the spectrum. Very high tem-peratures, greater than 3 ] 106 K in the case of oxygen, areneeded for the fraction of fully stripped ions to be largerthan that of the H-like stage ; however, at these tem-peratures the rate for collisional excitation continues todominate the emission of Lya.

The tentative identiÐcation of Lyman recombinationedges of Ne X in the spectra of 4U 1626[67 et al.(Angelini

and O VIII in the spectra of 4U 0614]09 provides1995)evidence of photoionization of the emitting plasmas asopposed to collisional ionization. This conclusion agreeswith the results of previous studies by Bu†, &Hatchett,McCray and & Paerels for the case of(1976) Liedahl (1996)

5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6−20

−10

0

10

log

(j Sat

ellit

es /

j(Lyα

) Col

l.)

(a)

5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6

−20

−10

0

10

log(Te) [K]

log

(IS

atel

lites

/ I(

Lyα)

Col

l.)

(b)

852 BAUTISTA ET AL. Vol. 509

of collisionally excited Lya to satellite lines emissionFIG. 5.ÈLog10rate coefficients (a) and line emissivities (b) vs. for Z\ 8,log10 (Te) N

e\

1010 cm~3, and N(O7`)/N(O6`) \ 1.

Cyg X-3. However, some contribution from collisional exci-tation of Ne X to the Lya intensity cannot be ruled out onthe basis of the Ne X Lyman continuum alone. It is possiblethat Ne is only partially ionized and a signiÐcant fraction ofit is in the form of Ne`9, which under sufficiently hightemperature conditions would be collisionally excited. Theorigin of temperatures D106 K that are needed for efficientcollisional excitation is unclear. Apart from a strong X-rayÑux, no other heating mechanism has been unambiguouslyidentiÐed.

shows the various phases of recombination andFigure 4collisional emissivities of O VIII Lya in the versusT

eN

espace. From this diagram one can see four di†erent regimes :(1) the radiative recombination regime that occurs at lowtemperatures and low electron densities ; (2) the three-bodyrecombination regime at low and high where moreT

eN

e,

than 50% of the Lya emissivity is due to three-body recom-bination ; (3) an intermediate radiative plus three-bodyrecombination regime where three-body recombinationcontributes between 10% and 50% of the total Lya emiss-ivity ; and (4) the collisional excitation regime at high T

e.

Note that the separation between the collisional and recom-bination regimes as indicated in corresponds toFigure 4Lya rate coefficients per ion, as opposed to line intensitiesthat depend on the actual ionic fractions. This separationwhen considering actual line intensities will shift upward ordownward depending on the ratio of fully stripped to H-likeoxygen being greater or smaller than unity, respectively.

4. RECOMBINATION SATELLITE EMISSION

Various emission lines at essentially the same energy asthe Lya line of a given H-like ion may be produced bydielectronic recombination onto double-excited levels of theHe-like stage of the same species. These satellite lines corre-spond to transitions of the form 2s2pÈ1s2s, 2s2pÈ1s2p, 2p2È1s2p, and 2s2È1s2p, and their energies cannot bedistinguished from that of H-like Lya using observedspectra with resolution less than dv/vB 50. For example,for the case of oxygen & SafronovaVainshtein (1978)predict at least 11 di†erent lines, all within 0.627È0.653 keV,compared with the central energy of the O VIII Lya line of0.653 keV.

The emission rates of these satellite lines per He-like ionwere calculated using transition branch coefficients from

& Safronova These emission-rate coeffi-Vainshtein (1978).cients and line emissivities are compared in Figures and5a

to those for collisionally excited Lya. In the5b Figure 5bionic fractions correspond to those of coronal equilibriumconditions. It can be seen that for similar ionic fractions ofH- and He-like oxygen, satellite emission is much strongerthan the collisional line for K. Moreover,T

e\ 2 ] 105

under coronal equilibrium conditions satellite emissiondominates over both collisional and recombination emis-sion for temperatures up to near 4 ] 104 K, at which 90%of the oxygen is in its He-like stage ; however, it is importantto point out that the total rate emissivity per ion of satellitelines is very small, e.g., 1.6] 10~26 ergs s~1 at KT

e\ 105

and N \ 1010 cm~3 compared with the recombination rateemissivity per fully striped ion at the same temperature of5.6] 10~11 ergs s~1. Thus, satellite emission will be weak ;yet in the absence of photoionization satellites it will domi-nate the emission spectra at low temperatures.

5. RESONANT FLUORESCENT EXCITATION

Excitation to the n \ 2 levels by absorption of photons ofthe continuum may also be a viable mechanism for Lyaemission, provided the right geometrical conÐguration ofthe plasma; that is, one can see the object from a directiondi†erent from that of the exciting radiation Ðeld. In addi-tion, it is necessary that a sufficiently strong photoexcitingradiation can reach the H-like ions without being absorbedby photoionization. This could happen if the gas imme-diately surrounding the radiation source is completelyionized and the photoexcitation of ions in the H-like stateoccurs in the outer cooling region. Resonant Ñuorescentexcitation is discussed in more detail by et al.Band (1990)and et al. in the context of iron emissionKallman (1996)from K and L shells in active galactic nuclei.

In the presence of a weak radiation Ðeld, and assumingtemperatures too low for efficient collisional excitation, thepopulation of the 2p state with respect to the 1s state in anH-like ion is

N2pN1s

\ B1s,2p J1s,2pB2p,1sJ1s,2p] A2p,1s

, (9)

where A and B represent the Einstein spontaneous andinduced transition probabilities, and is the radiationJ1s,2pdensity. Here the B Einstein coefficients are related to theA-value as cm2B2p,1s \ (4.5 ergs~1)A2p,1s/Z6 \ 2.82] 109/Z2 and Furthermore, as the nuclearB1s,2p\ 3B2p,1s.charge of the ion increases, much higher radiation Ðelds areneeded for the ion to be photoexcited. Nevertheless, pho-

5 5.2 5.4 5.6 5.8 6 6.20

.1

.2

.3

log(Te) [K]

I(Ly

β) /

I(Ly

α)

Recombination

Fluorescence

Coll. excitation

No. 2, 1998 HYDROGEN-LIKE ION EMISSION 853

toexcitation of O VIII may be quite efficient in the presenceof hard radiation Ðelds. For example, a plasma illuminatedby a 10 keV bremsstrahlung input spectrum with ionizationparameter m \ 300 yields a Lya line emissivity rate perO VIII ion of 6.3]104 ergs s~1, nearly independent of tem-perature and density but directly proportional to m. In asofter bremsstrahlung radiation Ðeld of 1 keV the Lya lineemissivity rate per O VIII ion is 2.3] 103 ergs s~1. By con-trast, collisional excitation yields Lya line emissivity rates at

cm~3 and K of 2.0] 10~31 ergs s~1, atNe\ 1013 T

e\ 105

K of 2.1] 10~5 ergs s~1, and at K ofTe\ 5 ] 105 T

e\ 106

3.2] 10~2 ergs s~1.Under a very strong radiation Ðeld all of the levels of the

H-like ion tend to populate proportionally to their sta-tistical weights ; however, as the population of the excitedlevels becomes comparable to that of the ground-state,photoionization from the excited levels should becomeimportant.

It seems clear that provided the right geometry forLMXBs, resonant Ñuorescent excitation could be quite effi-cient in enhancing Lya line emission.

6. OTHER LINES IN THE H-LIKE SPECTRUM

In the previous sections we have studied three di†erentmechanisms that could explain the observed Lya to Lymancontinuum ratio in X-ray spectra of LMXBs (e.g., three-body recombination, collisional excitation, satellite linesemission, and Ñuorescent excitation). However, lines otherthan Lya may be present in the spectra. For example, Whiteet al. report possible detections of O VIII and Ne X(1997)Lyb. These lines from higher n should be useful in pinpoint-ing the nature of the emission spectra and the ionizingmechanism of the plasma. This is because each of the excita-tion mechanisms described above is expected to yield di†er-ent Lya/Lyb ratios.

Recombination is an e†ective mechanism for populatingthe upper n levels of the recombining ion. Three-bodyrecombination can contribute signiÐcantly to the popu-lation of high-n levels, although the departure of theLyb/Lya ratio from the radiative ratio in ions like O VIII

and Ne X is very small, except for electron densities in excessof 1018 cm~3. By contrast, collisional excitation of excitedlevels from the ground state becomes very inefficient as theprincipal quantum number, and consequently the energy ofthe excited level increases. Thus the Lyb/Lya ratio shouldbe much lower under collisional excitation conditions thanfor the recombination case.

Contributions from satellite lines to the Lya featureshould not a†ect other lines of the H-like recombinationspectra ; then comparisons of lines like Lyb and Lyc withthe recombination spectrum may indicate the relativeimportance of satellite lines. In addition, since these linesare proportional to the fraction of ions in the He-like stage,these satellite lines and lines and emission from He-like ionsmust be related.

Fluorescent excitation of O VIII populates the excitedlevels above the values set up by collisional excitation. Thishas the general e†ect of enhancing the Lyb/Lya ratio withrespect to the collisional case. Nevertheless, the Lyb/Lyaratio photoexcited by a relatively weak radiation Ðeld willremain lower than that from radiative recombination.

The expected Lyb/Lya ratios for each of these scenariosare shown in for the case of O VIII atFigure 6 N

e\ 1015

cm~3 and m \ 300. Clearly, any combined contribution of

FIG. 6.ÈLyb/Lya emissivities ratio as a function of the temperaturesfor recombination emission, resonant Ñuorescent excitation with m \ 300,and collisional excitation at cm~3.N

e\ 1015

collisional excitation, satellites emission, or Ñuorescenceand recombination to the emitted spectra must yieldLyb/Lya ratios in between those shown in Figure 6.

The observed Ne X Lyb/Lya ratio in 4U 1626[67 iset al. and in 4U 0614]09 the0.18~0.07`0.11 (Angelini 1995),

ratio is Unfortunately, these measurements are0.32~0.26`0.20.insufficiently accurate to be used as constraints on theactual excitation mechanism for the lines. Moreover, itis possible that the weak features identiÐed as Lyb inthese spectra are unresolved blends that include lines otherthan Lyb.

7. IMPLICATIONS FOR ACCRETION MODELS OF LMXBs

In the previous sections we have shown that Lyman linesfrom H-like ions can be excited by a variety of mechanisms,each which imply a distinct set of physical conditions. If theconditions in the likely reprocessing regions of LMXBswere known with sufficient accuracy, it would be possible todiscriminate between these various mechanisms as originsof the observed lines. In practice, however, the conditions inthe accretion Ñows and reprocessing regions are highlyuncertain, owing to the inÑuence of several physical pro-cesses that are not thoroughly understood. As a result,instead of using theoretical models of LMXBs to limit therange of possible X-ray line emission, we consider linespectra to be a potential diagnostic of the accretion Ñows.

The most likely site for X-ray reprocessing in LMXBs isthe accretion disk or structures associated with it. An upperlimit for the disk size is given by the Roche lobe size, whichfor Cyg X-2 is D7 ] 1011 cm and in 4U 1626[67 isD7 ] 109 cm. Estimates of the conditions in the accretiondisk depend on the assumptions concerning viscosity.Under the customary a-disk model (see, e.g., &ShakuraSunyaev a disk around a 1 neutron star will1973), M

_range in midplane temperature from D104 K near the diskouter radius to D107 K near the innermost radius, and themidplane density would range from D1020 to D1024 cm~3over the same region. In the vertical direction the densitywill decrease exponentially with a characteristic scale heightdetermined by the temperature, and the temperature willdecrease due to the di†usive transport of radiation. Thissuggests that essentially any value of density or temperatureconsidered in our discussion of emission mechanisms can befound somewhere in the disk.

854 BAUTISTA ET AL. Vol. 509

Recent work on disk structure has shown that a likelymechanism for angular momentum loss is the magneto-rotational instability & Balbus in which dis-(Hawley 1995),sipation is provided by the stretching of magnetic Ðeld linesin the strongly shearing Keplerian Ñow. This mechanismimplies magnetic activity that may heat the surface layers ofthe disk to temperatures signiÐcantly greater than thosepredicted by the a-disk model. This provides a possibleorigin for the temperatures necessary for collisional excita-tion emission of Lyman lines ; however, models for diskmagnetic activity are not yet sufficiently reÐned to accu-rately predict the heating rates and temperatures.

Illumination of the disk outer layers by X-rays will alsochange the disk structure and can provide conditions suit-able for line emission. The temperature and ionization ofX-rayÈilluminated gas can be parameterized in terms of theionization parameter m \ L /NR2 Tucker, & Salpe-(Tarter,ter At high values of this quantity, say m º 105 ergs1969).cm s~1, the gas is fully ionized and the temperatureapproaches the ““ Compton temperature ÏÏ K),(TIC D 107which is the temperature where Compton heating is bal-anced by inverse Compton cooling. At lower values of m thegas is partially ionized and cooler ; therefore, illumination ofthe hydrostatic disk will produce a hot, fully ionized coronaat above the disk photosphere, transition region, andTICchromosphere in a structure reminiscent of the Sun

McKee, & Shields Conditions suitable for(Begelman, 1983).emission of O VIII and Ne X Lyman lines will exist at someheight where the ionization parameter is m ^ 300. At thisionization parameter ionization heats the gas to D3 ] 105K, a temperature too low to allow efficient collisional exci-tation. The density in this region is given by

N17R92\ 3.3L 38m300

, (10)

where cm~3, cm,N17 \ N/1017 R9\ R/109 L 38 \ L /1038ergs s~1, and ergs cm s~1. This shows thatm300 \ m/300three-body recombination will dominate the Lyman lineemission at radii less than ^109 cm. One additional uncer-tainty is the inÑuence of radiation transport through thecorona, which may limit the illumination to radii less than109 cm & White Chiang, &(Kallman 1987 ; Murray,Chiang This provides additional support for the1996).three-body recombination as the dominant Lyman lineemission mechanism.

8. CONCLUSIONS

We have studied the various excitations mechanisms forLya, Lyb, and Lyman continuum emission from H-likeions, particularly O VIII and Ne X, which are observed in theX-ray spectra of LMXBs. We Ðnd that the observed Lymancontinuum edge can only be explained if the plasma is pre-dominantly photoionized, in agreement with previousresults by et al. and & PaerelsHatchett (1976) Liedahl

Furthermore, the large Lya to Lyman continuum(1996).ratios observed could be explained by the following :

1. Three-body recombination in a plasma cooler thanD3 ] 105 K with an electron density of the order of 1017cm~3 or higher.

2. Contributions to the line emission from collisionalexcitation of the H-like ionization stage in addition torecombination of the fully stripped ions.

3. Satellite lines from recombination onto the He-likeionization stage.

4. Resonant Ñuorescent excitation by the continuum.

In terms of the Lya emissivities one can deÐne variousregimes in the space according to the relative(T

e, N

e)

importance of radiative recombination, three-body recom-bination, and collisional excitation. Three-body recombi-nation and collisional excitation would requite very highdensities or temperatures, respectively. Such conditionsmay exist at some point within the accretion disks ofLMXBs. Then observed line spectra should provide impor-tant constraints on hydrodynamic models of LMXBs.Under low temperature conditions and in the absence ofstrong radiation Ðelds, satellite lines are the dominant emis-sion mechanism at energies around that of Lya, althoughvery large column densities are needed for these lines to beobservable. Resonant Ñuorescent excitation may be a muchmore efficient mechanism, but it depends critically on thegeometry, intensity, and shape of the radiation Ðeld.

Additional spectroscopic observations of LMXBs withinstruments of higher resolving power and sensitivity, suchas those on AXAF, will yield accurate measurements of Lyband other lines from higher n. These lines in combinationwith Lya and the Lyman continuum measurements shouldhelp to determine the excitation mechanism of the plasma,as well as its ionization structure and physical conditions.Reliable measurements of emission from other ionizationstages such as He-like emission should also be useful.

Optical thickness of the emission may be another impor-tant e†ect to consider in the analysis of H-like emissionspectra ; however, this e†ect depends speciÐcally on thegeometry and bulk motions of the plasma. Observations oflines from higher n should also provide some informationon this regard. Under many astrophysical situations,Lyman series transitions become optically thick while allother series transitions remain optically thin. In these con-ditions Lyman series photons emitted by a recombiningH-like ion will be immediately absorbed by another ion inthe vicinity and then reemitted. After a few such resonantscatters the excited electron makes a less-probable tran-sition into lower energy levels with n [ 1 and particularlyn \ 2. This results in a degradation of the high-orderLyman series photons into emission from other series suchas Lya and a two-photon continuum. A detailed calculationof optical depth e†ects will have to await observationalinformation about column density and the bulk motions ofthe plasma.

More detailed modeling of the spectra of LMXBs isunderway by incorporating the physics mechanismsdescribed in this paper into the photoionization modelingcode XSTAR & Krolik(Kallman 1994).

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