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Gas Flow and Generation of X-Ray Emission in WR + OB Binaries v.v. usOv Institute of Space Research ABSTRACT The supersonic flow of the ionized gas in WR+OB binaries and X-ray generation are considered. X-ray emission is caused by gas heating up to temperatures of 107-108 K behind the front of shock waves. These are formed in the collision of gas flowing out from the WR star with either the OB star's surface or the gas of the OB star's wind. The distribution of temperature and concentration behind the shock front are obtained. Using these distributions, the spectral power of bremsstrahlung X-ray emission of hot gas is calculated. Possible reasons that lead to considerable difference between the observed parameters of X-ray emission of the WR binary of the V 444 Cygni and the theoretically expected are discussed. INTRODUCTION Wolf-Rayet stars (WR) possess a very intense stellar wind. The mass loss rate for WR stars, MOOR, and the velocity of the matter outflow, DOWRY, far from the star amount to 10-5 M~,/year and ~~1-3~-108 cm/s, respectively. No less than 40% of WR stars belong to rather close binaries. Young mas- sive stars of the specnal type O and B are the second components of these systems. OB stars also possess the intense stellar (MOB ~ 10~6Mfyear, NOB 1~ cmlS). More than a decade ago it was shown by Prilutskii and Usov (1975, 1976) that binary systems consisting of WR and OB stars should be rather strong X-ray sources (the X-ray luminosity can reach about 1033 to 1034 erg/s). According to Priluts~i and Usov (1975, 1976) the X-ray emission of such systems is due to heating the gas up to temperatures of 394

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HIGH-ENERGY ASTROPHYSICS 395 about 107 to 108 K behind the front of shock waves which are formed from the collision of the gas flowing out from a WR star either with the OB star surface or with We gas of the OB star stellar wind. 1b date, X-ray emission has been observed from more than twenty WR stars (Seward et al. 1979; Moffat et al. 1982; Caillout et al. 1985; Pollock 1987) and at least some of these stars possess X-ray emission of the nature described in Prilutskii and Usov (1975, 1976~. Below we will discuss parameters of the X-ray emissions calculated for WR+OB binaries. CLASSIFICATION OF lam GAS WOW IN WR+OB BINARIES If the intensity of the stellar wind of WR and OB stars are comparable or if the distance D between the components of a binary is great enough (see below) the winds flowing out of WR and OB stars can collide. ~ estimate approximately the distances row and row from WR or OB stars, respectively, to the region where these winds meet, it is necessary to put dynamical gas pressures of both winds equal to each other: PwR(rwR) tV( )] = Pos~rogiv(0B)42 Thus we can get (1) [MWRV(WR)] 1~2 [MOB V(OB)1 1/2 (2) MWR.V(WR)11/2 + EMOBV(B)11/2 ' here and below the index oo means that the given value should be taken at the great distance r from the star where this value is already independent of r. The velours of the matter outflow vower) is varying from zero on the OB star surface to v(B) for r > r* (Barlow 1982), where r* Is approximately equal to (3-5)R, R is the OB star radius. If row > r* the stellar winds collide (see Figure 1~. If row< r* the stellar wind from an OB star may be suppressed from the side facing a WR star, and the gas of the WR stellar wind is colliding win the OB star surface. Below we will consider these cases. COLLISION OF WR STE:LI^R WIND WITH OB STAR SURFACE First, let us discuss the flow of the completely ionized gas, flowing spherically-symmetrically out of a WR star, over an OB star. The effect of the OB star's gravitational field on the gas stream around this star will be

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396 A---.] 1 r l D i" -_ 1 AMERICAN AND SOVIET PERSPECTIVES / W~ '-1 ~- ,- rWR L-, , _ - TO - ' l FIGURE 1 Formation of shock waves in WR+OB binaries: a) the flow over an OB star by the gas outflowing from a WR star, by the collision of two stellar winds; F and G are shock waves; E is the contact surface. The region of hot gas is shaded. negligible. In this case, since D >> R. the undisturbed gas stream in the vicinity of an OB star can be assumed plane-parallel. For WR + OB binaries and with Apical parameters of WR stars (I'm = 108 cm/s, M = 10-5 M/year, D = 10~3cm, the stellar wind gas temperature T = 105 K) the parameters of the gas ahead of the shock front in the OB star vicinity will be the following: the gas density pod = 10-~4 g/cm3, the sound speed v, = 106 cm/s, the free-path length of particles 1 = 109 cm, the Mach number M = Z/oo/~5 = 102, and the Reynolds number Re = (R/l)(voo/v5) = 1~ Mere R = 10 Rat is the OB star radius). In this Section we will not write the index WR. With the above values of RID, M, and Re, the gas Dow in the shock layer around a star can be suggested to be supersonic, uniform, unviscous, and non-heat conductive. The set of equations which describes the gas flow between the shock wave and the body will be the continuity equation: div~pv) = 0 the momentum equation the energr equation: (3) (pv=)v = -Vp QpvVH = - , (4) (5) where H=HO+~v~2/2 Since the gas in the shock layer is almost totally ionized its pressure p and its specific enthalpy Ho can be expressed as

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HIGH-ENERGY ASTROPHYSICS 397 p=(N++N_)kT=P ,Ho= ~ P. mall ~-l p (6) here N+ = p/mpA is the concentration of nuclei N+ = N+Z Is the concentration of electrons; A is the atomic weight; Z is their electrical charge; k is the Boltunann's constant; mp is the proton mass; ~ = A/~1+Z3 is the mean molecular weight; ~ is the ratio of heat capacities with the constant pressure and the constant volume, equal to S/3 for the rarefied totally ionized plasma. Helium predominates in the gas of the WR stellar wind. In this case, A = 4; Z = 2; ~ = 4/3. The ionized gas heated in the shock layer is emitted mainly due to free-free transitions of electrons in Coulomb fields of ions. Here the energy loss per unit gas volume by radiation is (Hayakawa 1973~: Q = /Q~,d~ = C~N+IV_Z2Ti12 erg/s cm3 (7) where T is in degrees; Cat = 1.42~> 10-27 g(l); g(T) is the Gaunt factor which changes slightly with varying T (from 1.1 to 1.45), Qua Cih N~N_Z2ex~t-kT]erg/s cm3 Nz (8) k''/~ is spectral power of the bremsstrahlung at a frequency of z'. Let us now consider the boundary conditions for the set of equations (3) through (S). Gas parameters ahead of the shock front (index 1) and behind (index 2) are interrelated via the Rankine-Hugoniot relations pi v( ) = P2 V2n) Pi + pi~v( )42 = P2 + p2iV(n)32 V(~) = V(T) .H = H (9) Indices n and ~ denote the normal and tangential components of the vector v. The condition v(n) = 0 is met on the star surface. The set (3) to (S) with the boundary conditions (9) can be solved by the method of expansion in terms of the small parameter ~ which is the ratio of gas densities ahead and behind the shock front (Cherry l9S9). For our purposes, M >> 1, and the value ~ is equal to ~y-1)/(~+1) = 1/4. Using only the first elements of expansion in terms of ~ one can get the following expressions for the pressure and temperature of the gas behind the shock front (Galeev et al. 1989~: P(0, ~) = p=V2 (COS2 ~ _ ~ sm2 ~ ~ ~ S=3 ~ ~ (10)

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398 AMERICAN AND SOVIET PERSPECTIVES / NOR \ FIGURE 2 The bow over a star by the plane-parallel stream of the ionized gas. Here N is the point where the stream line with K-point on it intersects with the shocl: Bond T(6, A) = T3(0) {costs ~-3 . ~ [O-~ + sin26-sinew + sins = (I tg (~/2~] }, Where (11) T3(0) = ep~pv2 k-1 = 3 107(v=/108 ~s-1)2K, (12) 4RClpoovoo lo= 15k2~/2(o (13) In the shock layer, the angles ~ and ~ are employed as coordinates of an arbitrary point K (see Figure 2). With a distribution of p and T lmown behind the shock front it is easy to find the spectral power of the bremsstrahlung of the gas heated in the shock

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HIGH-ENERGY ASTROPHYSICS 399 Lv= ~QudV=; ~ 2HR3Q PA =3~d~dO (14) Not to decrease essentially the accuracy of calculations of X-ray em~s- sion parameters, one can neglect the Busemann correction in the ex- pressions for P(O,~) and T Em,; (the Newton approximation). In this approximation for the case when the energy losses of the hot gas via ra- diation are small (E << 1) the value L,is determined by the expression (Galeev e! al. 1989) V kT,tO3( ~ 2)/ i2 where L = Jr( ~ ~ 2) 1 A2RTP(=oyly2k / ~ 2 M \ ~ 10~5M~ >/yr ) (l0~3cm) (10sCm/s ~ erg/s ( ~ )3 Van ~ ~ -1 2 e]exp [ kT~(O)cos2~3] do (15) (16) is the total hot-gas bremsstrahlung power. The bremsstrahlung spectrum of the gas heated in the shock wave during the supersonic flow over the star has an exponential drop at high frequencies (hi, >> kT5~0~) and a relatively complicated shape at the frequencies he ~ kT5 (O). COI T. ISION OF SUPERSONIC WINDS Here we could discuss only parameters of the bremsstrahlung (X-ray) emission of rather wide binaries WR + OB (roB ~ ray. The stellar wind of a WR star Is much more powerful Ban that of an OB star (WRY v(WR) >> Mod v(B)~. In this case, one might assume that there Is a collision of the stellar wind flowing out of an OB star with the plane-parallel gas Dow whose density and velocity are pea = MWR/4D2r(WR) and v(WR) respective". In a Newtonian approximation the contact surface equation will be: r(43) ~ rod SO ~ e (17)

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400 AMERICAN AND SOVIET PERSPECTIVES Using the method of expansion in terms of the small parameter ~ to solve the problem where the plane-parallel gas Bows over an anal- symmetric body with a surface described by equation (17), similar to the solution above for the case of the Dow over the sphere we obtained the hot gas temperature and pressure distributions. With these values Mown we also got the total and spectral powers of the hot gas bremsstrahlung. This emission spectrum shape turned out to be close to that described by equation (15~. The bremsstrahlung power increases significantly as compared with equation (163 and is equal to io36 ~ MOOR/ ) (1013Cm) (iO'cm/6) (I ) g/ (18) This is due to increasing the size of an "obstacle" flowed over by the WR stellar wind gas. INTERPRETATION OF TlIE V 444 CYGNI X-RAY EMISSION The system V 444 pygni is one of the well-studied WR + OB binanes. It consists of the Wolf-Rayet star WN4 and the star of the 06 spectral type, and it has the following parameters (see Shore and Brown 19883: D-40 R OCR for page 394
HIGH-ENERGY ASTROPHYSICS 401 the order of magnitude lower than those expected from the simple theory for collisions of stationary weds (Prilutskii and Usov 1975, 1976). The accuracy of calculations of gas parameters behind the shock front and the gas emissions is of the order of c, i.e., several tens of percent. Thus, it is evident that the model for the gas Dow in V 444 Cygni before its collision should be changed qualitatively. A relatively low gas temperature behind the shock front (kT ~ O.5keV) evaluated from the V 444 C`,rgni X-ray data shows that ahead of the shock front the stellar wind gas of the WR star has the velocity not higher than 108 calls. At first sight, it seems to be unbelievable since at such a distance from the WR star (row ~ 28 Rat ~ 10RW R) the gas Dow velocity should be equal to v(WR). Note, however, that with V 444 pygni parameters given above the distance from the contact surfact to the O star center is rO6 ~ 1.2 Roe (see equation (2~), he. the wind collision occurs near the O star surface. In this case, the gas Dowing out of We O star is accelerated due to the emission pressure only by a small fraction of v(06). In turn, the stellar wind gas of the WR star will be decelerated by the pressure of its emission while approaching the O star. The law of how the velocity of the stellar wind gas of the WR star varies along the line connecting the centers of the WR and O stars can be written as: of ~ (r) = ~ (v(WR)] + tV(06~(r)] - tV(06~] ~ (19) where v(06) (r) is the O star's wind velocity at a distance of r > Ro6. The distance rO6 to the stagnation point of the contact surface from the O star center can be determined from the condition: MOBV(O6)(rO6) MWRV (rO6) (20) roe (D-roe) From (19) and (20) we can get MO6V( (D-ro6)2V(6)(rO6) = MWRVOO r 7 2 )/[v(wR)]2 + [V(6)(ro6)]2-[BOO] (21) In our case, v(WR)OO = v(06)00 from Equation (21) it is evident that rO6 coincides with (2) derived above,, the allowance for the WR star wind deceleration does not change the position of the stagnation point of the contact surface. The velocity equalibr, v(WR) (rO6) ~ v(06) (rO6), holds

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402 AMERICAN AND SOVIET PERSPECTIVES true in this case. But the gas velocity ahead of the shock front can decrease drastically. Let us estimate the value v(WR) (rO6~- So far the problem of how me velocity of the outflowing gas in the vicinity of the O star changes has been studied insufficiently (Barlow 1982~. For example, assuming the linear law of the velocity change as v(06) (r) = voO(06) [(r/RO6~-l] we can get v(wR) (rO6) ~ 0.2 v(WR) :~ 0.5 108 cm/s. If ,^~` _ . _ ~ race , ~ fnRN ~ ~ _ , ~ ~ . . the v`U0J(r) changes obeying the law view (r) = voO-)~/l - (Ko6/~) wick seems to be more real, we can get v(WR) (rO6) ~ 108 cm/s. Thus, the allowance for the deceleration of the gas of the WR star's stellar wind in the O star's vicinity can lead to gas velocities ahead of the shock front equal to about (0.5 to 1) 108 cm/s. This makes it possible to explain a low temperature in the X-ray spectrum of V 444 Cygni. The deceleration of the gas of the WR star's stellar wind and the X-ray absorption can result lowering the X-ray luminosity of V 444 Cygni down to the observed value. REFE:RENCES Barlow, MJ. 1982. Observations of mass loss from OB and Wolf-Rayet stars. Pages 149-172. In: Deloore, CW.H, and AJ. Willis (eds.). Wolf-Rayet stars: Observations, Physics, Evolution. IAU Symp. No. 99. D. Reidel, Dordrecht Caillaut, J.P, GA Chanan, DJ. Helfand, J. Patterson, Joy Nousek, UP. Talako, G.D. Bothun, and R.H. Becker. 1985. The peculiar X-ray and radio star AS 431. Nature 313:376-378. Chernyi, G.G. 1959. The Gas Flow with High Supersonic Velocity. Fizmatgiz, Moscow. Galeev, AA, N.N. Pil~ugin, and V.V. Usov 1989. Generation of X-ray and radio emission lay binary Wolf-Rayet stars. Pages 125-129. In: Proc. Varenna-Abastum~ni International School and Workshop on Plasma Astrophysics, held in Varenna, Italy. Vol. 1. Hayakawa, S. 1973. Ongina of Cosmic Ray. Nagoya, Japan. Moflat, AFJ., C F~rmani, I.S. Moran, and W. Seggewiss. 198Z Time-dependent X- ray observations of Wolf-Rayet binaries with O-type and with suspected compact companions. Pages 577-581. In: de Loore, CW.H., and AJ. Willis (eds.~. Wolf-Rayet Stars: Observations, Physics, Evolution. IAU Symp. No. 99. Reidel: Dordrecht. Pollock AM.T 1987. The EINSTEIN view of the Wolf-Rayet stem. Astrophys. J. 320:283. Prilutskii, O.F., and V.V. Usov. 1975. On X-ray radiation of the close binaries with young massive stars. Astron. Circ. 854:1-2. Prilutskii, O.F., and V.V. Usov. 19 76. On X-radiation of double systems containing Wolf-Rayet-type stars. Sonet Astr. 20:2. Seward, F.D., W. Forman, R. Giacconi, R. Griffiths, F.R. Harnden, Jr., ~ Jones, and J. Pye 1979. X-ray mom Eta Cannae and the surrounding nebula. Ap. J. ~etters3 234:L55-L58. Shore, S.~. and D.N. Brown. 1988. Colliding stellar winds in the eclipsing Wolf-Rayet binary V 444 Cygni. Ap. J. 334:1021-1037.