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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

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, i.ee, 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.