*Astron. Astrophys. 330, 999-1004 (1998)*
## 2. Formation of absorption lines in the spectra of self-irradiated discs
Let us first describe the method used to calculate the total
radiation spectrum of self-irradiated, optically thick, geometrically
thin, accretion discs (Suleimanov 1992, 1996). We denote as *F
* the final spectrum that results from the
addition of the individual local ring spectra
:
where *i* is the inclination angle of the disc with respect to
the line of sight, *R* is the radius of the local ring and
and are the inner and
outer boundary disc radii, respectively.
For , we will adopt the spectrum of a stellar
atmosphere with the same effective temperature
and log *g*, provided that the ring effective temperature is less
than 50000 K and the relation of incident X-ray flux
to intrinsic ring flux
is less than a certain critical parameter *A*. If these
conditions do not hold, the ring is assumed to radiate as a black body
with a temperature equal to .
The intrinsic ring flux is determined by the following equation
(Shakura & Sunyaev 1973):
where *M* is the mass of the central compact object and
is the accretion rate.
The incident flux is described following Ko & Kellman (1991)
as:
where is the energy conversion factor,
*c* is the speed of light and *f* is the fraction of the
total incident flux on the disc at a given radius *R*.
Using formulae (2) and (3), the boundary disc radius
can be obtained:
where it has been assumed that /
equals *A*. Here .
We note that the ratio to
is greater than *A* if *R* is larger
than .
The value of the parameter *A* depends on the structure of the
irradiated atmosphere of the disc and it is different for different
lines. Since no precise calculations are available, *A* should be
regarded as a free parameter for each line. Sakhibullin &
Shimansky (1996) found from exact LTE calculations of irradiated
stellar model atmospheres, that lines of ions are more affected by
external X-ray radiation than neutral element lines. The effect of
X-ray irradiation on the lines of neutral elements is even lower if
departures from LTE are taken into account (Sakhibullin &
Shimansky 1995). The results obtained by these authors support our
approach here.
The second parameter that characterizes a spectral line is the line
temperature, , determined as the T
of the stellar model giving the highest
equivalent width of the line. As a consequence of the adopted
self-irradiation model, it is required that is
higher than the temperatures of the outer disc and boundary disc
radii. These conditions can be re-written by using the usual
parameters of accretion discs, , *M*, and
relative disc luminosity :
The previous conditions allow us to establish which absorption
lines might be observed in the spectra of X-ray novae if the accretion
disc parameters *M*, *L*, and
were known. Conversely, the values of these
parameters may be estimated from the observation of absorption lines
in these spectra.
For example, the relation (6) can be rewritten as
where the Balmer lines temperature was taken as 10000 K. Since the
current estimates of the masses of the compact primaries in X-ray
novae lie in the range 1-10 M and relative
luminosities of X-ray novae can be estimated as
0.1-0.01 during outburst decay, the value of the parameter
cannot be greater than 10^{-4}
-10^{-5} if the Balmer lines have absorption wings as seen in
the spectra of GRO J0422+32 and XN Vel 1993 (see references above). We
note that direct calculations of give similar
values (Suleimanov 1996). This implies that the parameter *A*
has a value close to 1 or smaller if scattering radiation in a wind or
corona were important in the irradiation of the accretion disc.
© European Southern Observatory (ESO) 1998
Online publication: January 27, 1998
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