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Astron. Astrophys. 330, 999-1004 (1998)

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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 [FORMULA] the final spectrum that results from the addition of the individual local ring spectra [FORMULA]:

[EQUATION]

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 [FORMULA] and [FORMULA] are the inner and outer boundary disc radii, respectively.

For [FORMULA], we will adopt the spectrum of a stellar atmosphere with the same effective temperature [FORMULA] and log g, provided that the ring effective temperature is less than 50000 K and the relation of incident X-ray flux [FORMULA] to intrinsic ring flux [FORMULA] 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 [FORMULA].

The intrinsic ring flux is determined by the following equation (Shakura & Sunyaev 1973):

[EQUATION]

where M is the mass of the central compact object and [FORMULA] is the accretion rate.

The incident flux is described following Ko & Kellman (1991) as:

[EQUATION]

where [FORMULA] 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 [FORMULA] can be obtained:

[EQUATION]

where it has been assumed that [FORMULA] / [FORMULA] equals A. Here [FORMULA]. We note that the ratio [FORMULA] to [FORMULA] is greater than A if R is larger than [FORMULA].

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, [FORMULA], determined as the T [FORMULA] 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 [FORMULA] 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, [FORMULA], M, and relative disc luminosity [FORMULA]:

[EQUATION]

[EQUATION]

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, [FORMULA] and [FORMULA] 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

[EQUATION]

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 [FORMULA] and relative luminosities [FORMULA] of X-ray novae can be estimated as 0.1-0.01 during outburst decay, the value of the parameter [FORMULA] 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 [FORMULA] 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.

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© European Southern Observatory (ESO) 1998

Online publication: January 27, 1998
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