## 3. The Li I 6708 line in spectra of self-irradiated accretion discsAccording to our assumptions in Sect. 2, the equivalent width, , of a spectral line in the spectrum of a self-irradiated accretion disc can be determined by the expression where (R) is the equivalent width of the
line in the spectrum of the disc ring of radius R and
is the local continuum flux at the line
wavelength. In our case is adopted as the
in the spectrum of a star with the same
and log Here , and = 4530 K are the fit parameters, which depend on the Li abundance. This analytical approximation has been found from our LTE calculations of the equivalent widths of the resonance doublet which were performed using Kurucz (1993) stellar model atmospheres. A comparison of our results with those of Gerbaldy et al. (1995) is shown in Fig. 1. The accuracy of the fit is better than 20 in the range 4500 K to 6000 K, and it is of the same order for higher temperatures (up to 9000 K) if mÅ.
A rough estimate of the equivalent width of the Li I line in the spectrum of the accretion disc can be obtained by adopting a black body approximation for the flux in the continuum. We have from Eq. (8) where and the integral in the denominator has been calculated assuming an infinitely large disc (Lynden-Bell 1969). A first-order approximate integration yields: which is accurate to better than 12 as
compared with the exact results from Eq. (10). This last expression
can be used as a crude estimate of the Li I 6708
line equivalent width in spectra of X-ray novae. In order to
illustrate this we show in Fig. 2 the dependence of the smallest outer
disc radii which allows the equivalent width of the Li I line to be
greater than 10 mÅ versus the relative disc luminosity for
three values of the mass of the compact central object. We assume log
In order to explore the behaviour of the Li I
6708 line equivalent widths we have applied Eqs. (10) and (11) in a
wide range of accretion parameters and Li abundances. Masses were
ranged from 1 to 10 ,
from 0.001 to 0.3, from 10 It was then decided to conduct a more precise calculation of the
equivalent widths of the Li I resonance doublet and
in the spectra of the self-irradiated
geometrically thin optically thick accretion
-discs around Schwarzschild black holes. The spectra were calculated
following the prescriptions given in Sect. 2 and in previous work by
Suleimanov (1996) using the computer code STARDISK based on the code
ATLAS5 (1970). The value of was calculated
assuming The computations were done for a set of reasonable disc model
parameters:
As it is evident from Figs. 3-7, the Li I resonance line may be observed provided the disc luminosity is less than 0.01 . The equivalent width depends slightly on and the central object mass, but the larger and the Li abundance the greater the of the Li I line. And, vice versa, the smaller the disc inclination the greater the of the Li I line. According to our calculations if the equivalent width of is greater than 10 the Li I line has 20 m and can be detected. The exact results seem to be identical to estimate calculations and have close correlation with conditions (5) and (6). This means that conditions (5) and (6) may be used for other lines too. © European Southern Observatory (ESO) 1998 Online publication: January 27, 1998 |