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Astron. Astrophys. 363, 1055-1064 (2000)

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5. Discussion

In the previous section we have presented equations of a stellar model atmosphere irradiated by the external hard X-ray flux. In contrast to the existing photoionization codes (cf. Sect. 2), we were able to compute precisely transfer of radiation both in optically thin and thick layers, using all tools of the model stellar atmosphere computations. In other words, our new code ATM21 accurately reproduces radiative transfer and temperature structure both in the hot and cold region simultaneously. At the same time conditions of radiative and hydrostatic equilibrium are rigorously fulfilled. All the models were computed with the LTE equation of state, and with exact treatment of Compton scattering.

As a result, we are able to present and discuss realistic model atmospheres of a B3 V star, isotropically illuminated by very hot X-rays ([FORMULA] K). We stress here, that the model equations and in particular Compton scattering redistribution formulae are valid for arbitrarily large photon energies and for very hot electrons even with relativistic thermal motion. Also for gas temperatures in which electrons are not relativistic, all the expressions and coefficients in model equations are determined from fully relativistic formulae.

Perhaps the most prominent effect of the external irradiation by X-rays on a stellar atmosphere is the development of high temperature outermost zone, with a very steep temperature drop at some optical depth. This is the penetration depth [FORMULA] defined as

[EQUATION]

introduced by Hubeny (1990b), who considered analytically the atmosphere of a grey accretion disk with the external illumination. Below the penetration depth the influence of external irradiation gets negligible.

Fig. 1 and Fig. 2 show qualitative agreement with Hubeny (1990b), since our model calculations show that there is distinct temperature jump between the zone with obvious effects of the external illumination, and the deeper zone where heating effects are less pronounced. Both figures demonstrate, that the [FORMULA] increases roughly linearly with [FORMULA]. There exist, however, very large quantitative differences. For example, at [FORMULA], Eq. 27 predicts that the penetration depth is of the order unity, whereas model atmospheres plotted in Fig. 1 and Fig. 2 exhibit the transition [FORMULA] two orders smaller. Such a disagreement is not surprising, since the meaning of [FORMULA] in our models is different from the meaning of grey optical depth in Hubeny (1990b).

Theoretical spectra of iron-rich models exhibit numerous b-f iron opacity edges in emission, for wavelengths [FORMULA] Å (Fig. 6). They belong to various ionization states, ranging from Fe XVI-XVII (emission edges at 8.48 and 9.15 Å in the spectrum of [FORMULA]), up to Fe XXIII (edge at 6.25 Å in spectra with larger [FORMULA]). Hubeny (2000) noted, however, that the identification of Fe ionization states in LTE models is highly inaccurate. He estimates, that in typical NLTE model atmosphere there is a shift of 2-3 iron ionization degrees up, as compared with the LTE model.

In our computations we did not obtain any evidences for thermal instabilities. It is widely believed that such instabilities should develop in illuminated disk atmospheres (Krolik et al. 1981; Rózanska & Czerny 1996; Rózanska 1999). Most likely we did not encounter such instabilities, because the method of iterating model stellar atmospheres requires the radiative equilibrium, and the numerical methods simply do not allow for ambiguous temperature profile, which can be achieved in simple cooling and heating balance calculations presented by Rózanska & Czerny (1996).

This paper was designed for the study of external illumination effects in the atmosphere of a star. However, we believe that the results of our paper can be directly applied to the interpretation of very distinct spectral features observed in AGN. The difference between stellar atmosphere and accretion disk atmosphere is that in the latter case we cannot neglect dissipation of energy via viscous processes. Therefore strict radiative equilibrium cannot be assumed there. Also gravity is not constant across the atmosphere of a disk.

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© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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