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Astron. Astrophys. 362, 1-8 (2000)

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5. Discussion and conclusions

We have considered a model for the X-ray emission from an accretion disk illuminated by virialized protons from an ion supported torus or an ADAF. This situation may arise in the transition region between a cool disk and an ADAF, or in cases where a cool disk survives to some distance inside an ADAF. Another possibility might be a magnetic flare-heated disk corona (e.g. di Matteo et al. 1999), if ions are heated there to values near the virial temperature.

For definiteness of the model, we have assumed that the dissipation of gravitational energy mainly takes place in the ADAF or corona which supplies the hot ions, and only a small fraction of the gravitational energy is released in the cool disk that acts as target.

The heating of the cool disk by the protons produces X-ray spectra that are very reminiscent of the hard spectra of accreting galactic black holes and AGN. The spectra have a power law slope in [FORMULA] with spectral index [FORMULA] in the galactic BH case and [FORMULA] in the AGN case. There are only small deviations between the spectra depending on the distance from the hole and the mass of the hole.

The constancy of the spectral slope can be traced to two factors. One is the Haardt-Maraschi regulating mechanism. By the energy balance of the Comptonizing layer, the contributions of the soft and hard photons to the luminosity adjust to become roughly equal. The spectra still depend on the assumed thermalization depth, however, as seen in Fig. 3. To get an approximate fix for this depth, we have adjusted it such that the free-free emission from the layer matches the downward flux of photons at the base of the layer. With this approximation, the thermalization depth closely tracks the maximum penetration depth of the ions, so that the Comptonization conditions are quite similar in all cases. This further increases the similarity of the spectra. This similarity can be checked also by computing, as an approximate indicator of the degree of Comptonization, a generalized Compton-y parameter. Since the temperature varies through the Comptonizing layer, we measure this by the quantity


where [FORMULA] is the local disk temperature in units of the electron rest mass, [FORMULA]. Some values are shown in Table 1. This Compton y-parameter is of the order 0.4 and does not change significantly with distance r from the central object. In the model of Haardt & Maraschi (1993) y was of order 0.6.


Table 1. Compton y-parameter of the proton heated layer in the galactic BH case. [FORMULA] is the Thomson depth of the layer as a function of distance.

The main difference between the spectra are the soft photon energy (the shoulder at the left side in Fig. 4 and Fig. 5), which increases with luminosity, and the high-energy cutoff. The cutoff is seen to increase slightly with distance from the central mass. This can be traced to the fact that with increasing distance the temperatures at the top of the Comptonizing layer increase somewhat (though the average temperature, proportional to y, is nearly constant). This somewhat increases the flux of photons at the highest energies.

A questions unanswered by the present results is of course whether a significant region of interaction between a hot ion plasma and a cool disk can exist. Since the cool disk absorbs all incident ions, the cool disk is a strong sink of both mass and energy for the hot ion plasma. A second question relates to the thermalization of the downward flux of energetic photons in the cool disk. As our results show, the slope of the resulting X-ray spectrum depends somewhat on the effective depth of thermalization of these photons. A correct treatment of the thermalization requires detailed consideration of the contributing atomic processes (Matt et al. 1993).

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100