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

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1. Introduction

A variety of models have been invoked to explain the hard X-ray spectra of galactic Black Hole Candidates and AGN. The similarity between the spectra of these classes of sources suggests a common mechanism in spite of a large difference in length and time scales. Inverse Compton scattering of soft photons by energetic electrons is the most likely radiation process, and can explain the spectra for a variety of geometries for the assumed soft photon source and hot electron plasma. The source of soft photons could plausibly be a cool disk, extending outward from an assumed distance [FORMULA] around the central mass. The hot Comptonizing plasma could either form a cloud around the central mass, or a corona above the cool disk. The simultaneous presence of a cool disk and a hot Comptonizing plasma is clearly indicated in some observations of black hole transients. These components are identifiable in the spectra of such sources in their very high, high and intermediate states (Rutledge et al. 1999). A central hot cloud could be provided physically by an optically thin, radiatively inefficient accretion flow or ADAF (Rees et al. 1982; Narayan & Yi 1994; Narayan et al. 1996). A corona could be magnetically heated (Galeev et al. 1979; di Matteo et al. 1999), with the magnetic field being provided by the cool disk, and the energy input being due to the Keplerian shear in the disk. By adjusting the soft photon flux, the temperature, and the optical depth of the hot plasma, photon spectra can be produced that closely resemble the observations.

The interaction between the hot plasma and the cool disk, either in the ADAF or in the coronal model, is traditionally seen in terms of an exchange of photons. Soft photons from the disk illuminate the hot plasma and gain energy by inverse Compton scattering on the hot electrons. A part of the resulting energetic photons in turn illuminates the cool disk, is absorbed there and reprocessed into a larger number of photons of lower energy. Haardt & Maraschi (1991, 1993) have shown that the energy balance between the hot and cool plasma illuminating each other in this way determines a combination of temperature and optical depth of the hot plasma (the Compton y-parameter), in such a way that spectra with approximately the right slope are produced.

If the hot plasma is due to an ADAF flow, it is in a two-temperature state (Shapiro et al. 1976) with the ions near their local virial temperature, and the electrons at a much lower temperature near 100 keV. If such a hot two-temperature cloud exists near a cool disk, as the observations indicate, it is conceivable that interaction with this cool disk takes place not only by photons, but also by the some fraction of the ions losing their energy by penetrating into the cool disk and slowing down there (`ion illumination').

Heating of a neutron star surface by impinging ions has been proposed very early in the history of X-ray astronomy. It was suggested as the cause of X-ray emission by Zel'dovitch & Shakura (1969) and Alme & Wilson (1973) but was subsequently eclipsed by the development of accretion through a cool disk.

The possible importance of the process for disks embedded in a hot corona has been proposed by Spruit (1997) and Spruit & Haardt (2000). In these models, the hot Comptonizing plasma is identified with the thin surface layer on top of the cool disk that is produced by the incident flux of ions. The penetration of the ions into the disk, and the propagation of photons through such a layered structure is a well defined problem. The temperature as a function of depth in the layer, and the output spectrum depend only on the temperature and energy flux of the incident ions (and weakly on the local acceleration of gravity). The resulting spectra obtained with an approximate treatment of the radiative transfer (Spruit & Haardt 2000) are promising. The optical depth and temperature of the heated layer are in the right range and produce the right spectral slope and high-energy cutoff, depending only weakly on parameters such as the distance from the central mass and energy flux.

Here, we present more detailed calculations of the process, with a more accurate treatment of the Comptonization process. The interaction between the ion torus and the disk is computed time dependently in a one-dimensional, plane-parallel approximation. For each time step we calculate the energy gain of the electrons slowing down the penetrating hot protons, and their energy loss through Compton cooling of soft blackbody photons, until an equilibrium state is obtained. The density distribution through the region is found from hydrostatic equilibrium. The Comptonization is done by a Monte-Carlo calculation. The result is the Comptonized spectrum at the top of the accretion disk. The production of soft photons by the thermalization of hard photons is not included explicitly but represented by a reprocessing surface at an appropriate depth in the model (see Sect. 3.2 for details).

In Sect. 2 we specify the cool disk model into which the protons penetrate. In Sect. 3 we describe the heating of the electrons at the surface of this disk through Coulomb interactions with the incident protons as well as their cooling by Comptonization in the stratified layer. Sect. 4 presents results and conclusions from these calculations and Sect. 5 gives a discussion and summary.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100