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

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4. Results from the model computations

For our model computations we use fixed values for the the accretion luminosity, the viscosity parameter of the cool disk, and the fraction of energy released in the corona, [FORMULA], [FORMULA] and [FORMULA], respectively. We choose a galactic BH case with [FORMULA] and an AGN case with [FORMULA]. The thermalization depth is calculated according to Sect. 3.2.

Fig. 3 shows the spectra resulting when a fixed value of the thermalization depth is assumed. For [FORMULA] the spectrum shows a prominent signature of soft photons, which cross the heated layer without scattering. Increasing the thermalization depth reduces the probability for the soft photons to leave the slab unscattered, and the spectra become harder. Thus the general shape of the emergent spectra is influenced by the depth of the thermalization layer.

If, instead of fixing the depth of the thermalizing boundary, its depth is adjusted such that the free-free emission of the layer matches the downward flux of hard photons to be thermalized (see Sect. 3.2), the spectra only depend on the energy input rate and the distance from the central mass. The temperature profiles through the proton heated layers are shown in Fig. 6 and Fig. 7. The thermalization depth [FORMULA] turns out to be located just below the largest depth to which the protons penetrate (seen as the slight kink above [FORMULA]). This is because the free-free emissivity increases rapidly towards the base of the layer, where the density increases as [FORMULA]. The shape of the temperature profile is different from that in Spruit (1997) and Spruit & Haardt (2000), where the proton heating was treated more crudely as constant with depth.

Fig. 8 shows the dependence of the depth of the thermalization layer with increasing distance from the compact object for the galactic BH and the AGN cases. With increasing distance the thermalization depth moves closer to the disk surface, i.e. the Thomson depth of the Comptonizing layer is reduced. This is a consequence of the energy dependence of the proton penetration depth. With distance, the proton temperature, the penetration depth, and thereby the thermalization depth decrease. The effect of this distance dependence on the spectra is seen in Fig. 4, Fig. 5. At larger radii the spectra become slightly softer and the contribution of the unscattered soft photons becomes stronger. The AGN spectra are softer than the galactic BH spectra, and the cutoff energy increases slightly with distance from the central mass.

[FIGURE] Fig. 4. Dependence of the spectrum on the distance from the compact object for a galactic BH with [FORMULA]. The spectra become slightly softer with increasing radius as the optical depth of the heated scattering layer gets smaller.

[FIGURE] Fig. 5. Dependence of the spectrum on the distance from the compact object for an AGN with [FORMULA] for [FORMULA]. Spectra in the AGN case are softer compared to the galactic BH spectra as the optical depth of the scattering layer is smaller.

[FIGURE] Fig. 6. Temperature profile as a function of optical depth in the electron scattering layer heated by the virialized protons for five different distances from a galactic BH. With increasing distance from the BH the penetration depth of the protons decreases and the surface temperature of the disk increases.

[FIGURE] Fig. 7. Temperature profile as a function of optical depth in the electron scattering layer heated by the virialized protons for five different distances from an AGN.

[FIGURE] Fig. 8. Depth of the thermalization layer [FORMULA] as a function of distance from the central object for galactic BH case (diamonds) and AGN case (triangles). The thermalization depth is larger for the galactic black hole.

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© European Southern Observatory (ESO) 2000

Online publication: October 30, 19100
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