4 Results of the model computations

   
4.1 Proton illumination of cool disks in BH and AGN

Figure 1: X-ray spectra of proton- illuminated optically thick cool disks. Upper left panel: emergent model spectrum (solid line) and blackbody with temperature according to proton energy flux (dotted-dashed line); upper right panel: combined heating rates from proton heating and electron thermal conductivity (solid line) and radiative cooling rates due to Comptonization and bremsstrahlung (squares) - the dotted line shows the rates from electron conductivity alone; lower panels show from left to right and from top to bottom the electron temperature $T_{\rm e}$, pressure P, electron density $n_{\rm e}$ and the geometrical depth of the layer z/R, for a solution with $F_{\rm p} = 8.1\times 10^{21}$ erg cm-2 s-1, $T_{\rm p} = 15$ MeV, $M = 8~M_{\odot}$, $R = 10~R_{\rm g}$.

For the thick disks we use the same model parameters as in paper I, i.e. the accretion luminosity $L=0.1~L_{\rm Edd}$, the viscosity parameter $\alpha=0.1$ and the fraction of the energy released in the virialized atmosphere f=0.95. The mass of the galactic BH is $M_{\rm BH}=8~M_\odot$ and the mass of the AGN is $M_{\rm AGN}=8\times10^6~M_\odot$.

Figure 1 shows the solution at r=10 for a proton energy flux of $F_{\rm p} = 8.1\times 10^{21}$ erg cm^-2 s^-1, $T_{\rm p} = 15.6$ MeV. The cool disk is separated by a sharp temperature front from a hot part at an optical depth of order unity. This step like temperature profile is much more pronounced compared to the results of Paper I. The temperature of the hot part is $T_{\rm e}\approx60$ keV. The hot layer acts as an effective Comptonizing region and a hard spectrum is emitted. The power law index of the BH spectra in E F(E) is $s\approx 0.2$. At the soft end of the spectrum there is an excess of soft photons with respect to a blackbody with equivalent energy flux. This excess is due to a "reverse photosphere effect'', as explained in Deufel et al. (2001).

The upper right panel of Fig. 1 shows the heating and cooling rates. In the narrow transition zone ( $\Delta\tau\approx 0.1$) between the hot top and the cool bottom electron conductivity is not negligible. Elsewhere conductivity plays no role for the energy balance.

The geometrical depth of the heated layer is $z_{\rm tot}\approx6\times10^5$ cm. This is small compared to the distance from the compact object ( $R=2.3\times10^7$ cm). Thus a cool disk with a proton heated skin on top of it can still be considered a "thin'' disk.

Figure 2 shows the dependence of the emergent spectrum and the temperature profile on the distance from the compact object in the galactic BH case. We obtain a result comparable to Paper I, i.e. with increasing distance the temperature of the hot part increases somewhat, whereas the optical depth of the heated layer decreases. A discussion of these effects can be found in Paper I.

For distances $R>50 ~R_{\rm S}$ from the galactic BH we could not find heated solutions. With increasing distance from the central object the proton temperature ( $\propto R^{-1}$) as well as the proton energy flux ( $\propto R^{-3}$) decrease. In these conditions we find solutions in which the energy supplied by the incident protons is thermalized directly in the cool disk by bremsstrahlung, without forming a hot surface layer. It is likely that a very thin ( $\tau \ll 0.01$) hot layer still forms in these conditions, but we are unable to resolve it with the present method. This is indicated by the existence of thin hot atmosphere solutions at low incident energy flux in the case of protons heating a neutron star surface (Zampieri et al. 1995; Deufel et al. 2001). It probably also occurs in the present case, but since these thin layers at large distances from the hole do not contribute much to the overall spectrum, we have not pursued this further.

Figure 2: Dependence of the emergent model spectra and the temperature profiles on the distance from a galactic BH with $M = 8~M_{\odot}$. The surface temperature of the of the disk increases slightly with distance, whereas the optical depth of the hot surface layer decreases.

Figure 3: Dependence of the emergent model spectra and the temperature profiles on the distance from the hole in the AGN case with $M=8\times10^6~M_\odot$. The optical depth of the hot part is much smaller than in the galactic BH cases.

Figure 3 shows the dependence of the emergent spectrum and the temperature profile on the distance from the compact object in the AGN case. We obtain slightly different solutions compared to our results in Paper I. The optical depth of the heated layer is smaller ( $\tau\lesssim 0.5$), the temperature of the hot part is $T_{\rm e}\approx 70{-}90$ keV. Again a steep temperature jump separates it from the cool disk underneath. Due to the smaller optical depth of the heated layer Comptonization is not as efficient. A significant fraction of the incident ions passes through the hot layer and thermalizes in the cool disk underneath. This increases the soft photon flux relative to the Comptonized flux, and produces a steeper spectrum. The index of the AGN spectra in E F(E) is $s\approx 0.6$. Our model does not produce heated solutions at distances $R>20~R_{\rm S}$ from the compact object, though heated atmospheres might exist at very small optical depths (see note above).