## 4. Results and discussion## 4.1. The set of parametersThe method described above have been used to obtain spectra emitted by the accretion disk and the hot source. In the Newtonian case, as shown in Paper I, the disk emission depends only on the total luminosity and the height of the hot source above the disk. Furthermore, one finds a universal spectrum as a function of a reduced frequency and reduced luminosity where corresponding to the characteristic temperature In the relativistic calculations, one must also specify the mass
The high energy spectrum depends also on the relativistic particle distribution, which was taken as a exponentially cut-off power law (cf. Paper I): Thus, one needs also to specify the spectral index ## 4.2. Angular distribution of radiationAs already mentioned, the angular distribution of high energy radiation is entirely determined by the two parameters and , solutions of the linear system (2.3). Thus, it depends only on the 's values, which depend at turn on geometrical factors. Hence, the only relevant parameter is the ratio . We plot in Fig. 3 the curves and as a function of for . The differences with the Newtonian case become important for , reaching about at . The closer the source to the black hole is, the smaller and are. This corresponds to less anisotropic photon field. This is due to two effects: first the presence of a hole in the accretion disk inside the marginal stability radius; second the curvature of geodesics making the photons emitted near the black hole arrive at larger angle than in the Newtonian case. As shown in Fig. 3, the first effect has a weaker influence than the second one. The polar plot of is sketched in Fig. 4 for and .
## 4.3. The radial temperature distributionWe have plotted in Fig. 5 the radial temperature distribution of three models: the Newtonian model of Paper I, the
present relativistic model with and , and the standard accretion disk model including relativistic effects (Novikov & Thorne 1973 ) for the same total luminosity in each cases. The temperature profile is markedly different between the two illumination models and the standard accretion disk one. At large distances, all models give the same asymptotic behavior (cf. Paper I). In the inner part of the disk (), in the illumination models, the temperature saturates around the characteristic temperature . On the other hand, it keeps increasing in the accretion model, where the bulk of the gravitational energy is released at small radii. Thus, for rapidly rotating black hole, the main difference comes from the smaller marginal stability radius ( for , whereas for ). This increases a lot the accretion efficiency that goes from for a Schwarzschild black hole (), to for a maximally rotating Kerr black hole. In the same time the central temperature reaches much higher values. As seen in Fig. 5, these effects have much less influence in the illumination model. Indeed, the power radiated by the disk surface is essentially controlled by , which is approximately constant for (i.e. ) as shown in Fig. 4. So, the differences with the Newtonian model comes only from gravitational and Doppler shifts which are only appreciable for small radii (). Thus, they concern only a small fraction of the emitting area at , unless is itself small enough. ## 4.4. Overall spectrum## 4.4.1. Influence of the hot source's heightFig. 6 shows the overall spectrum, in reduced units, predicted by the model for different values of , for , and . The frequency shift at both ends of the spectrum is due to the variations of the characteristic frequency with (cf. Eq. (45)). The relativistic effects themselves become important for values of smaller than about 50. They produce a variation of intensity lowering the blue-bump and increasing the hard X-ray emission. The change in the UV range is due to the transverse Doppler effect between the rotating disk and the observer, producing a net redshift, the influence of this redshift being more important for small as already explained in the last paragraph. In the X-ray range, the variation is due to the change of the parameters and when decreases (cf. Fig. 3). The observed UV/X ratio can then be strongly altered by these effects. Quantitatively, the ratio between the maximum of the "blue-bump" and the X-ray plateau of our spectra, goes from in the Newtonian case (or, equivalently, for high values of in the Kerr metrics), to for and in the Kerr maximal case, as shown in Fig. 7. This ratio is highly dependent on the inclination angle . By taking the maximum of the"blue-bump" ,which may be not observed, we evidently overestimate the UV/X ratio compared to the observations. It appears also that a small value of
could explain the comparable UV and X-ray
fluxes observed in few Seyfert galaxies (Perola et al. 1986 , Clavel
et al. 1992 ). This behavior is clearly the opposite of what we would
expect for a hot source whose emission is independent of the disk
emission, and thus does not depend on . In such
a case, the smaller the height of the hot source is, the larger the
bending effects on the ray of light emitted by the hot source are,
increasing the illumination of the disk and thus increasing the UV/X
ratio (Martocchia & Matt 1996). It does not take into account the
changes in the hot source emission due to the same bending effects and
our model shows that, in this case, the global result is an increase
of the X-ray flux toward the observer. ## 4.4.2. Influence of the inclination angleOne can see on Fig. 8 Newtonian and Kerr maximal spectra for different inclination angles for . For small inclination angles, the Kerr spectra are always weaker in UV and brighter in X-ray than the Newtonian ones. However, the difference tends to be less visible for the highest inclination angles. These results can be easily explained: in the X-ray range, as shown in Fig. 4, it is due to the decreasing of the relative difference of the angular distribution between Newtonian and Kerr metrics, as the inclination angle increases. But, for very small values of , the gravitationnal shift can be so high that the Kerr X-ray spectra appears weaker than the Newtonian one. In the UV band, the relativistic effects (the gravitational shift and the Doppler transverse effect) produce a net redshift in the face-on case () compared to the Newtonian case. For higher inclination angle, the redshifted radiation is compensated by the blueshifted one, coming from the part of the disk moving toward the observer.
These effects are much less pronounced for high values because the emission area is much larger, and thus is less affected by relativistic corrections. © European Southern Observatory (ESO) 1997 Online publication: April 20, 1998 |