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Astron. Astrophys. 346, 713-720 (1999)

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4. Results

We have performed trial calculations of the ADAFs spectra employing the method described. We use the models of ADAFs from Paper I. For the black hole mass, accretion rate and parameter [FORMULA] we use the parameters of Lasota et al. (1996), [FORMULA], [FORMULA], [FORMULA], which they apply in the modeling of NGC 4258. We do not, however, attach cold, thin disks at large radii to our ADAF solutions. In Fig. 1 we show the input spectra of synchrotron and bremsstrahlung photons as well as the resulting Comptonized spectrum of the disk around [FORMULA] black hole. All the spectra in this and other diagrams are shown as [FORMULA] versus [FORMULA] plots. For the synchrotron input the results are based on calculations including [FORMULA] input photons and following more than [FORMULA] branches of photon trajectories. The Comptonization plays a less important role in the case of bremsstrahlung radiation, so we use [FORMULA] times fewer photon trajectories to obtain the spectra in this case. Since the Comptonization preserves the photon number, we normalize the spectra using Eq. 28 with either synchrotron or bremsstrahlung emissivity under the integral to obtain the relative numbers of seed photons of each kind.

[FIGURE] Fig. 1. The spectra of the input synchrotron and bremsstrahlung photons and the resulting spectrum after Comptonization for [FORMULA]. The resulting spectrum is shown as a solid line. Synchrotron input (left ) and bremsstrahlung (right ) use dotted lines.

The Comptonized spectra of synchrotron radiation are smooth enough to allow a power law fit with power index [FORMULA] (i.e. [FORMULA]). The fit is not valid at the vicinity of the first peak, which is due to the seed photons. In Fig. 2 we show synchrotron spectra with fits. As can be seen in the plots the slopes of the spectra depend on the model. Since the black hole mass and the accretion rate are the same for all three cases, the differences must be attributed to the black hole angular momentum and its influence on the flow structure. The power law indices estimated from fits are [FORMULA], 0.85, and 0.81 for [FORMULA], 0.5, and 0.9 respectively.

[FIGURE] Fig. 2. The power law fits to the Comptonized synchrotron emission for models with black hole angular momentum [FORMULA] (dashed lines), [FORMULA] (dotted) and [FORMULA] (solid). The corresponding straight lines represent the fits.

The three spectra resulting from combined effects of synchrotron and bremsstrahlung emission with Comptonization are shown in Fig. 3.

[FIGURE] Fig. 3. The resulting spectra of ADAFs for the three cases including the bremsstrahlung component. The conventions follow Fig. 2

We have also checked the dependence of the observed total luminosity of our models on the observer's position. For the bremsstrahlung photons the dependence is absent. The synchrotron radiation observed from the equatorial plane is stronger by 10 to 20% as compared to the measurement from the axis of rotation.

Following the photons we are able to find the fraction which goes under the horizon. For the synchrotron photons the numbers are: 0.07, 0.05, and 0.04 for [FORMULA], 0.5 and 0.9 respectively. The bremsstrahlung photons are emitted at relatively larger distances from the horizon and less than 1% of them are lost in all cases. The fraction of photons emitted by the fluid and going under the horizon is a decreasing function of the black hole angular momentum according to our simulations. We have checked this result of our simulations making an independent calculation. We have compared isotropic sources of radiation at the same distance from the black hole, comoving with the matter of the three models we use. Again the fraction of rays going under the horizon is the smallest for the case of the most rapidly rotating hole. The effect must be attributed to the differences in matter kinematics between the three models.

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© European Southern Observatory (ESO) 1999

Online publication: May 21, 1999