5. Discussion and conclusions
We use the ADAF models from Paper I, but we apply some changes to the treatment of the 3D structure of the flow. The models are still based on vertically averaged, stationary equations for the radial structure of the flow, which uses the vertical scale height and quantities measured at the equator as flow variables. Such treatment can be inadequate near the flow boundary, especially close to the rotation axis. We assume the specific angular momentum of matter, its radial velocity, and the sound speed to be constant on spheres. Under such assumptions it is possible to introduce an effective potential on each sphere, which acts as infinite centrifugal potential barrier near the rotation axis. This infinite barrier causes the sharp drop to zero of matter density there despite the fact that the gas is approximately isothermal on spheres; it effectively removes matter with artificially high angular velocity.
Our models are based on the assumption that all the heat dissipated in the flow goes into the ions. We neglect the direct viscous heating of electrons and the fact that their entropy changes as they fall toward the black hole, which represents the advection of heat. Both mechanisms influence the energy balance equation and, as shown by Nakamura et al. (1997), Narayan et al. (1998) and Quataert & Narayan (1998), have an impact on the electron temperature and the resulting spectrum of the model. While advection of heat by electrons is a well defined process, the viscous heating must be introduced using another free parameter. The combined effects of viscosity and advection on electrons would influence all our models in a similar way, not greatly changing the differences between them.
In our calculations we use three models of the matter flow onto the black hole, with the same accretion rate and the same black hole mass, but with different black hole angular momentum. The spin of the black hole has strong influence on the density and temperature of the matter near the horizon, which are both increasing functions of the rotation rate. Similar behavior of the gas parameters can also be seen in much broader investigation of ADAFs parameter space by Popham & Gammie (1998). We are not able to present a full discussion of the ADAF structure-spectrum dependence, but we can point out some trends.
Our calculations show a strong dependence of the ADAFs spectra on the flow structure resulting from the differences in the black hole angular momentum. The synchrotron seed photons are produced mainly in the central parts of the flow, which are the densest and the hottest. The total energy emitted as synchrotron photons increases with the black hole angular momentum. Also the influence of Comptonization is increased the same way. In the case of model, the Comptonized synchrotron radiation dominates all the way to the highest frequencies, making the usual bremsstrahlung peak invisible. For other cases considered ( or 0) this is not true and the bremsstrahlung components dominate at highest frequencies.
The standard theory of Comptonization (Rybicki & Lightman 1979) enables one to estimate the spectral index of low energy radiation, which undergoes multiple scatterings with thermal relativistic electrons of given temperature and optical depth. In our case both parameters can be defined as averages over the configuration. We have tried several simple prescriptions for calculating the averages, but we have not obtained a quantitative agreement between our results and the estimates, the calculated spectra having spectral indexes by higher (i.e. being steeper). The discrepancies must be attributed to the complexity of the flow and effects such as the relative motion of the starting point of a photon and the place of its interaction with the electrons.
We are not attempting to model NGC 4258, but using the parameters from the model of Lasota et al. (1996) we get the right luminosity in the X-rays for the model. The slope of the calculated spectrum at this frequency () is within the observational bounds. The spectrum of NGC 4258 has been also modeled by Gammie et al. (1998). Although they use slightly different values of the ADAF parameters, their results are very similar to those of Lasota et al. (1996).
© European Southern Observatory (ESO) 1999
Online publication: May 21, 1999