Abstract:
Advection-dominated, high-temperature, quasi-spherical accretion flow onto a compact object, recently considered by a number of authors, assume that the dissipation of turbulent energy of the flow heats the ions and that the dissipated energy is advected inward. It is suggested that the efficiency of conversion of accretion energy to radiation can be very much smaller than unity. However, it is likely that the flows have an equipartition magnetic field with the result that dissipation of magnetic energy at a rate comparable to that for the turbulence must occur by Ohmic heating. We argue that this heating occurs as a result of plasma instabilities and that the relevant instabilities are current driven in response to the strong electric fields parallel to the magnetic field. We argue further that these instabilities heat predominantly the electrons. We conclude that the efficiency of conversion of accretion energy to radiation can be much smaller than unity only for the unlikely condition that the Ohmic heating of the electrons is negligible.

Abstract:
I review particle heating by MHD turbulence in collisionless plasmas appropriate to advection-dominated accretion flows. These considerations suggest that the preferential turbulent heating of protons assumed by theoretical models is only achieved for relatively subthermal magnetic fields.

Abstract:
We solve the set of hydrodynamic (HD) equations for optically thin Advection Dominated Accretion Flows (ADAFs) by assuming radially self-similar in spherical coordinate system $ (r, \theta, \phi) $. The disk is considered to be steady state and axi-symmetric. We define the boundary conditions at the pole and the equator of the disk and to avoid singularity at the rotation axis, the disk is taken to be symmetric with respect to this axis. Moreover, only the $ \tau_{r \phi} $ component of viscous stress tensor is assumed and we have set $ v_{\theta} = 0 $. The main purpose of this study is to investigate the variation of dynamical quantities of the flow in the vertical direction by finding an analytical solution. As a consequence, we found that the advection parameter, $ f^{adv} $, varies along the $ \theta $ direction and reaches to its maximum near the rotation axis. Our results also show that, in terms of no-outflow solution, thermal equilibrium still exists and consequently advection cooling can balance viscous heating.

Abstract:
Using mean field MHD, we discuss the energetics of optically thin, two temperature, advection-dominated accretion flows (ADAFs). If the magnetic field is tangled and roughly isotropic, flux freezing is insufficient to maintain the field in equipartition with the gas. In this case, we expect a fraction of the energy generated by shear in the flow to be used to build up the magnetic field strength as the gas flows in; the remaining energy heats the particles. We argue that strictly equipartition magnetic fields are incompatible with a priori reasonable levels of particle heating; instead, the plasma $\beta$ in ADAFs (defined to be the gas pressure divided by magnetic/turbulent pressure) is likely to be $\gsim 5$; correspondingly, the viscosity parameter $\alpha$ is likely to be $\lsim 0.2$

Abstract:
We derive all relevant equations needed for constructing a global general relativistic model of advectively cooled, very hot, optically thin accretion disks around black holes and present solutions which describe advection dominated flows in the gravitational field of a Kerr black hole.

Abstract:
We study the global dynamics of advection-dominated accretion flows (ADAFs) with magnetically driven outflows. A fraction of gases in the accretion flow is accelerated into the outflows, which leads to decreasing of the mass accretion rate in the accretion flow towards the black hole. We find that the r-dependent mass accretion rate is close to a power-law one, m_dot r^s, as assumed in the advection-dominated inflow-outflow solution (ADIOS), in the outer region of the ADAF, while it deviates significantly from the power-law r-dependent accretion rate in the inner region of the ADAF. It is found that the structure of the ADAF is significantly changed in the presence of the outflows. The temperatures of the ions and electrons in the ADAF decreases in the presence of outflows, as a fraction of gravitational power released in the ADAF is tapped to accelerate the outflows.

Abstract:
We investigate the form of the momentum distribution function for protons and electrons in an advection-dominated accretion flow (ADAF). We show that for all accretion rates, Coulomb collisions are too inefficient to thermalize the protons. The proton distribution function is therefore determined by the viscous heating mechanism, which is unknown. The electrons, however, can exchange energy quite efficiently through Coulomb collisions and the emission and absorption of synchrotron photons. We find that for accretion rates greater than \sim 10^{-3} of the Eddington accretion rate, the electrons have a thermal distribution throughout the accretion flow. For lower accretion rates, the electron distribution function is determined by the electron's source of heating, which is primarily adiabatic compression. Using the principle of adiabatic invariance, we show that an adiabatically compressed collisionless gas maintains a thermal distribution until the particle energies become relativistic. We derive a new, non-thermal, distribution function which arises for relativistic energies and provide analytic formulae for the synchrotron radiation from this distribution. Finally, we discuss its implications for the emission spectra from ADAFs.

Abstract:
We calculate spectral models of advection-dominated accretion flows, taking into account the possibility that significant mass may be lost to a wind. We apply the models to the soft X-ray transient V404 Cyg in quiescence and the Galactic center source Sgr A*. We show that there are qualitative degeneracies between the mass loss rate in the wind and parameters characterizing the microphysics of the accretion flow; of particular importance is $\delta$, the fraction of the turbulent energy which heats the electrons. For small $\delta$, current observations of soft X-ray transients and Sgr A* suggest that at least $\sim 10 %$ of the mass originating at large radii must reach the central object. For large $\delta \sim 0.3$, however, models with significantly more mass loss are in agreement with the observations. We also discuss constraints on advection-dominated accretion flow models imposed by recent radio observations of NGC 4649 and other nearby elliptical galaxies. We conclude by highlighting future observations which may clarify the importance of mass loss in sub-Eddington accretion flows.

Abstract:
General properties of advection-dominated accretion flows are discussed. Special emphasis is given to the optically thin branch of solutions, which has very high ion and electron temperatures and is thermally stable. This solution branch has been applied to a number of low-luminosity accreting black holes. The models have resolved some puzzles and have provided a straightforward explanation of the observed spectra. The success of the models confirms that the central objects in these low-luminosity sources are black holes. There is some indication that advection-dominated models may be relevant also for higher luminosity systems. The properties of the Low state of accreting black holes, the transition from the Low state to the High state, and the similarity of hard X-ray/gamma-ray spectra of black hole X-ray binaries and active galactic nuclei, are explained.

Abstract:
We extend and reconcile recent work on turbulence and particle heating in advection-dominated accretion flows. For approximately equipartition magnetic fields, the turbulence primarily heats the electrons. For weaker magnetic fields, the protons are primarily heated. The division between electron and proton heating occurs between $\beta \sim 5$ and $\beta \sim 100$ (where $\beta$ is the ratio of the gas to the magnetic pressure), depending on unknown details of how Alfv\'en waves are converted into whistlers on scales of the proton Larmor radius. We also discuss the possibility that magnetic reconnection could be a significant source of electron heating.