We carried out three-dimensional global resistive magnetohydrodynamic (MHD) simulations of the cooling instability in optically thin hot black hole accretion flows by assuming bremsstrahlung cooling. General relativistic effects are simulated by using the pseudo-Newtonian potential. Cooling instability grows when the density of the accretion disk becomes sufficiently large. We found that as the instability grows the accretion flow changes from an optically thin, hot, gas pressure-supported state (low/hard state) to a cooler, magnetically supported, quasi-steady state. During this transition, magnetic pressure exceeds the gas pressure because the disk shrinks in the vertical direction almost conserving the toroidal magnetic flux. Since further vertical contraction of the disk is suppressed by magnetic pressure, the cool disk stays in an optically thin, spectrally hard state. In the magnetically supported disk, the heating rate balances with the radiative cooling rate. The magnetically supported disk exists for time scale

We present global models of optically thin, advection-dominated two-temperature accretion flows onto black holes, paying careful attention to transonic properties of the flows. We treat the physical quantities integrated over the vertical direction, and adopt the standard a-viscosity and the pseudo-Newtonian potential. Bremsstrahlung and synchrotron cooling amplified by Comptonization is considered as to be cooling processes of electrons. It is found that when moderate synchrotron cooling is included, the electron temperature distribution in the inner part of the disk is roughly flat with temperatures slightly lower than the electron rest mass energy. This high electron temperature is appropriate to explain the hard X-rays from X-ray sources and AGNs. It is also found that in the inner part of the disks the energy input to electrons from ions by the ion-electron Coulomb collision is negligible as the electron heating, i.e., the electron temperature is determined by the balance between advective heating and synchrotron cooling.

We present the results of linear analysis and two-dimensional local magnetohydrodynamic (MHD) simulations of the Parker instability, including the effects of cosmic rays (CRs), in magnetized gas disks (galactic disks). As an unperturbed state for both the linear analysis and the MHD simulations, we adopted an equilibrium model of a magnetized, two-temperature, layered disk with constant gravitational acceleration parallel to the normal of the disk. The disk comprises a thermal gas, CRs, and a magnetic field perpendicular to the gravitational acceleration. CR diffusion along the magnetic field is considered; cross-field-line diffusion is supposed to be small and is ignored. We investigate two cases in our simulations. In the mechanical perturbation case, we add a velocity perturbation parallel to the magnetic field lines, while in the explosive perturbation case, we add CR energy into the sphere in which the CRs are injected. Linear analysis shows that the growth rate of the Parker instability becomes smaller if the coupling between the CRs and the gas is stronger (i.e., if the CR diffusion coefficient is smaller). Our MHD simulations of the mechanical perturbation confirm this result. We show that the falling matter is impeded by the CR pressure gradient; this causes a decrease in the growth rate. In the explosive perturbation case, the growth of the magnetic loop is faster when the coupling is stronger in the early stage. However, in the later stage the behavior of the growth rate becomes similar to the mechanical perturbation case.

We obtained thermal equilibrium solutions for optically thin, two-temperature black hole accretion disks incorporating magnetic fields. The main objective of this study is to explain the bright/hard state observed during the bright/slow transition of galactic black hole candidates. We assume that the energy transfer from ions to electrons occurs via Coulomb collisions. Bremsstrahlung, synchrotron, and inverse Compton scattering are considered as the radiative cooling processes. In order to complete the set of basic equations, we specify the magnetic flux advection rate instead of β = p gas /p mag . We find magnetically supported (low-β), thermally stable solutions. In these solutions, the total amount of the heating via the dissipation of turbulent magnetic fields goes into electrons and balances the radiative cooling. The low-β solutions extend to high mass accretion rates ( α 2Ṁ Edd ) and the electron temperature is moderately cool (T e ∼ 10 8 − 10 9.5 K). High luminosities ( 0.1L Edd ) and moderately high energy cutoffs in the X-ray spectrum (∼ 50 − 200 keV) observed in the bright/hard state can be explained by the low-β solutions.

We obtained steady solutions of optically thin, single temperature, magnetized black hole accretion disks assuming thermal bremsstrahlung cooling. Based on the results of 3D MHD simulations of accretion disks, we assumed that the magnetic fields inside the disk are turbulent and dominated by azimuthal component. We decomposed magnetic fields into an azimuthally averaged mean field and fluctuating fields. We also assumed that the azimuthally averaged Maxwell stress is proportional to the total pressure. The radial advection rate of the azimuthal magnetic fluxΦ is prescribed as being proportional to ̟ −ζ , where ̟ is the radial coordinate and ζ is a parameter which parameterizes the radial variation ofΦ. We found that when accretion rateṀ exceeds the threshold for the onset of the thermal instability, a magnetic pressure dominated new branch appears. Thus the thermal equilibrium curve of optically thin disk has a 'Z'-shape in the plane of surface density and temperature. This indicates that as the mass accretion rate increases, a gas pressure dominated optically thin hot accretion disk undergoes a transition to a magnetic pressure dominated, optically thin cool disk. This disk corresponds to the X-ray hard, luminous disk in black hole candidates observed during the transition from a low/hard state to a high/soft state. We also obtained global steady transonic solutions containing such a transition layer.