Kenji E. Nakamura

Formation of Magnetically Supported Disks during Hard-to-Soft Transitions in Black Hole Accretion Flows

We carried out three-dimensional global resistive magnetohydrodynamic simulations of the cooling instability in optically thin hot black hole accretion flows by assuming bremsstrahlung cooling. General relativistic effects are simulated using the pseudo-Newtonian potential. The 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-supportedstate (low/hard state) to acooler, magnetically supported, quasi-steady state. During this transition, the magnetic pressure exceeds the gas pressure because the disk shrinks in the vertical direction while 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. The magnetically supported disk exists for a time scale much longer than the thermal time scale, and comparable to the accretion time scale. We examined the stability of the magnetically supported disk analytically, assuming that the toroidal magnetic flux is conserved, and found it to be thermally and secularly stable. Our findings may explain why black hole candidates stay in luminous, hard state even when their luminosity exceeds the threshold for the onset of the cooling instability.

THERMAL EQUILIBRIA OF OPTICALLY THIN, MAGNETICALLY SUPPORTED, TWO-TEMPERATURE, BLACK HOLE ACCRETION DISKS

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 ? = p gas/p mag. We find magnetically supported (low-?), 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-? solutions extend to high mass accretion rates () and the electron temperature is moderately cool (T e ~ 108-109.5 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-? solutions.

THERMAL EQUILIBRIA OF MAGNETICALLY SUPPORTED BLACK HOLE ACCRETION DISKS

We present new thermal equilibrium solutions for optically thin and optically thick disks incorporating magnetic fields. The purpose of this paper is to explain the bright hard state and the bright/slow transition observed in the rising phases of outbursts in black hole candidates. On the basis of the results of three-dimensional magnetohydrodynamic simulations, we assume that magnetic fields inside the disk are turbulent and dominated by the azimuthal component and that the azimuthally averaged Maxwell stress is proportional to the total (gas, radiation, and magnetic) pressure. We prescribe the magnetic flux advection rate to determine the azimuthal magnetic flux at a given radius. Local thermal equilibrium solutions are obtained by equating the heating, radiative cooling, and heat advection terms. We find magnetically supported (β = (p gas + p rad)/p mag < 1), thermally stable solutions for both optically thin disks and optically thick disks, in which the heating enhanced by the strong magnetic field balances the radiative cooling. The temperature in a low-β disk (T ~ 107-1011K) is lower than that in an advection-dominated accretion flow (or radiatively inefficient accretion flow) but higher than that in a standard disk. We also study the radial dependence of the thermal equilibrium solutions. The optically thin, low-β branch extends to , where is the mass accretion rate and is the Eddington mass accretion rate, in which the temperature anticorrelates with the mass accretion rate. Thus, optically thin low-β disks can explain the bright hard state. Optically thick, low-β disks have the radial dependence of the effective temperature T eff –3/4. Such disks will be observed as staying in a high/soft state. Furthermore, limit cycle oscillations between an optically thick low-β disk and a slim disk will occur because the optically thick low-β branch intersects with the radiation pressure dominated standard disk branch. These limit cycle oscillations will show a smaller luminosity variation than that between a standard disk and a slim disk.

Nonlinear Parker Instability with the Effect of Cosmic-Ray Diffusion

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.

DYNAMO ACTIVITIES DRIVEN BY MAGNETOROTATIONAL INSTABILITY AND THE PARKER INSTABILITY IN GALACTIC GASEOUS DISKS

We carried out global three-dimensional magnetohydrodynamic simulations of dynamo activities in galactic gaseous disks without assuming equatorial symmetry. Numerical results indicate the growth of azimuthal magnetic fields non-symmetric to the equatorial plane. As the magnetorotational instability (MRI) grows, the mean strength of magnetic fields is amplified until the magnetic pressure becomes as large as 10% of the gas pressure. When the local plasma β (=p gas/p mag) becomes less than 5 near the disk surface, magnetic flux escapes from the disk by the Parker instability within one rotation period of the disk. The buoyant escape of coherent magnetic fields drives dynamo activities by generating disk magnetic fields with opposite polarity to satisfy the magnetic flux conservation. The flotation of the azimuthal magnetic flux from the disk and the subsequent amplification of disk magnetic field by the MRI drive quasi-periodic reversal of azimuthal magnetic fields on a timescale of 10 rotation periods. Since the rotation speed decreases with radius, the interval between the reversal of azimuthal magnetic fields increases with radius. The rotation measure computed from the numerical results shows symmetry corresponding to a dipole field.

Steady models of optically thin, magnetically supported black hole accretion disks

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 an azimuthal component. We decomposed the magnetic fields into an azimuthally averaged mean field and fluctuating fields. We also assumed that the azimuthally averaged Maxwel ls tress i sp roportional to the total pressure. The radial advection rate of the azimuthal magnetic flux, P Φ ,i s prescribed as being proportional to

Global Structure of Optically Thin, Magnetically Supported, Two-Temperature, Black Hole Accretion Disks

� � ,w here

Steady Models of Magnetically Supported Black Hole Accretion Disks

is the radial coordinate

Global 3D MHD Simulations of Optically Thin Black Hole Accretion Disks

We present global solutions of optically thin, two-temperature black hole accretion disks incorporating magnetic fields. We assume that the (omega) over bar phi-component of the Maxwell stress is proportional to the total pressure, and prescribe the radial dependence of the magnetic flux advection rate in order to complete the set of basic equations. We obtained magnetically supported (low-beta) disk solutions, whose luminosity exceeds the maximum luminosity for an advection-dominated accretion flow (ADAF), L greater than or similar to 0.4 alpha L-2(Edd), where L-Edd is the Eddington luminosity. The accretion flow is composed of the outer ADAF, a luminous hot accretion flow (LHAF) inside the transition layer from the outer ADAF to the low-beta disk, the low-beta disk, and the inner ADAF. The low-beta disk region becomes wider as the mass-accretion rate increases further. In the low-beta disk, the magnetic heating balances the radiative cooling, and the electron temperature decreases from similar to 10(9.5) K to similar to 10(8) K as the luminosity increases. These results are consistent with the anti-correlation between the energy cutoff in X-ray spectra (hence the electron temperature) and the luminosity when L greater than or similar to 0.1 L-Edd, observed in the bright/hard state during the bright hard-to-soft transitions of transient outbursts in galactic black hole candidates.

Global Magneto-Hydrodynamic Simulations of Differentially Rotating Accretion Disk by Astrophysical Rotational Plasma Simulator

We obtained steady solutions of magnetized black hole accretion disks taking into account the gas pressure, magnetic pressure, and radiation pressure. We assumed the bremsstrahlung cooling in the optically thin limit and the black body cooling in the optically thick limit. W assumed that magnetic fields inside the disk are turbulent and dominated by azimuthal component and that the azimuthally averaged Maxwell stress is proportional to the total pressure. We found that when accretion rate exceeds the threshold for the onset of the thermal instability for optically thin disks, a magnetic pressure dominated, cool branch appears in the thermal equilibrium curve. This disk corresponds to the “Bright/Hard” state in black hole candidates observed during the transition from a Low/Hard state to a High/Soft state.