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 MHD 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 = (pgas + prad) /pmag < 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 ∼ 10K) 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 Ṁ & 0.1ṀEdd where Ṁ is the mass accretion rate and ṀEdd is the Eddington mass accretion rate, in which the temperature anti-correlates 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 Teff ∝ ̟. 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. Subject headings: accretion, accretion disks — black hole physics— magnetic fields — X-ray: binaries Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan; [email protected] Division of Theoretical Astronomy, National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan Department of Sciences, Matsue National College of Technology, 14-4 Nishiikuma-cho, Matsue, Shimane 6908515, Japan Department of Physics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 2638522, Japan