Thermal equilibria of magnetically supported black hole accretion disks

H. Oda, M. MacHida, K. E. Nakamura, R. Matsumoto

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32 Citations (Scopus)


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 10 7-1011K) 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.

Original languageEnglish
Pages (from-to)16-28
Number of pages13
JournalAstrophysical Journal
Issue number1
Publication statusPublished - 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


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