  We present new thermal equilibrium solutions for optically thin and 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 BHCs. On the basis of the results of 3D 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 pressure. We prescribe the magnetic flux advection
rate to determine the azimuthal magnetic flux at a given radius.
  We find magnetically supported, thermally stable solutions for both optically
thin and thick disks, in which the heating enhanced by the strong magnetic
field balances the radiative cooling. The temperature in a low-$\beta$ disk is
lower than that in an ADAF/RIAF but higher than that in a standard disk. We
also study the radial dependence of the thermal equilibrium solutions.
  The optically thin, low-$\beta$ branch extends to $ \dot M \gtrsim 0.1 {\dot
M}_{\rm Edd}$, in which the temperature anti-correlates with the mass accretion
rate. Thus optically thin low-$\beta$ disks can explain the bright hard state.
Optically thick, low-$\beta$ disks have the radial dependence of the effective
temperature $T_{\rm eff} \propto \varpi^{-3/4}$. Such disks will be observed as
staying in a high/soft state. Furthermore, limit cycle oscillations between an
optically thick low-$\beta$ disk and a slim disk will occur because the
optically thick low-$\beta$ 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.

High Energy Astrophysical Phenomena