We present global solutions of optically thin, two-temperature black hole accretion disks incorporating magnetic fields. We assume that the ςφ-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-β) disk solutions, whose luminosity exceeds the maximum luminosity for an advection-dominated accretion flow (ADAF), L ≳ 0.4α2 LEdd, where LEdd 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-β disk, the low-β disk, and the inner ADAF. The low-β disk region becomes wider as the mass-accretion rate increases further. In the low-β disk, the magnetic heating balances the radiative cooling, and the electron temperature decreases from ∼109.5K to ∼108 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 ≳ 0.1LEdd, observed in the bright/hard state during the bright hard-to-soft transitions of transient outbursts in galactic black hole candidates.
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