We obtained steady solutions of optically thin two-temperature magnetized accretion disks around a black hole. We included relativistic bremsstrahlung cooling, synchrotron cooling and inverse Compton effects and assumed that the disk is threaded by toroidal magnetic field. We found that a magnetic pressure dominated new branch, which we call a ‘low-β branch’, appears in the thermal equilibrium curves. The luminosity of the optically thin, magnetically supported disk can exceed 10% of the Eddington luminosity (0.1 LEdd).
