Thermal stability of a thin disk with magnetically driven winds

The absence of thermal instability in the high/soft state of black hole X-ray binaries, in disagreement with the standard thin disk theory, has been a long-standing riddle for theoretical astronomers. We have tried to resolve this question by studying the thermal stability of a thin disk with magnetically driven winds in the M-dot −Σ plane. It is found that disk winds can greatly decrease the disk temperature and thus help the disk become more stable at a given accretion rate. The critical accretion rate, M-dot _crit, corresponding to the thermal instability threshold, is significantly increased in the presence of disk winds. For α = 0.01 and B _φ = 10B _p, the disk is quite stable even for a very weak initial poloidal magnetic field [β_p,0∼2000,β_p=(P_gas+P_rad)/(B_p²/8π)]. However, when B _φ = B _p or B _φ = 0.1B _p, a somewhat stronger (but still weak) field (β_{p, 0} ∼ 200 or β_{p, 0} ∼ 20) is required to make the disk stable. Nevertheless, despite the great increase of M-dot _crit, the luminosity threshold, corresponding to instability, remains almost constant or decreases slowly with increasing M-dot _crit due to decreased gas temperature. The advection and diffusion timescales of the large-scale magnetic field threading the disk are also investigated in this work. We find that the advection timescale can be smaller than the diffusion timescale in a disk with winds, because the disk winds take away most of the gravitational energy released in the disk, resulting in the decrease of the magnetic diffusivity η and the increase of the diffusion timescale.