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Thermal stability of 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, is 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 $\dot{M}- Σ$ 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 $\dot{M}_{\rm crit}$ corresponding to the thermal instability threshold is increased significantly in the presence of disk winds. For $α=0.01$ and $B_{\rm ϕ}=10B_{\rm _p}$, the disk is quite stable even for a very weak initial poloidal magnetic field [$β_{\rm p,0}\sim 2000, β_{\rm p}=(P_{\rm {gas}}+P_{\rm rad})/(B_{\rm p}^2/8π)$]. But when $B_{\rm ϕ}=B_{\rm _p}$ or $B_{\rm ϕ}=0.1B_{\rm _p}$, a somewhat stronger (but still weak) field ($β_{\rm p,0}\sim 200$ or $β_{\rm p,0}\sim 20$) is required to make the disk stable. Nevertheless, despite the great increase of $\dot{M}_{\rm crit}$, the luminosity threshold corresponding to instability remains almost constant or even decreases slowly with increasing $\dot{M}_{\rm crit}$ due to the decrease of 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.