Thermal stability of thin disk with magnetically driven winds

Abstract

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

26 pages, 11 figures, accepted for publication in ApJ

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