Analytical Model of Disk Evaporation and State Transitions in Accreting Black Holes

Abstract

State transitions in black hole X-ray binaries are likely caused by gas evaporation from a thin accretion disk into a hot corona. We present a height-integrated version of this process which is suitable for analytical and numerical studies. With radius $r$ scaled to Schwarzschild units and coronal mass accretion rate ${\dot{m}}_c$ to Eddington units, the results of the model are independent of black hole mass. State transitions should thus be similar in X-ray binaries and AGN. The corona solution consists of two power-law segments separated at a break radius $r_b\sim 10^3(\alpha /0.3{)}^{-2}$, where $\alpha$ is the viscosity parameter. Gas evaporates from the disk to the corona for $r>r_b$, and condenses back for $r<r_b$. At $r_b$, ${\dot{m}}_c$ reaches its maximum, ${\dot{m}}_{c,\max }\approx 0.02(\alpha /0.3{)}^3$. If at $r\gg r_b$ the thin disk accretes with ${\dot{m}}_d<{\dot{m}}_{c,\max }$, then the disk evaporates fully before reaching $r_b$, giving the hard state. Otherwise, the disk survives at all radii, giving the thermal state. While the basic model considers only bremsstrahlung cooling and viscous heating, we also discuss a more realistic model which includes Compton cooling and direct coronal heating by energy transport from the disk. Solutions are again independent of black hole mass, and $r_b$ remains unchanged. This model predicts strong coronal winds for $r>r_b$, and a $T\sim 5\times 10^8\mathrm{K}$ Compton-cooled corona for $r<r_b$. Two-temperature effects are ignored, but may be important at small radii.

40 pages, 12 figures, published in ApJ

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