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

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 <(m) over dot>(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 an active galactic nucleus. The corona solution consists of two power-law segments separated at a break radius r(b) similar to 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), <(m)over dot>(c), reaches its maximum, <(m) over dot>(c,)(max) approximate to 0.02 (alpha/0.3)(3). If at r >> r(b) the thin disk accretes with <(m) over dot>(d) < <(m) over dot>(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 that 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 similar to 5 x 10(8) K Compton-cooled corona for r < r(b). Two-temperature effects are ignored, but may be important at small radii.