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

Abstract

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 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 an active galactic nucleus. The corona solution consists of two power-law segments separated at a break radius r b ∼ 103(α/0.3)−2, where α 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 ̇ c reaches its maximum, m ̇ c , max ≈ 0.02 ( α / 0.3 ) 3 . If at r ≫ r b the thin disk accretes with m ̇ d < 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 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 ∼ 5 × 108 K Compton-cooled corona for r < r b . Two-temperature effects are ignored, but may be important at small radii.