2022ApJ...932...97C

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 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, {\dot{m}}_{c} reaches its maximum, {\dot{m}}_{c,\max }\approx 0.02\,{(\alpha/0.3)}^{3}. If at r ≫ r_b the thin disk accretes with {\dot{m}}_{d}\lt {\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 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 x 10⁸ K Compton-cooled corona for r < r_b. Two-temperature effects are ignored, but may be important at small radii.