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

Presentation #243.01 in the session Accreting Black Holes & Tidal Disruption Events — iPoster Session.

Published onJun 29, 2022
Analytical Model of Disk Evaporation and State Transitions in Accreting Black Holes

A well-studied model of state transitions in black hole X-ray binaries postulates that gas evaporates from a thin accretion disk into a hot corona. We present a height-integrated version of this model which can be solved analytically and provides a physical understanding of different regimes. With radius r scaled in Schwarzschild units and coronal mass accretion rate ṁc in Eddington units, the results are independent of black hole mass. Thus state transitions should be similar in X-ray binaries and AGN. The analytical solution consists of two power-law segments separated at a break radius, rb ~ 103 (α / 0.3)-2, where α is the viscosity parameter. Gas evaporates from the disk to the corona for r > rb, but condenses back for r < rb. At r ~ rb, ṁc reaches its maximum, ṁc,max ≈ 0.03 (α / 0.3)3. If at r ≫ rb the thin disk accretes at a rate less than ṁc,max, then the disk evaporates fully before reaching rb, giving the hard state. If the thin disk has a larger accretion rate than ṁc,max, it does not evaporate fully at any radius, giving the thermal state. The basic height-integrated model has only viscous heating in the corona. We also present a generalized model which includes direct coronal heating by energy transport from the thin disk. Again, the analytical solutions are independent of black hole mass, and rb remains the same. This model predicts strong coronal winds for r > rb, and relativistic temperatures for r ≪ rb.


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