Abstract In the theory of protoplanetary disk turbulence, a widely adopted ansatz, or assumption, is that the turnover frequency of the largest turbulent eddy, ΩL, is the local Keplerian frequency ΩK. In terms of the standard dimensionless Shakura–Sunyaevαparameter that quantifies turbulent viscosity or diffusivity, this assumption leads to characteristic length and velocity scales given respectively by and , in whichHandcare the local gas scale height and sound speed. However, this assumption is not applicable in cases when turbulence is forced numerically or driven by some natural processes such as vertical shear instability. Here, we explore the more general case where ΩL≥ ΩKand show that, under these conditions, the characteristic length and velocity scales are respectively and , where is twice the Rossby number. It follows that , where is the root-mean-square average of the turbulent velocities. Properly allowing for this effect naturally explains the reduced particle scale heights produced in shearing box simulations of particles in forced turbulence, and it may help with interpreting recent edge-on disk observations; more general implications for observations are also presented. For , the effective particle Stokes numbers are increased, which has implications for particle collision dynamics and growth, as well as for planetesimal formation.
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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 radiusrscaled to Schwarzschild units and coronal mass accretion rate 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 radiusrb∼ 103(α/0.3)−2, whereαis the viscosity parameter. Gas evaporates from the disk to the corona forr>rb, and condenses back forr<rb. Atrb, reaches its maximum, . If atr≫rbthe thin disk accretes with , then the disk evaporates fully before reachingrb, 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, andrbremains unchanged. This model predicts strong coronal winds forr>rb, and aT∼ 5 × 108K Compton-cooled corona forr<rb. Two-temperature effects are ignored, but may be important at small radii.
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- PAR ID:
- 10367979
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- The Astrophysical Journal
- Volume:
- 932
- Issue:
- 2
- ISSN:
- 0004-637X
- Format(s):
- Medium: X Size: Article No. 97
- Size(s):
- Article No. 97
- Sponsoring Org:
- National Science Foundation
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