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Radiation Hydrodynamic Simulations of Gravitational Instability in AGN Accretion Disks: The Radiation-modified Fragmentation Boundary

Presentation #213.01 in the session AGN and Quasars III.

Published onJun 29, 2022
Radiation Hydrodynamic Simulations of Gravitational Instability in AGN Accretion Disks: The Radiation-modified Fragmentation Boundary

Gravitational Instability has been extensively studied in contexts of protoplanetary disks as well as AGN accretion disks around supermassive blackholes (SMBHs). When a gravitationally stable standard Shakura-Sunyaev accretion disk, with its accretion parameter alpha driven primarily by Magnetorotational Instability (MRI), extends outwards from the inner region of a quasar disk, at some critical radius the Toomre parameter Q will drop below order unity. Beyond this radius, the disk becomes gravitationally unstable, but is thought to be able to eventually self-regulate at a state where Q ~ 1, with the effective sound speed/pressure given by the combination of gas and radiation pressure. Analytical models have been applied to described this region as a constant-Q disk where steady state alpha is an explicit function of distance to the SMBH r, parametrized by the constants Q and accretion rate Ṁ (e.g. Goodman 2003).

To gain energy balance this radius-dependent effective viscosity alpha needs to be ~ tcool /Omega in steady state, here tcool is the local characteristic energy cooling time. However, extensive gas-pressure-only simulations show that typically when tcool is smaller than some threshold value tc ~ 3/Omega, the disk will fragment into a number of clumps, although the accurate value for the boundary threshold tc is uncertain (e.g. Gammie 2001, Johnson & Gammie 2003, Rice et al. 2005).

For a disk with a constant accretion rate Ṁ, tc ≪ 1/Omega far enough from the SMBH so fragmentation/star formation always occurs at large distances, but towards the central SMBH the radiation pressure fraction increases and inevitably dominates the total pressure at smaller radii. A radiation-supported disk has an effective adiabatic index of 4/3 and is much more prone to fragmentation than disk supported by gas pressure (Jiang & Goodman 2011). In this study we perform 3D local shearing box simulations with radiation transfer, using state-of-the-art implicit radiation module of Athena++ to determine how tc depends on radiation-over-gas pressure ratio Pr/Pg along the fragmentation/steady-turbulence boundary, in particular how non-negligible fractions of radiation pressure extends tc to be much larger than the classical order-unity threshold. Our simulations imply that if the increase of local tcool cannot overcome the destabilizing effects of growing Pr/Pg as we follow a constant Ṁ accretion disk inwards towards the SMBH, a steady state may never be reached at Q~1 and fragmentation is inevitable for gravitationally unstable regions.

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