3D Radiation Hydrodynamic Simulations of Gravitational Instability in AGN Accretion Disks: Effects of Radiation Pressure

We perform 3D radiation hydrodynamic local shearing-box simulations to study the outcome of gravitational instability (GI) in optically thick active galactic nuclei (AGNs) accretion disks. GI develops when the Toomre parameter Q _T ≲ 1, and may lead to turbulent heating that balances radiative cooling. However, when radiative cooling is too efficient, the disk may undergo runaway gravitational fragmentation. In the fully gas-pressure-dominated case, we confirm the classical result that such a thermal balance holds when the Shakura-Sunyaev viscosity parameter (α) due to the gravitationally driven turbulence is ≲0.2, corresponding to dimensionless cooling times Ωt _cool ≳ 5. As the fraction of support by radiation pressure increases, the disk becomes more prone to fragmentation, with a reduced (increased) critical value of α (Ωt _cool). The effect is already significant when the radiation pressure exceeds 10% of the gas pressure, while fully radiation-pressure-dominated disks fragment at t _cool ≲ 50 Ω⁻¹. The latter translates to a maximum turbulence level α ≲ 0.02, comparable to that generated by magnetorotational instability. Our results suggest that gravitationally unstable (Q _T ∼ 1) outer regions of AGN disks with significant radiation pressure (likely for high/near-Eddington accretion rates) should always fragment into stars, and perhaps black holes.