Star Formation in Quasar Disk

TL;DR

This study uses two-dimensional simulations to explore star formation in quasar accretion disks, identifying conditions for fragmentation, fragment masses, and the effects of radiation pressure and cooling times.

Contribution

It provides new insights into the conditions under which fragmentation occurs in quasar disks, including the role of radiation pressure and cooling times, and estimates initial and final fragment masses.

Findings

Fragmentation occurs beyond 4000 Schwarzschild radii at Eddington accretion.

Maximum viscosity parameter is approximately 0.4.

Initial fragment masses are several hundred solar masses, increasing with sheet size.

Abstract

Using a version of the ZEUS code, we carry out two-dimensional simulations of self-gravitating shearing sheets, with application to QSO accretion disks at a few thousand Schwarzschild radii, corresponding to a few hundredths of a parsec for a 10^8 solar-mass black hole. Radiation pressure and optically thick radiative cooling are implemented via vertical averages. We determine dimensionless versions of the maximum surface density, accretion rate, and effective viscosity that can be sustained by density-wave turbulence without fragmentation. Where fragments do form, we study the final masses that result. The maximum Shakura-Sunyaev viscosity parameter is approximately 0.4. Fragmentation occurs when the cooling time is less than about twice the shearing time, as found by Gammie and others, but can also occur at very long cooling times in sheets that are strongly radiation-pressure dominated. For accretion at the Eddington rate onto a 10^8 solar-mass black hole, fragmentation occurs beyond four thousand Schwarzschild radii, r_s. Near this radius, initial fragment masses are several hundred suns, consistent with estimates from linear stability; final masses after merging increase with the size of the sheet, reaching several thousand suns in our largest simulations. With increasing black-hole mass at a fixed Eddington ratio, self-gravity prevails to smaller multiples of r_s, where radiation pressure is more important and the cooling time is longer compared to the dynamical time; nevertheless, fragmentation can occur and produces larger initial fragment masses. We also find energy conservation is likely to be a challenge for all eulerian codes in self-gravitating regimes where radiation pressure dominates.