Gravitational Instability in Radiation Pressure Dominated Backgrounds

I consider the physics of gravitational instabilities in the presence of dynamically important radiation pressure and gray radiative diffusion, governed by a constant opacity κ. For any non-zero radiation diffusion rate on an optically-thick scale k−1, the medium is unstable unless the classical gas-only isothermal Jeans criterion is satisfied. If the radiation acoustic sound crossing timescale on a scale k−1 (tr) is less than the geometric mean of the dynamical and radiative diffusion timescales (tdiff and tdyn), then diffusion is “slow.” In this limit, although the dynamical Jeans instability is stabilized by radiation pressure on scales smaller than the adiabatic Jeans length, on these same spatial scales the medium is unstable to a diffusive mode. In this regime, neglecting gas pressure, the characteristic timescale for growth of this mode is independent of spatial scale and given by (3κcs )/(4πGc), where cs is the adiabatic sound speed. This characteristic timescale is that required for a fluid parcel to radiate away its thermal energy content at the Eddington limit, the Kelvin-Helmholz timescale for a radiation pressure-supported self-gravitating object. In the limit of “rapid” diffusion — defined by the inequality tr > (tdiff tdyn) — radiation does nothing to suppress the Jeans instability and the medium is dynamically unstable unless the gas-only Jeans criterion is satisfied. I connect with treatments of Silk damping in the early universe. I briefly discuss several astrophysical applications, including photons diffusing in regions of extreme star formation (starburst galaxies & pc-scale AGN disks), and the diffusion of cosmic rays in normal galaxies and galaxy clusters. The former (particularly, starbursts) are “rapidly” diffusing and thus cannot be supported against dynamical instability in the linear regime by radiation pressure alone. The latter are more nearly “slowly” diffusing. I speculate that the turbulence in starbursts may be driven by the dynamical coupling between the radiation field and the self-gravitating gas, perhaps mediated by magnetic fields, and that this diffusive instability operates in individual massive stars. Appendices contain a more detailed treatment of radiation transport and consideration of uniform rotation in the background medium. Subject headings: Instabilities, Hydrodynamics, Radiative Transfer, ISM: Cosmic Rays, Stars: Oscillations, Galaxies: Starburst