A Linear Instability and Damping in the Acoustic Dispersion Relation of Fluids Subject to Inverse Compton Drag

Abstract

Radiation drag from inverse-Compton scattering of an external radiation field changes the acoustic dispersion relation of a relativistic fluid. We derive the linear dispersion relation and show that, depending on the electron distribution and fluid sound speed, radiation drag either damps both modes or damps one while driving the other unstable. The unstable growth is robust at short wavelengths but slow and overdamped at long wavelengths, where the linear analysis is limited by the background acceleration. The resulting growth and damping rates are of order the bulk radiative acceleration rate, so whenever radiation drag is important for the background flow, its effects on fluid perturbations are also important. A purely damped region exists for a wide range of parameters. Radiation drag also makes acoustic waves dispersive: The phase speed deviates from the ordinary sound speed at longer wavelengths, and approaches the sound speed at short wavelengths. We validate the derived rates using special-relativistic hydrodynamic simulations. We apply the derived relation to astrophysical jets such as gamma-ray bursts, blazars in the broad-line region of the host active galactic nucleus, and quasar jets traveling through the CMB and galactic radiation field. We find that the derived instability, damping and dispersion may be relevant across a range of relativistic outflow conditions.