@MISC{Syer_relativisticdynamical, author = {D. Syer}, title = {Relativistic Dynamical Friction in the Weak Scattering Limit}, year = {} }

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Abstract

A test mass, M, moving through an ambient medium of light particles with lower average kinetic energy than itself su ers a deceleration caused by its scattering of the light particles. The phenomenon is usually referred to as dynamical friction. The velocity, v, of the test mass decays on a timescale independent of v in the non-relativistic case. We derive expressions for dynamical friction in the case that the test mass and the light particles are relativistic, and that the scattering is weak (with impact parameter, b M). In the case that the light particles are ultra-relativistic, and isotropic in the frame in which M moves with velocity v, we nd an explicit expression for the dynamical friction. The well known factor of 2 correcting the Newtonian scattering of photons to give the Einstein angle, 4 M=b, has the largest e ect on the resulting friction, which is modi ed by a factor of roughly 16= 3 v over the simple non-relativistic case. In the non-relativistic case, the largest contribution to the friction comes from light particles moving slower than v. We nd that this is not the case for ultra-relativistic scattering, essentially because the scattering angle is independent of v. Some astrophysical implications are discussed. 1