2009/11/18 by Todd A. Thompson
Physics and Astronomy · #Adiabatic process #Astrophysical Phenomena and Observations #Cosmology #Cosmology and Gravitation Theories #Decoupling (probability) #Gravitational wave #Instability #Perturbation (astronomy) #Pulsars and Gravitational Waves Research #Quadrupole #Radiative transfer #WKB approximation #Wavenumber #astro-ph.CO
paper · pdf · doi:10.1088/0004-637x/709/2/1119
published as Astrophys.J.709:1119-1124,2010 · 6 pages, 1 figure, emulateapj, comments welcome
arxiv created 2009/11/18 · openalex publication_date 2010/01/12 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Radiative diffusion damps acoustic modes at large comoving wavenumber ( k ) before decoupling ("Silk damping"). In a simple WKB analysis, neglecting moments of the temperature distribution beyond the quadrupole (the tight-coupling limit), damping appears in the acoustic mode as a term of order , where is the scattering rate per unit conformal time. Although the Jeans instability is stabilized on scales smaller than the adiabatic Jeans length, I show that the medium is linearly unstable to first order in to a slow diffusive mode. At large comoving wavenumber, the characteristic growth rate becomes independent of spatial scale and constant: ( t KH a ) −1 ≈ (128π G /9κ T c )(ρ m /ρ b ), where a is the scale factor, ρ m and ρ b are the matter and baryon energy density, respectively, and κ T is the Thomson opacity. This is the characteristic timescale for a fluid parcel to radiate away its total thermal energy content at the Eddington limit, analogous to the Kelvin–Helmholz (KH) timescale for a radiation pressure-dominated massive star or the Salpeter timescale for black hole growth. Although this mode grows at all times prior to decoupling and on scales smaller than roughly the horizon, the growth time is long, about 100 times the age of the universe at decoupling. Thus, it modifies the density and temperature perturbations on small scales only at the percent level. The physics of this mode in the tight-coupling limit is already accounted for in the popular codes CMBFAST and CAMB , but is typically neglected in analytic studies of the growth of primordial perturbations. The goal of this work is to clarify the physics of this diffusive instability in the epoch before decoupling, and to emphasize that the universe is formally unstable on scales below the horizon, even in the limit of very large . Analogous instabilities that might operate at yet earlier epochs are also mentioned.