Silk damping

Definition

Before recombination, let $n_e$ be the density of free electrons, $\sigma_T$ the Thomson cross-section and $\lambda = 1/(n_e \sigma_T)$ the mean free path of a photon. Let $a$ be the scale factor and $\eta$ the conformal time, $d\eta = c \, dt / a$. Consider a perturbation of the photon-baryon fluid with comoving wavenumber $k$. Define the damping wavenumber $k_D$, with the integral running up to the time of decoupling, by $$k_D^{-2} \sim \int \frac{d \eta}{6 \, a \, n_e \sigma_T}.$$ Silk damping is the suppression by photon diffusion of the amplitude of the perturbation by a factor of about $e^{-k^2 / k_D^2}$. Perturbations with $k \ll k_D$ are almost unaffected, and perturbations with $k \gg k_D$ are erased.