= Cosmic microwave background diffusion damping
{c}
{title2=CMB diffusion damping}
= Silk damping
{c}
{synonym}
<Cosmic microwave background diffusion damping>, or <Silk damping>, damps the <photon-baryon acoustic oscillator> on small scales because <Thomson scattering> gives photons a finite <mean free path>. Repeated scatterings mix hotter and colder regions. Departures from perfect <tight coupling> also appear as <photon-baryon velocity slip> and a <photon quadrupole>, producing heat-conduction and shear-viscosity damping.
In <natural units>, the positive conformal scattering rate is $\Gamma_T=a n_e\sigma_T$, with proper free-electron <number density> $n_e$. A random-walk estimate gives squared comoving diffusion distance of order $\int d\eta/\Gamma_T$. More precisely, the leading polarization-inclusive tight-coupling amplitude contains
$$
e^{-k^2/k_D^2},\qquad
k_D^{-2}(\eta)=\frac16\int^{\eta}\frac{d\widetilde\eta}{\Gamma_T}
\left[\frac{R^2}{(1+R)^2}+\frac{16}{15(1+R)}\right],
$$
where $R=3\rho_b/(4\rho_\gamma)$ is the <baryon loading parameter>. The corresponding <power spectrum> suppression is $e^{-2k^2/k_D^2}$. The approximation applies while the expansion in scattering time is controlled; it cannot be extended through a transparent universe by simply integrating $1/\Gamma_T$ indefinitely.<The Damping Tail of CMB Anisotropies by Wayne Hu and Martin White>[Sections 2.1–2.2, imperfect coupling and diffusion damping]{ref}
Diffusion accumulates before last scattering and becomes especially important as the free-electron population falls. The finite width of the <cosmological visibility function> can also average oscillating line-of-sight sources; that averaging is a distinct mechanism acting in the same epoch. Both effects help shape the small-angular-scale damping tail, whose scale probes the ionization and baryon history.
Back to article page
