= Saha-Thomson decoupling estimate
{c}
{title2=$X_en_H\sigma_Tc\sim H$}
Combining the <hydrogen-only Saha equation> with the <Thomson decoupling rate criterion> gives an elementary estimate of <photon decoupling>. With present <baryon> density about $0.25\ \mathrm{m^{-3}}$, <hydrogen> fraction about $0.75$, present <photon> <temperature> $2.725\ \mathrm K$ and a matter-era normalization $H_0\sqrt{\Omega_m}\simeq38\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, the coupled estimate gives a <temperature> near $3100\ \mathrm K$. <Hydrogen> chemical equilibrium fails during the actual kinetic recombination history, and the local scattering-rate criterion differs from the maximum of the visibility function; the estimate is not a precision prediction.
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