Diffusion damping calibration. In the absence of both
diffusion damping and gravitational sources, the rms temperature
fluctuation at recombination (short-dashed line)
exhibits simple acoustic oscillations.
These are mapped onto anisotropies on the sky in a near one to
one fashion (solid line). The inclusion of diffusion terms in the
Boltzmann equation allows for a simple numerical calibration of its
Reionization damping calibration. By removing the relative
Doppler effect from a reionized Boltzmann calculation and comparing
the result to the same model (here
standard CDM $\Omega_0=1$, $h=0.5$, $\Omega_b h^2=0.0125$) with no
reionization, the effects of rescattering damping are isolated.
The reionization damping envelope is fit by two parameters,
the optical depth during reionization and the horizon scale at
last scattering (see Eq.~24).
Diffusion scale calibration. Analytic estimates of
$k_D(\Omega_0 h^2, \Omega_b h^2)$
based on the tight-coupling approximation trace the results to
reasonable accuracy and explains their general behavior
The fitting function of Eq.~(17) tracks the numerical
calibration to better than the $1\%$ level.