Photon diffusion scale. The photon diffusion scale grows rapidly near last scattering due to the increasing mean free path of the photons but remains well under the horizon scale $k_*^{-1} = (\dot a/a)|_{a_*}$ at last scattering. The small difference between $a_*$ and $a_d$ is sufficient to cause a significant difference in the effective damping if $\Omega_b h^2$ differs substantially from the crossover point $0.03$. The inclusion of the angular dependence of Compton scattering enhances damping by a small factor $f_2 = 9/10$ as does the further inclusion of polarization $f_2 = 3/4$.

Baryon drag effect in adiabatic CDM models. (a) Baryons cause a drag effect on the photons leading to a temperature enhancement of $-R\Psi = |R\Psi|$ inside potential wells which shifts the zero point of the oscillation (short dashed lines). (b) This contribution yields alternating peak heights in the rms and is also retained after diffusion damping. Here numerical results are displayed.

The residual baryon drag effect after last scattering in an adiabatic CDM model. On scales under the width of the visibility function, cancellation between contributions which came from potential wells and hills at last scattering damps fluctuations from the baryon drag effect. Note that cancellation damping is weak and scales as $(k\eta_*)^{-1/2}$ in contrast to the exponential diffusion damping. Projection relates the rms fluctuation in (a) to the anisotropy power spectrum in (b).