Doppler Effect

Naively, velocity fields of order $v \sim 10^{-3}$ (see e.g. [Strauss & Willick, 1995] for a review) and optical depths of a few percent would imply a Doppler effect that rivals the acoustic peaks themselves. That this is not the case is the joint consequence of the cancellation described in §4.2.1 and the fact that the acoustic peaks are not ``Doppler peaks'' (see §3.8). Since the Doppler effect comes from the peculiar velocity along the line of sight, it retains no contributions from linear modes with wavevectors perpendicular to the line of sight. But as we have seen, these are the only modes that survive cancellation (see Plate 3 and [Kaiser, 1984]). Consequently, the Doppler effect from reionization is strongly suppressed and is entirely negligible below $\ell \sim 10^2$ unless the optical depth in the reionization epoch approaches unity (see Plate 5b).