Supersonic baryon-CDM velocities and CMB B-mode polarization

It has recently been shown that supersonic relative velocities between dark matter and baryonic matter can have a significant effect on formation of the first structures in the universe. If this effect is still non-negligible during the epoch of hydrogen reionization, it generates large-scale anisotropy in the free electron density, which gives rise to a CMB B-mode. We compute the B-mode power spectrum and find a characteristic shape with acoustic peaks at l ~ 200, 400, ... The amplitude of this signal is a free parameter which is related to the dependence of the ionization fraction on the relative baryon-CDM velocity during the epoch of reionization. However, we find that the B-mode signal is undetectably small for currently favored reionization models in which hydrogen is reionized promptly at z ~ 10, although constraints on this signal by future experiments may help constrain models in which partial reionization occurs at higher redshift, e.g. by accretion onto primordial black holes.