Observational Limits on Patchy Reionization: Implications for B-modes

The recent detection of secondary CMB anisotropy by the South Pole Telescope places a conservative bound on temperature fluctuations from the optical depth-modulated Doppler effect of T3000 < √ 13μK at multipoles l ∼ 3000. This bound is the first empirical constraint on reionization optical depth fluctuations at arcminute scales, τ3000 = 0.001 T3000/μK, implying that these fluctuations are no more than a few percent of the mean. Optical depth modulation of the quadrupole source to polarization generates B-modes that are correspondingly bounded as B3000 = 0.003 T3000. The maximal extrapolation to the l ∼ 100 gravitational wave regime yields B100 = 0.1 T3000 and remains in excess of gravitational lensing if the effective comoving size of the ionizing regions is R ∼ 80Mpc. If patchy reionization is responsible for much of the observed arcminute scale temperature fluctuations, current bounds on B100 already require R ∼ 200Mpc and can be expected to improve rapidly. Frequency separation of thermal Sunyaev-Zel’dovich contributions to the measured secondary anisotropy would also substantially improve the limits on optical depth fluctuations and B-modes from reionization.