Observational limits on patchy reionization: Implications for B modes

The recent detection of secondary CMB anisotropy by the South Pole Telescope limits temperature fluctuations from the optical depth-modulated Doppler effect to T3000<√(13)μK at multipoles l∼3000. This bound is the first empirical constraint on optical depth fluctuations at arcminute scales, τ3000=0.001T3000/μK, implying that these fluctuations are no more than a few percent of the mean. Modulation of the quadrupole source to polarization generates B modes that are bounded as B3000=0.003T3000. The maximal extrapolation to the l∼100 gravitational wave regime yields B100=0.1T3000 and remains in excess of gravitational lensing if the comoving size of ionized regions is R > or approx. 80 Mpc. If patchy reionization produces much of the observed arcminute scale temperature fluctuations, current bounds on B100 already require R < or approx. 200 Mpc, and limits on both T3000 and B100 can be expected to improve rapidly.