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 T_{3000} < sqrt{13} microK at multipoles
l~3000. This bound is the first empirical constraint on reionization optical
depth fluctuations at arcminute scales, tau_{3000} = 0.001 T_{3000}/microK,
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 B_{3000} = 0.003 T_{3000}. The
maximal extrapolation to the l~100 gravitational wave regime yields B_{100} =
0.1 T_{3000} and remains in excess of gravitational lensing if the effective
comoving size of the ionizing regions is R > 80 Mpc. If patchy reionization is
responsible for much of the observed arcminute scale temperature fluctuations,
current bounds on B_{100} already require R < 200 Mpc 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.
