Observational Limits on Patchy Reionization: Implications for B-modes

TL;DR

This paper provides the first empirical constraints on small-scale reionization optical depth fluctuations and their impact on B-mode polarization, with implications for detecting primordial gravitational waves.

Contribution

It introduces observational bounds on reionization patchiness and B-modes at arcminute scales, linking these to the size of ionizing regions and gravitational wave detection.

Findings

Optical depth fluctuations are limited to a few percent of the mean.

B-modes from patchy reionization are bounded and can exceed lensing if ionized regions are large.

Current bounds suggest ionized regions are smaller than 200 Mpc, affecting gravitational wave searches.

Abstract

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.