The cosmic reionization history as revealed by the cosmic microwave background Doppler-21 cm correlation

We show that the epoch(s) of reionization when the average ionization fraction of the universe is about half can be determined by correlating CMB temperature maps with 21 cm line maps at degree scales (l similar to 100). During reionization peculiar motion of free electrons induces the Doppler anisotropy of the CMB, while density fluctuations of neutral hydrogen induce the 21 cm line anisotropy. In our simplified model of inhomogeneous reionization, a positive correlation arises as the universe reionizes whereas a negative correlation arises as the universe recombines; thus, the sign of the correlation provides information on the reionization history that cannot be obtained by present means. The signal comes mainly from large scales (k similar to 10(-2) Mpc(-1)) where linear perturbation theory is still valid and complexity due to patchy reionization is averaged out. Since the Doppler signal comes from ionized regions and the 21 cm comes from neutral ones, the correlation has a well- defined peak(s) in redshift when the average ionization fraction of the universe is about half. Furthermore, the cross- correlation is much less sensitive to systematic errors, especially foreground emission, than the autocorrelation of 21 cm lines; this is analogous to the temperature- polarization correlation of the CMB being more immune to systematic errors than the polarization-polarization. Therefore, we argue that the Doppler-21 cm correlation provides a robust measurement of the 21 cm anisotropy, which can also be used as a diagnostic tool for detected signals in the 21 cm data-detection of the cross-correlation provides the strongest confirmation that the detected signal is of cosmological origin. We show that the Square Kilometer Array can easily measure the predicted correlation signal for 1 yr of survey observation.