We study cross-correlations of the kinetic Sunyaev-Zel ’ dovich effect ( kSZ ) and 21 cm signals during the epoch of reionisation ( EoR ) to measure the effects of patchy reionisation .
Since the kSZ effect is proportional to the line-of-sight velocity , the kSZ-21 cm cross correlation suffers from cancellation at small angular scales .
We thus focus on the correlation between the kSZ-squared field ( kSZ ^ { 2 } ) and 21 cm signals .
When the global ionisation fraction is low ( x _ { e } \lesssim 0.7 ) , the kSZ ^ { 2 } fluctuation is dominated by rare ionised bubbles which leads to an anti-correlation with the 21 cm signal .
When 0.8 \lesssim x _ { e } < 1 , the correlation is dominated by small pockets of neutral regions , leading to a positive correlation .
However , at very high redshifts when x _ { e } < 0.15 , the spin temperature fluctuations change the sign of the correlation from negative to positive , as weakly ionised regions can have strong 21 cm signals in this case .
To extract this correlation , we find that Wiener filtering is effective in removing large signals from the primary CMB anisotropy .
The expected signal-to-noise ratios for a \sim 10-hour integration of upcoming Square Kilometer Array data cross-correlated with maps from the current generation of CMB observatories with 3.4 \mu K arcmin noise and 1.7 arcmin beam over 100 deg ^ { 2 } are 51 , 60 , and 37 for x _ { e } = 0.2 , 0.5 , and 0.9 , respectively .