A direct measure of free electron gas via the kinematic Sunyaev-Zel'dovich effect in Fourier-space analysis

We present the measurement of the kinematic Sunyaev-Zel'dovich (kSZ) effect in Fourier space, rather than in real space. We measure the density-weighted pairwise kSZ power spectrum, the first use of this promising approach, by cross-correlating a cleaned Cosmic Microwave Background (CMB) temperature map, which jointly uses both Planck Release 2 and Wilkinson Microwave Anisotropy Probe nine-year data, with the two galaxy samples, CMASS and LOWZ, derived fr om the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12. With the current data, we constrain the average optical depth $\tau$ multiplied by the ratio of the Hubble parameter at redshift $z$ and the present day, $E=H/H_0$; we find $\tau E = (3.95\pm1.62)\times10^{-5}$ for LOWZ and $\tau E = ( 1.25\pm 1.06)\times10^{-5}$ for CMASS, with the optimal angular radius of an aperture photometry filter to estimate the CMB temperature distortion associ ated with each galaxy. By repeating the pairwise kSZ power analysis for various aperture radii, we measure the optical depth as a function of aperture ra dii. While this analysis results in the kSZ signals with only evidence for a detection, ${\rm S/N}=2.54$ for LOWZ and $1.24$ for CMASS, the combination of future CMB and spectroscopic galaxy surveys should enable precision measurements. We estimate that the combination of CMB-S4 and data from DESI shoul d yield detections of the kSZ signal with ${\rm S/N}=70-100$, depending on the resolution of CMB-S4.