Title: A direct measure of free electron gas via the Kinematic Sunyaev-Zel'dovich effect in Fourier-space analysis,
Abstract: 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.