The kinetic Sunyaev-Zel'dovich tomography II: probing the circumgalactic medium

We propose the use of the kinetic Sunyaev-Zel'dovich (kSZ) effect to probe the circumgalactic medium (CGM), with the aid of a spectroscopic survey covering the same area of a SZ survey. One can design an optimal estimator of the kSZ effect of the CGM with a matched filter, and construct the cross correlation between the estimator and the peculiar velocity recovered from the galaxy survey, which can be measured by stacking a number of galaxies. We investigate two compelling profiles for the CGM, the MB profile (Maller & Bullock 2004) and the $\beta$ profile, and estimate the detectability against the synergy of a fiducial galaxy survey with number density $10^{-3}h^3\,$ Mpc$^{-3}$ and an ACT-like SZ survey. We show that the shape of the filter does not change much with redshift for the $\beta$ profile, while there are significant side lobes at $z<0.1$ for the MB profile. By stacking $\sim 10^4$ Milky Way-size halos around z $\sim 0.5$, one can get $\gtrsim$ 1 $\sigma$ signal to noise (S/N) for the both profiles. The S/N increases with decreasing redshift before it reaches a maximum ($\sim$ 7.5 at z $\simeq$ 0.15 for the MB profile, $\sim 19$ at $z\simeq 0.03$ for the $\beta$ profile). Due to the large beam size, a Planck-like CMB survey can marginally detect the kSZ signal by stacking the same number of galaxies at $z<0.1$. The search for the CGM in realistic surveys will involve dividing the galaxies into subsamples with similar redshift and mass of host halos, and scaling the results presented here to obtain the S/N.