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.
