The kinetic Sunyaev Zeldovich effect (kSZ) effect is a potentially powerful probe to the missing baryons. However, the kSZ signal is overwhelmed by various contaminations and the cosmological application is hampered by loss of redshift information due to the projection effect. We propose a kSZ tomography method to alleviate these problems, with the aid of galaxy spectroscopic redshift surveys. We propose to estimate the large scale peculiar velocity through the 3D galaxy distribution, weigh it by the 3D galaxy density and adopt the product projected along the line of sight with a proper weighting as an estimator of the true kSZ temperature fluctuation $Theta$. We thus propose to measure the kSZ signal through the $Hat{Theta}$-$Theta$ cross correlation. This approach has a number of advantages (see details in the abstract of the paper). We test the proposed kSZ tomography against non-adiabatic and adiabatic hydrodynamical simulations. We confirm that $hat{Theta}$ is indeed tightly correlated with $Theta$ at $kla 1h/$Mpc, although nonlinearities in the density and velocity fields and nonlinear redshift distortion do weaken the tightness of the $hat{Theta}$-$Theta$ correlation. We further quantify the reconstruction noise in $Hat{Theta}$ from galaxy distribution shot noise. Based on these results, we quantify the applicability of the proposed kSZ tomography for future surveys. We find that, in combination with the BigBOSS-N spectroscopic redshift survey, the PLANCK CMB experiment will be able to detect the kSZ with an overall significance of $sim 50sigma$ and further measure its redshift distribution at many redshift bins over $0<z<2$.
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