Kinetic Sunyaev-Zel'dovich tomography with spectroscopic redshift surveys

The kinetic Sunyaev-Zel'dovich (kSZ) effect is potentially a powerful tool that can be used to search for missing baryons. However, the kSZ signal is overwhelmed by various contaminations and the cosmological application is hampered by the loss of redshift information as a result of 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 three-dimensional (3D) galaxy distribution, to weigh it using the 3D galaxy density and to adopt the product projected along the line of sight with a proper weighting as an estimator of the true kSZ temperature fluctuation Theta. Because the underlying directional dependence in the estimator (Theta) over cap closely resembles that in the true kSZ signal Theta, (Theta) over cap is tightly correlated with Theta. Thus, it avoids the problem of null correlation between the galaxy density and Theta, which prohibits the kSZ extraction through the usual density-cosmic microwave background (CMB) two-point cross-correlation measurement. Thus, we propose to measure the kSZ signal through the (Theta) over cap-Theta cross-correlation. This approach has a number of advantages. (i) Because of the underlying directional dependence of (Theta) over cap, it is uncorrelated with the primary CMB, the thermal SZ effect and astrophysical contaminations, such as dusty star-forming galaxies. Thus, the (Theta) over cap-Theta> cross-correlation picks up the kSZ signal in the SZ survey in a clean manner. (ii) With the aid of galaxy redshifts, the cross-correlation recovers the redshift information of the kSZ signal and allows for a more detailed investigation of missing baryons. (iii) As galaxy surveys usually have a high signal-to-noise (S/N) ratio, the S/N ratio of the kSZ measurement through the (Theta) over cap-Theta cross-correlation can be significantly improved. We test the proposed kSZ tomography against non-adiabatic and adiabatic hydrodynamical simulations. We confirm that (Theta) over cap is indeed tightly correlated with Theta at k less than or similar to 1 h Mpc-1, although non-linearities in the density and velocity fields and non-linear redshift distortion do weaken the tightness of the (Theta) over cap-Theta correlation. We further quantify the reconstruction noise in (Theta) over cap 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 effect with an overall significance of similar to 50 sigma and further measure its redshift distribution at many redshift bins over 0 < z < 2.