Velocity reconstruction in the era of DESI and Rubin (part II): Realistic samples on the light cone

Reconstructing the galaxy peculiar velocity field from the distribution of large-scale structure plays an important role in cosmology. On one hand, it gives us an insight into structure formation and gravity; on the other, it allows us to selectively extract the kinetic Sunyaev-Zeldovich (kSZ) effect from cosmic microwave background (CMB) maps. In this work, we employ high-accuracy synthetic galaxy catalogs on the light cone to investigate how well we can recover the velocity field when utilizing the three-dimensional spatial distribution of the galaxies in a modern large-scale structure experiment such as the Dark Energy Spectroscopic Instrument (DESI) and Rubin Observatory (LSST). In particular, we adopt the standard technique used in baryon acoustic oscillation (BAO) analysis for reconstructing the Zeldovich displacements of galaxies through the continuity equation, which yields a first-order approximation to their large-scale velocities. We investigate variations in the number density, bias, mask, area, redshift noise, and survey depth, and smoothing. Since our main goal is to provide guidance for planned kSZ analysis between DESI and the Atacama Cosmology Telescope (ACT), we apply velocity reconstruction to a faithful representation of DESI spectroscopic and photometric targets. We report the cross-correlation coefficient between the reconstructed and the true velocities along the line of sight. For the DESI Y1 spectroscopic survey, we expect the correlation coefficient to be $r \approx 0.64$, while for a photometric survey with $σ_z/(1+z) = 0.02$, as is approximately the case for the Legacy Survey used in the target selection of DESI galaxies, $r$ shrinks by half to $r \approx 0.31$. We hope the results in this paper can be used to inform future kSZ stacking studies. All scripts used in this paper can be found here: \url{https://github.com/boryanah/abacus_kSZ_recon}.