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Peculiar velocities of galaxies and halos can be reconstructed from their spatial distribution alone. This technique is analogous to the baryon acoustic oscillations reconstruction, using the continuity equation to connect density and velocity fields. The resulting reconstructed velocities can be used to measure imprints of galaxy velocities on the cosmic microwave background like the kinematic Sunyaev-Zel'dovich effect or the moving lens effect. As the precision of these measurements increases, characterizing the performance of the velocity reconstruction becomes crucial to allow unbiased and statistically optimal inference. In this paper, we quantify the relevant performance metrics: the variance of the reconstructed velocities and their correlation coefficient with the true velocities. We show that the relevant velocities to reconstruct for kSZ and moving lens are actually the halo---rather than galaxy---velocities. We quantify the impact of redshift-space distortions, photometric redshift errors, satellite galaxy fraction, incorrect cosmological parameter assumptions and smoothing scale on the reconstruction performance. We also investigate hybrid reconstruction methods, where velocities inferred from spectroscopic samples are evaluated at the positions of denser photometric samples. We find that using exclusively the photometric sample is better than performing a hybrid analysis. The 2 Gpc/h length simulations from abacussummit with realistic galaxy samples for DESI and Rubin LSST allow us to perform this analysis in a controlled setting. In the companion paper B. Hadzhiyska, S. Ferraro, B. Ried Guachalla, and E. Schaan, companion paper, Phys. Rev. D 109, 103534 (2024). , we further include the effects of evolution along the light cone and give realistic performance estimates for DESI luminous red galaxies, emission line galaxies, and Rubin LSST-like samples.
Guachalla et al. (Wed,) studied this question.