The Velocity Field Olympics: Assessing velocity field reconstructions with direct distance tracers
Published in MNRAS (Submitted), 2025
Recommended citation: R. Stiskalek, H. Desmond, J. Devriendt, A. Slyz, G. Lavaux, M.J. Hudson, D.J. Bartlett, and H.M. Courtois. (2025). "The Velocity Field Olympics: Assessing velocity field reconstructions with direct distance tracers." arXiv:2502.00121.
Abstract
The peculiar velocity field of the local Universe provides direct insights into its matter distribution and the underlying theory of gravity, and is essential in cosmological analyses for modelling deviations from the Hubble flow. Numerous methods have been developed to reconstruct the density and velocity fields at z≲0.05, typically constrained by redshift-space galaxy positions or by direct distance tracers such as the Tully-Fisher relation, the fundamental plane, or Type Ia supernovae. We introduce a validation framework to evaluate the accuracy of these reconstructions against catalogues of direct distance tracers. Our framework assesses the goodness-of-fit of each reconstruction using Bayesian evidence, residual redshift discrepancies, velocity scaling, and the need for external bulk flows. Applying this framework to a suite of reconstructions – including those derived from the Bayesian Origin Reconstruction from Galaxies (BORG) algorithm and from linear theory – we find that the non-linear BORG reconstruction consistently outperforms others. We highlight the utility of such a comparative approach for supernova or gravitational wave cosmological studies, where selecting an optimal peculiar velocity model is essential. Additionally, we present calibrated bulk flow curves predicted by the reconstructions and perform a density-velocity cross-correlation using a linear theory reconstruction to constrain the growth factor, yielding S8=0.69±0.034. This result is in significant tension with Planck but agrees with other peculiar velocity studies.
Differences in logarithmic evidences $Z$ from our flow validation model for various local Universe reconstructions (shown on the $x$-axis, see Table 1), compared against peculiar velocity samples (individual panels, see Table 2). Higher bars indicate a preferred model, and a bar of zero height indicates the reference (least successful) model. The logarithmic evidences are normalised with respect to the reference model as only relative differences are meaningful. Solid bars show evidences using the highest available resolution for each model, while hatched bars show evidences when all fields are smoothed to the resolution of $7.8\,h^{-1} \, {\rm Mpc}$, twice that of Courtois et al. (2023). Overall, CSIBORG2 is the preferred model while the CosmicFlows-based reconstructions (Sorce 2018 and Courtois et al. 2023) are disfavoured. Upon smoothing, the linear reconstruction of Carrick et al. 2015 becomes marginally preferred.