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Abstract:

We present a systematic statistical analysis of an informal astrophysical phenomenon known as Renzo’s rule (or Sancisi’s law), which states that ‘for any feature in a galaxy’s luminosity profile, there is a corresponding feature in the rotation curve, and vice versa’. This is often posed as a challenge for the standard Λ cold dark matter (CDM) model while supporting alternative theories such as modified Newtonian dynamics (MOND). Indeed, we identify clear features in the dwarf spiral NGC 1560 – a prime example for Renzo’s rule – and find correlation statistics which support Renzo’s rule with a slight preference for MOND over CDM halo fits. However, a broader analysis on galaxies in the Spitzer Photometry & Accurate Rotation Curves (SPARC) data base reveals an excess of features in rotation curves that lack clear baryonic counterparts, with correlation statistics deviating up to on average from that predicted by both MOND and CDM haloes, challenging the validity of Renzo’s rule. Thus we do not find clear evidence for Renzo’s rule in present galaxy data overall. We additionally perform mock tests, which show that a definitive test of Renzo’s rule is primarily limited by the lack of clearly resolved baryonic features in current galaxy data.

Abstract:

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 = 0.793 ± 0.035. The result is in good agreement with both weak lensing and Planck, but is in strong disagreement with some peculiar velocity studies.

Abstract:

To maximize the amount of information extracted from cosmological datasets, simulations that accurately represent these observations are necessary. However, traditional simulations that evolve particles under gravity by estimating particle-particle interactions (𝑁-body simulations) are computationally expensive and prohibitive to scale to the large volumes and resolutions necessary for the upcoming datasets. Moreover, modeling the distribution of galaxies typically involves identifying virialized dark matter halos, which is also a time- and memory-consuming process for large 𝑁-body simulations, further exacerbating the computational cost. In this study, we introduce CHARM, a novel method for creating mock halo catalogs by matching the spatial, mass, and velocity statistics of halos directly from the large-scale distribution of the dark matter density field. We develop multistage neural spline flow-based networks to learn this mapping at redshift 𝑧 =0.5 directly with computationally cheaper low-resolution particle mesh simulations instead of relying on the high-resolution 𝑁-body simulations. We show that the mock halo catalogs and painted galaxy catalogs have the same statistical properties as obtained from 𝑁-body simulations in both real space and redshift space. Finally, we use these mock catalogs for cosmological inference using redshift-space galaxy power spectrum, bispectrum, and wavelet-based statistics using simulation-based inference, performing the first inference with accelerated forward model simulations and finding unbiased cosmological constraints with well-calibrated posteriors.