One Law To Rule Them All: The Radial Acceleration Relation of Galaxies

Abstract: We study the link between baryons and dark matter in 240 galaxies with spatially resolved kinematic data. Our sample spans 9 dex in stellar mass and includes all morphological types. We consider (i) 153 late-type galaxies (LTGs; spirals and irregulars) with gas rotation curves from the SPARC database; (ii) 25 early-type galaxies (ETGs; ellipticals and lenticulars) with stellar and HI data from ATLAS^3D or X-ray data from Chandra; and (iii) 62 dwarf spheroidals (dSphs) with individual-star spectroscopy. We find that LTGs, ETGs, and "classical" dSphs follow the same radial acceleration relation: the observed acceleration (gobs) correlates with that expected from the distribution of baryons (gbar) over 4 dex. The relation coincides with the 1:1 line (no dark matter) at high accelerations but systematically deviates from unity below a critical scale of ~10^-10 m/s^2. The observed scatter is remarkably small (<0.13 dex) and largely driven by observational uncertainties. The residuals do not correlate with any global or local galaxy property (baryonic mass, gas fraction, radius, etc.). The radial acceleration relation is tantamount to a Natural Law: when the baryonic contribution is measured, the rotation curve follows, and vice versa. Including ultrafaint dSphs, the relation may extend by another 2 dex and possibly flatten at gbar<10^-12 m/s^2, but these data are significantly more uncertain. The radial acceleration relation subsumes and generalizes several well-known dynamical properties of galaxies, like the Tully-Fisher and Faber-Jackson relations, the "baryon-halo" conspiracies, and Renzo's rule.

• The paper analyzes the Radial Acceleration Relation (RAR) across 240 diverse galaxies, finding it holds with extraordinary tightness over 4 dex of acceleration, predominantly limited by observational uncertainties.
• The RAR shows a systematic transition from a baryon-dominated regime at high accelerations to a dark matter dominated regime at low accelerations, unifying relations like the Tully-Fisher law.
• The remarkable consistency of the RAR challenges standard cold dark matter models and suggests a fundamental acceleration scale aligned with predictions from alternative gravity theories like MOND.

Analysis of the Radial Acceleration Relation in Galaxies

The radial acceleration relation (RAR) presented in this study represents a significant consolidation of galactic dynamics and baryonic mass distribution across a diverse array of 240 galaxies. This analysis, conducted by Lelli et al., examines the correlation between observed gravitational accelerations and those predicted purely from baryonic components, revealing an extraordinary consistency across differing galactic types and sizes.

The sample includes 153 late-type galaxies (LTGs), 25 early-type galaxies (ETGs), and 62 dwarf spheroidals (dSphs), expanding over a range of nine orders of magnitude in stellar mass and incorporating all major morphological classifications. The RAR is found to hold remarkably tight over four dex of accelerations, with the scatter predominantly due to observational uncertainties rather than intrinsic galactic variability.

A pivotal finding is the clear delineation of the acceleration relation following a systematic deviation from the baryon-dominated regime at high accelerations, converging at higher baryonic-to-total acceleration ratios, to a dark-matter dominated regime at low accelerations. The relation approximates unity at high accelerations, highlighting dominant baryonic effects in the dynamics of massive, high-surface-brightness galaxies, transitioning as dark matter becomes more pronounced in low-surface-brightness systems.

Moreover, the research subsumes well-known scaling laws, evidencing the RAR's comprehensiveness: this includes the Tully-Fisher relation for LTGs, alongside the Faber-Jackson relation observable in ETGs. This investigation extends to the grundnorm proposed by Renzo's rule, offering a quantitative correspondence between luminous structures and velocity features in rotation curves.

From a theoretical perspective, these persistent galactic relations present intriguing dilemmas for standard cold dark matter models. The profound regularity and minimal intrinsic scatter challenge the stochastic nature presumed by hierarchical galaxy formation contexts within these frameworks. Moreover, addressing the apparent baryon-dark matter coupling arises as an intricate task, potentially signaling gaps in our understanding of either dark matter physics or necessitating amendments to gravitational theory. Notably, the empirical constant $g_\dag$ identified aligns with the foundational accelerative threshold postulated by MONDian theories, reinforcing debates around alternative gravitation frameworks or novel dark sector physics.

This work compels a re-evaluation of galactic dynamics models, directing attention toward detailed explorations in both hydrodynamical simulations and empirical tuning processes within gravitational paradigms. The implications are profound, inviting deeper inquiries into the constituents of cosmic structures and possibly nudging the boundaries of established astrophysical laws. The RAR finds itself as a compelling empirical touchstone amidst these investigations, guiding future theoretical and observational pursuits within the domain of galaxy formation and evolution.