Observational constraints on the slope of the radial acceleration relation at low accelerations

TL;DR

This paper investigates the low-acceleration behavior of the radial acceleration relation (RAR) in galaxies, finding evidence for a break to a steeper slope that challenges the idea of RAR as a universal natural law.

Contribution

It provides observational constraints on the low-acceleration slope of the RAR, using independent data sets to test the extrapolation of the relation beyond observable kinematic regions.

Findings

Data favor a steeper low-acceleration slope in the RAR.

Unphysical mass profiles arise if the RAR is extrapolated without modification.

Weak lensing and galaxy dynamics data support a break in the RAR slope.

Abstract

The radial acceleration relation (RAR) locally relates the `observed' acceleration inferred from the dynamics of a system to the acceleration implied by its baryonic matter distribution. The relation as traced by galaxy rotation curves is one-to-one with remarkably little scatter, implying that the dynamics of a system can be predicted simply by measuring its density profile as traced by e.g. stellar light or gas emission lines. Extending the relation to accelerations below those usually probed by practically observable kinematic tracers is challenging, especially once accounting for faintly emitting baryons, such as the putative warm-hot intergalactic medium, becomes important. We show that in the low-acceleration regime, the (inverted) RAR predicts an unphysical, declining enclosed baryonic mass profile for systems with `observed' acceleration profiles steeper than $g_{\rm obs}\propto r^{-1}$ (corresponding to density profiles steeper than isothermal - $\rho(r)\propto r^{-2}$). If the RAR is tantamount to a natural law, such acceleration profiles cannot exist. We apply this argument to test the compatibility of an extrapolation of the rotation curve-derived RAR to low accelerations with data from galaxy-galaxy weak lensing, dwarf spheroidal galaxy stellar kinematic, and outer Milky~Way dynamical measurements, fully independent of the uncertainties inherent in direct measurements of the baryonic matter distribution. In all cases we find that the data weakly favour a break to a steeper low-acceleration slope. Improvements in measurements and modelling of the outer Milky~Way, and weak lensing, seem like the most promising path toward stronger constraints on the low-acceleration behaviour of the RAR.