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The radial acceleration relation (RAR) locally relates the `observed'acceleration inferred from the dynamics of a system to the acceleration impliedby its baryonic matter distribution. The relation as traced by galaxy rotationcurves is one-to-one with remarkably little scatter, implying that the dynamicsof a system can be predicted simply by measuring its density profile as tracedby e.g. stellar light or gas emission lines. Extending the relation toaccelerations below those usually probed by practically observable kinematictracers is challenging, especially once accounting for faintly emittingbaryons, such as the putative warm-hot intergalactic medium, becomes important.We show that in the low-acceleration regime, the (inverted) RAR predicts anunphysical, 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 - $\rho(r)\proptor^{-2}$). If the RAR is tantamount to a natural law, such acceleration profilescannot exist. We apply this argument to test the compatibility of anextrapolation of the rotation curve-derived RAR to low accelerations with datafrom galaxy-galaxy weak lensing, dwarf spheroidal galaxy stellar kinematic, andouter Milky~Way dynamical measurements, fully independent of the uncertaintiesinherent in direct measurements of the baryonic matter distribution. In allcases we find that the data weakly favour a break to a steeper low-accelerationslope. Improvements in measurements and modelling of the outer Milky~Way, andweak lensing, seem like the most promising path toward stronger constraints onthe low-acceleration behaviour of the RAR.

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