On the functional form of the radial acceleration relation

Understand

We apply a new method for learning equations from data -- Exhaustive Symbolic Regression (ESR) -- to late-type galaxy dynamics as encapsulated in the radial acceleration relation (RAR).

• Relating the centripetal acceleration due to baryons, $g_\text{bar}$, to the total dynamical acceleration, $g_\text{obs}$, the RAR has been claimed to manifest a new law of nature due to its regularity and tightness, in agreement with Modified Newtonian Dynamics (MOND).
• Fits to this relation have been restricted by prior expectations to particular functional forms, while ESR affords an exhaustive and nearly prior-free search through functional parameter space to identify the equations optimally trading accuracy with simplicity.
• Working with the SPARC data, we find the best functions typically satisfy $g_\text{obs} \propto g_\text{bar}$ at high $g_\text{bar}$, although the coefficient of proportionality is not clearly unity and the deep-MOND limit $g_\text{obs} \propto \sqrt{g_\text{bar}}$ as $g_\text{bar} \to 0$ is little evident at all.