Distilling Dark Matter Halo Profiles: Symbolic Regression on Rotation Curve Data

Rotation curves of spiral galaxies directly probe the underlying dark matter halo structure, yet no halo profile model universally describes the diversity observed across galaxies. We use symbolic regression applied to the Spitzer Photometry \& Accurate Rotation Curves (SPARC) database to distil a new family of dark matter halo velocity profiles directly from observational data. The resulting expression is parameterised by an amplitude $c$, dimensionless radial coordinate $x$, and a galaxy-specific shape parameter $\gamma$. To formally evaluate performance, we fit the new profile, alongside seven established literature profiles, to SPARC using Markov Chain Monte Carlo (MCMC) methods. Trained on a subset of 115 galaxies from the 175-galaxy sample, the profile achieves good fits, as defined by a reduced chi-squared statistic $\chi^2_\nu<2$, on 81\% of the out-of-distribution test sample and 76\% of the full SPARC sample, outperforming all comparison profiles. We interpret the model physically, and quantify the correlation between the model parameters and observable galaxy properties, thereby exploring the link between dark matter halo structure and galaxy morphology. The results demonstrate the potential of symbolic regression as a tool for data-driven discovery in galactic dynamics.