Inferring the Total Mass of Galaxy Halos Using Photometry

Galaxy size, as defined as the radius at which the stellar surface density reaches $1~\mathrm{M}_\odot\,\mathrm{pc}^{-2}$ ($R_1$), has been shown to correlate more tightly with stellar mass than the effective radius. Cosmological simulations further predict a tight relation between $R_1$ and dark matter halo mass ($M_{200}$), but this prediction has not yet been tested observationally. We present the first observational test of the predicted $R_1$--$M_{200}$ relation and assess whether galaxy size, defined through $R_1$, can serve as a robust estimator of dark matter halo mass. We analyze galaxies from the SPARC database, combining high-quality rotation curves to infer dark matter halo masses with stellar surface density profiles derived from photometric data to measure $R_1$. We then compare the observed relation with the predictions from state-of-the-art cosmological simulations. We find good agreement between observations and simulations: galaxies follow the same tight $R_1$--$M_{200}$ relation predicted by numerical models across the explored mass range, with low intrinsic scatter. We provide the first observational validation of the $R_1$--$M_{200}$ relation, demonstrating that $R_1$ is a simple, physically motivated, and robust estimator of dark matter halo mass. Because $R_1$ is determined entirely from photometric observations, it provides a tool for inferring halo masses from imaging data alone, with applications to studies of galaxy formation and evolution.