Connecting SDSS central galaxies to their host halos using total satellite luminosity

The total luminosity of satellite galaxies around a central galaxy, L-sat, is a powerful metric for probing dark matter haloes. We utilize data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys to explore the relationship between L-sat and galaxy properties for a sample of 117 966 central galaxies with z <= 0.15. At fixed stellar mass, we find that every galaxy property we explore correlates with L-sat, suggesting that dark matter haloes can influence them. We quantify these correlations by computing the mutual information between L-sat and secondary properties and explore how this varies as a function of stellar mass and star-formation activity. We find that absolute r-band magnitude correlates more strongly with L-sat than stellar mass across all galaxy populations; and that effective radius, velocity dispersion, and Sersic index do so as well for star-forming and quiescent galaxies. L-sat is influenced by the mass of the host halo as well as the halo formation history, with younger haloes having higher L-sat. L-sat cannot distinguish between these two effects, but measurements of galaxy large-scale environment can break this degeneracy. For star-forming centrals, R-eff, sigma(v), and Sersic index all correlate with large-scale density, implying that the halo age affects these properties. For quiescent galaxies, all secondary properties are independent of environment, implying that correlations with L-sat are driven only by halo mass. These results are a significant step forward in quantifying the extent of the galaxy-halo connection, and present a new test of galaxy formation models.