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The total luminosity of satellite galaxies around a central galaxy,L$_{sat}$, is a powerful metric for probing dark matter halos. In this paper weuse data from the Sloan Digital Sky Survey and DESI Legacy Imaging Surveys toexplore the relationship between L$_{sat}$ and various observable galaxyproperties for a sample of 117,966 central galaxies out to $z = 0.15$. At fixedstellar mass, every galaxy property we explore shows a correlation withL$_{sat}$. This implies that dark matter halos play a possibly significant rolein determining these secondary galaxy properties. We quantify thesecorrelations by computing the mutual information between L$_{sat}$ andsecondary properties and explore how this mutual information varies as afunction of stellar mass and when separating the sample into star-forming andquiescent central galaxies. We find that absolute r-band magnitude correlatesmore strongly with L$_{sat}$ than stellar mass across all galaxy populations;and that effective radius, velocity dispersion, and S\'ersic index do so aswell for star-forming and quiescent galaxies. L$_{sat}$ is sensitive to boththe mass of the host halo as well as the halo formation history, with youngerhalos having higher L$_{sat}$. L$_{sat}$ by itself cannot distinguish betweenthese two effects, but measurements of galaxy large-scale environment can breakthis degeneracy. For star-forming central galaxies, we find that r$_{\rm eff}$,$\sigma_v$, and S\'ersic index all correlate with large-scale density, implyingthat these halo age plays a role in determining these properties. For quiescentgalaxies, we find that all secondary properties are independent of environment,implying that correlations with L$_{sat}$ are driven only by halo mass. Theseresults are a significant step forward in quantifying the full extent of thegalaxy-halo connection, and present a new test of galaxy formation models.

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