Photometric Mass Estimation and the Stellar Mass-Halo Mass Relation for Low Mass Galaxies

Abstract: We present a photometric halo mass estimation technique for local galaxies that enables us to establish the stellar mass-halo mass (SMHM) relation down to stellar masses of 10$^5$ M$\odot$. We find no detectable differences among the SMHM relations of four local galaxy clusters or between the cluster and field relations and we find agreement with extrapolations of previous SMHM relations derived using abundance matching approaches. We fit a power law to our empirical SMHM relation and find that for adopted NFW dark matter profiles and for M$* < 10^9$ M$\odot$, the halo mass is M$_h = 10^{10.35\pm0.02}({\rm M}/10^8 {\rm M}\odot)^{0.63\pm0.02}$. The normalisation of this relation is susceptible to systematic modelling errors that depend on the adopted dark matter potential and the quoted uncertainties refer to the uncertainties in the median relation. For galaxies with M$ < 10^{9}$ M$\odot$ that satisfy our selection criteria, the scatter about the fit in $M_h$, including uncertainties arising from our methodology, is 0.3 dex. Finally, we place lower luminosity Local Group galaxies on the SMHM relationship using the same technique, extending it to M$* \sim 10^3$ M$\odot$ and suggest that some of these galaxies show evidence for additional mass interior to the effective radius beyond that provided by the standard dark matter profile. If this mass is in the form of a central black hole, the black hole masses are in the range of intermediate mass black holes, $10^{(5.7\pm0.6)}$ M$\odot$, which corresponds to masses of a few percent of M$_h$, well above values extrapolated from the relationships describing more massive galaxies.