Abundance matching with the mean star formation rate: there is no missing satellites problem in the Milky Way above ${\mathbf{M}}_{200}\sim 10^9{\mathbf{M}}_{\odot }$

Abstract

We introduce a novel abundance matching technique that produces a more accurate estimate of the pre-infall halo mass, $M_{200}$, for satellite galaxies. To achieve this, we abundance match with the mean star formation rate, averaged over the time when a galaxy was forming stars, $⟨\mathrm{SFR}⟩$, instead of the stellar mass, $M_{\ast }$. Using data from the Sloan Digital Sky Survey, the GAMA survey and the Bolshoi simulation, we obtain a statistical $⟨\mathrm{SFR}⟩-{\mathrm{M}}_{200}$ relation in $\Lambda \mathrm{CDM}$. We then compare the pre-infall halo mass, $M_{200}^{\mathrm{abund}}$, derived from this relation with the pre-infall dynamical mass, $M_{200}^{\mathrm{dyn}}$, for 21 nearby dSph and dIrr galaxies, finding a good agreement between the two. As a first application, we use our new $⟨\mathrm{SFR}⟩-{\mathrm{M}}_{200}$ relation to empirically measure the cumulative mass function of a volume-complete sample of bright Milky Way satellites within 280 kpc of the Galactic centre. Comparing this with a suite of cosmological 'zoom' simulations of Milky Way-mass halos that account for subhalo depletion by the Milky Way disc, we find no missing satellites problem above $M_{200}\sim 10^9{\mathrm{M}}_{\odot }$ in the Milky Way. We discuss how this empirical method can be applied to a larger sample of nearby spiral galaxies.

15 pages, 7 figures. Final version accepted for publication in MNRAS. The methodology has been substantially clarified and improved throughout, including a significantly expanded method section and two new Figures that explain how we derive the cumulative <SFR> number density function of galaxies, required for our abundance matching. The key results are unchanged from previously