Forward-modelling the Luminosity, Distance, and Size distributions of the Milky Way Satellites

Abstract: We use \texttt{GRUMPY}, a simple regulator-type model for dwarf galaxy formation and evolution, to forward model the dwarf galaxy satellite population of the Milky Way (MW) using the Caterpillar zoom-in simulation suite. We show that luminosity and distance distributions of the model satellites are consistent with the distributions measured in the DES, PS1 and SDSS surveys, even without including a model for the orphan galaxies. We also show that our model for dwarf galaxy sizes can simultaneously reproduce the observed {\it distribution} of stellar half-mass radii, $r_{1/2}$, of the MW satellites and the overall $r_{1/2}-M_\star$ relation exhibited by observed dwarf galaxies. The model predicts that some of the observed faint stellar systems with $r_{1/2}<10$ pc are ultra-faint dwarf galaxies. Scaling of the stellar mass $M_\star$ and peak halo mass $M_{\rm peak}$ for the model satellites is not described by a power law, but has a clear flattening of $M_\star-M_{\rm peak}$ scaling at $M_{\rm peak}<10^8\,M_\odot$ imprinted by reionization. As a result, the fraction of low mass haloes ($M_{\rm peak} < 10^8\, M_\odot$) hosting galaxies with $M_V<0$ is predicted to be 50% at $M_{\rm peak} \sim 3.6 \times 10^7\,M_\odot$. We find that such high fraction at that halo mass helps to reproduce the number of dwarf galaxies discovered recently in the HSC-SSP survey. Using the model we forecast that there should be the total of $440^{+201}_{-147}$ (68\% confidence interval) MW satellites with $M_V < 0$ and $r_{1/2} > 10$ pc within 300 kpc and make specific predictions for the HSC-SSP, DELVE-WIDE and LSST surveys.