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The abundance of the faintest galaxies provides insight into the nature ofdark matter and the process of dwarf galaxy formation. In the LCDM scenario,low mass halos are so numerous that the efficiency of dwarf formation mustdecline sharply with decreasing halo mass in order to accommodate the relativescarcity of observed dwarfs and satellites in the Local Group. The nature ofthis decline contains important clues to the mechanisms regulating the onset ofgalaxy formation in the faintest systems. We explore here two possible modelsfor the stellar mass ($M_*$)-halo mass ($M_{200}$) relation at the faint end,motivated by some of the latest LCDM cosmological hydrodynamical simulations.One model includes a sharp mass threshold below which no luminous galaxiesform, as expected if galaxy formation proceeds only in systems above theHydrogen-cooling limit. In the second model, $M_*$ scales as a steep power-lawof $M_{200}$ with no explicit cutoff, as suggested by recent semianalytic work.Although both models predict satellite numbers around Milky Way-like galaxiesconsistent with current observations, they predict vastly different numbers ofultra-faint dwarfs and of satellites around isolated dwarf galaxies. Ourresults illustrate how the satellite mass function around dwarfs may be used toprobe the $M_*$-$M_{200}$ relation at the faint end and to elucidate themechanisms that determine which low-mass halos "light up" or remain dark in theLCDM scenario.

Satellite mass functions and the faint end of the galaxy mass-halo mass relation in LCDM