  The cold dark matter halo mass function is much steeper than the galaxy
stellar mass function on galactic and subgalactic scales. This difference is
usually reconciled by assuming that the galaxy formation efficiency drops
sharply with decreasing halo mass, so that virtually no dwarf galaxies form in
halos less massive than ~ 10^10 M_sun. In turn, this implies that, at any given
radius, the dark mass enclosed by a galaxy must exceed a certain minimum. We
use rotation curves of dwarf galaxies compiled from the literature to explore
whether their enclosed mass is consistent with these constraints. We find that
almost one half of the dwarfs in our sample with stellar mass between 10^6-10^7
M_sun are at odds with this restriction: either they live in halos with masses
substantially below 10^10 M_sun or there is a mechanism capable of reducing the
dark mass enclosed by some of the faintest dwarfs. Neither possibility is
easily accommodated within the standard LCDM scenario. Extending galaxy
formation to halos well below 10^10 M_sun would lead to large numbers of dwarf
galaxies in excess of current estimates; at the same time, the extremely low
stellar mass of the systems involved makes it unlikely that baryonic effects
can reduce their dark matter content. Resolving this challenge seems to require
new insights into dwarf galaxy formation, or perhaps a radical revision of the
prevailing paradigm.
