The stellar mass-halo mass relation of isolated field dwarfs: a critical
  test of $\Lambda$CDM at the edge of galaxy formation
  We fit the rotation curves of isolated dwarf galaxies to directly measure the
stellar mass-halo mass relation ($M_*-M_{200}$) over the mass range $5 \times
10^5 < M_{*}/{\rm M}_\odot < 10^{8}$. By accounting for cusp-core
transformations due to stellar feedback, we find a monotonic relation with
little scatter. Such monotonicity implies that abundance matching should yield
a similar $M_*-M_{200}$ if the cosmological model is correct. Using the 'field
galaxy' stellar mass function from the Sloan Digital Sky Survey (SDSS) and the
halo mass function from the $\Lambda$ Cold Dark Matter Bolshoi simulation, we
find remarkable agreement between the two. This holds down to $M_{200} \sim 5
\times 10^9$M$_\odot$, and to $M_{200} \sim 5 \times 10^8$M$_\odot$ if we
assume a power law extrapolation of the SDSS stellar mass function below $M_*
\sim 10^7$M$_\odot$.
  However, if instead of SDSS we use the stellar mass function of nearby galaxy
groups, then the agreement is poor. This occurs because the group stellar mass
function is shallower than that of the field below $M_* \sim 10^9$M$_\odot$,
recovering the familiar 'missing satellites' and 'too big to fail' problems.
Our result demonstrates that both problems are confined to group environments
and must, therefore, owe to 'galaxy formation physics' rather than exotic
cosmology.
  Finally, we repeat our analysis for a $\Lambda$ Warm Dark Matter cosmology,
finding that it fails at 68% confidence for a thermal relic mass of $m_{\rm
WDM} < 1.25$keV, and $m_{\rm WDM} < 2$keV if we use the power law extrapolation
of SDSS. We conclude by making a number of predictions for future surveys based
on these results.
