Abstract
We fit the rotation curves of isolated dwarf galaxies to directly measure the stellar mass-halo mass relation (M∗ − M200) over the mass range 5 × 105 <∼ M∗/M <∼ 108 . 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∗ − M200 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 Λ Cold Dark Matter Bolshoi simulation, we find remarkable agreement between the two. This holds down to M200 ∼ 5 × 109 M , and to M200 ∼ 5 × 108 M if we assume a power law extrapolation of the SDSS stellar mass function below M∗ ∼ 107 M . 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∗ ∼ 109 M , 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 Λ Warm Dark Matter cosmology, finding that it fails at 68% confidence for a thermal relic mass of mWDM < 1.25 keV, and mWDM < 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.