A statistical investigation of the mass discrepancy-acceleration
  relation
  We use the mass discrepancy-acceleration relation (the correlation between
the ratio of total-to-visible mass and acceleration in galaxies; MDAR) to test
the galaxy-halo connection. We analyse the MDAR using a set of 16 statistics
that quantify its four most important features: its shape, its scatter, the
presence of a "characteristic acceleration scale," and the correlation of its
residuals with other galaxy properties. We construct an empirical framework for
the galaxy-halo connection in LCDM to generate predictions for these
statistics, starting with conventional correlations (halo abundance matching;
AM) and introducing more where required. Comparing to the SPARC data, we find
that: 1) the approximate shape of the MDAR is readily reproduced by AM, and
there is no evidence that the acceleration at which dark matter becomes
negligible has less spread in the data than in AM mocks; 2) even under
conservative assumptions, AM significantly overpredicts the scatter in the
relation and its normalisation at low acceleration, and furthermore positions
dark matter too close to galaxies' centres on average; 3) the MDAR affords 2
sigma evidence for an anticorrelation of galaxy size and Hubble type with halo
mass or concentration at fixed stellar mass. Our analysis lays the groundwork
for a bottom-up determination of the galaxy-halo connection from relations such
as the MDAR, provides concrete statistical tests for specific galaxy formation
models, and brings into sharper focus the relative evidence accorded by galaxy
kinematics to LCDM and modified gravity alternatives.
