The Tully–Fisher and mass–size relations from halo abundance matching

The Tully–Fisher relation (TFR) expresses the connection between rotating galaxies and the dark matter haloes they inhabit, and therefore contains a wealth of information about galaxy formation. We construct a general framework to investigate whether models based on halo abundance matching are able to reproduce the observed stellar mass TFR and mass–size relation (MSR), and use the data to constrain galaxy formation parameters. Our model tests a range of plausible scenarios, differing in the response of haloes to disc formation, the relative angular momentum of baryons and dark matter, the impact of selection effects, and the abundance matching parameters. We show that agreement with the observed TFR puts an upper limit on the scatter between galaxy and halo properties, requires weak or reversed halo contraction, and favours selection effects that preferentially eliminate fast-rotating galaxies. The MSR constrains the ratio of the disc to halo specific angular momentum to be approximately in the range 0.6–1.2. We identify and quantify two problems that models of this nature face. (1) They predict too large an intrinsic scatter for the MSR, and (2) they predict too strong an anticorrelation between the TFR and MSR residuals. We argue that resolving these problems requires introducing a correlation between stellar surface density and enclosed dark matter mass. Finally, we explore the expected difference between the TFRs of central and satellite galaxies, finding that in the favoured models this difference should be detectable in a sample of ∼700 galaxies