Uncorrelated velocity and size residuals across galaxy rotation curves

The mass–velocity–size relation of late-type galaxies decouples into independent correlations between mass and velocity (the Tully–Fisher relation), and between mass and size. This behaviour is different to early-type galaxies which lie on a Fundamental Plane. We study the coupling of the Tully–Fisher and mass–size relations in observations [the Spitzer Photometry and Accurate Rotation Curves (SPARC) sample], empirical galaxy formation models based on halo abundance matching, and rotation curve fits with a hydrodynamically motivated halo profile. We systematically investigate the correlation coefficient between the Tully–Fisher residuals ΔVr and mass–size residuals ΔR as a function of the radius r at which the velocity is measured, and thus present the ΔVr–ΔR relation across rotation curves. We find no significant correlation in the data at any r, aside from r ≪ Reff where baryonic mass dominates. We show that this implies an anticorrelation between galaxy size and halo concentration (or halo mass) at fixed baryonic mass, and provides evidence against the hypothesis that galaxy and halo specific angular momentum are proportional. Finally, we study the ΔVr–ΔR relations produced by the baryons and dark matter separately by fitting halo profiles to the data. The balance between these components illustrates the ‘disc–halo conspiracy’ required for no overall correlation