Uncorrelated velocity and size residuals across galaxy rotation curves

Understand

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 SPARC sample) and in 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 $\Delta V_r$ and mass-size residuals $\Delta R$ as a function of the radius $r$ at which the velocity is measured, and thus present the $\Delta V_r-\Delta R$ relation across rotation curves.