Uncorrelated velocity and size residuals across galaxy rotation curves

TL;DR

This study investigates the relationship between galaxy rotation curve residuals and size/mass relations, finding no significant correlation and providing insights into galaxy-halo dynamics and the disk-halo conspiracy.

Contribution

It systematically analyzes the residual correlations across rotation curves in observations and models, revealing the lack of correlation and implications for galaxy-halo angular momentum.

Findings

No significant correlation between velocity and size residuals at most radii.

Evidence against proportionality of galaxy and halo specific angular momentum.

Illustration of the disk-halo conspiracy maintaining the balance between baryons and dark matter.

Abstract

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. We find no significant correlation in either the data or models for any $r$, aside from $r \ll R_\text{eff}$ 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 $\Delta V_r-\Delta R$ relations produced by the baryons and dark matter separately by fitting halo profiles to the rotation curves. The balance between these components illustrates the "disk-halo conspiracy" required for no overall correlation.