A matter of measurement: rotation velocities and the velocity function of dwarf galaxies

TL;DR

This paper investigates how different observational measures of dwarf galaxy rotation velocities relate to dark matter halo properties, reconciling observed velocity functions with LCDM predictions through a semi-empirical approach.

Contribution

It introduces a method to accurately connect observed galaxy rotation velocities with dark matter halo characteristics, clarifying discrepancies in the velocity function at low velocities.

Findings

W50 velocity function can be aligned with LCDM cosmology.

Dwarfs' Vrot is measured at a fraction of Rmax, explaining rising rotation curves.

Provides formulae linking RHI, Reff, and halo virial radius.

Abstract

The velocity function derived from large scale surveys can be compared with the predictions of LCDM cosmology, by matching the measured rotation velocities Vrot of galaxies to the maximum circular velocity of dark matter (DM) halos Vmax. For Vrot<50km/s, a major discrepancy arises between the observed and LCDM velocity functions. However, the manner in which different observational measures of Vrot are associated with Vmax is not straight forward in dwarf galaxies. We instead relate galaxies to DM halos using the empirical baryon- mass to halo-mass relation, and show that different observational measures of Vrot result in very different velocity functions. We show how the W50 velocity function, i.e. using the HI profile line width at 50% of peak HI flux to measure Vrot, can be reconciled with a LCDM cosmology. Our semi-empirical methodology allows us to determine the region of rotation curves that are probed by HI measurements (RHI), and shows that the Vrot of dwarfs are generally measured at a fraction of Rmax, explaining their tendency to have rising rotation curves. We provide fitting formulae for relating RHI and Reff (the effective radius) to the virial radius of DM halos. To continue to use velocity functions as a probe of LCDM cosmology, it is necessary to be precise about how the different measures of rotation velocity are probing the mass of the DM halos, dropping the assumption that any measure of rotational velocity can be equally used as a proxy for Vmax.