# The baryonic Tully-Fisher relation for different velocity definitions and implications for galaxy angular momentum

## TL;DR

This study analyzes the baryonic Tully-Fisher relation at zero redshift using various velocity definitions, finding the mean velocity along the flat rotation curve yields the tightest relation with minimal scatter, and discusses implications for galaxy angular momentum.

## Contribution

It identifies the most accurate velocity measure for the BTFR and provides statistical tools to infer flat rotation velocities from different observational data.

## Key findings

- The tightest BTFR has a slope of 3.85 with 6% intrinsic scatter.
- Systematic uncertainties can alter the slope between 3.5 and 4.0.
- The BTFR is more fundamental than the Fall relation, with less scatter.

## Abstract

We study the baryonic Tully-Fisher relation (BTFR) at z=0 using 153 galaxies from the SPARC sample. We consider different definitions of the characteristic velocity from HI and H-alpha rotation curves, as well as HI line-widths from single-dish observations. We reach the following results: (1) The tightest BTFR is given by the mean velocity along the flat part of the rotation curve. The orthogonal intrinsic scatter is extremely small (6%) and the best-fit slope is 3.85+/-0.09, but systematic uncertainties may drive the slope from 3.5 to 4.0. Other velocity definitions lead to BTFRs with systematically higher scatters and shallower slopes. (2) We provide statistical relations to infer the flat rotation velocity from HI line-widths or less extended rotation curves (like H-alpha and CO data). These can be useful to study the BTFR from large HI surveys or the BTFR at high redshifts. (3) The BTFR is more fundamental than the relation between angular momentum and galaxy mass (the Fall relation). The Fall relation has about 7 times more scatter than the BTFR, which is merely driven by the scatter in the mass-size relation of galaxies. The BTFR is already the "fundamental plane" of galaxy discs: no value is added with a radial variable as a third parameter.