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

We study the baryonic Tully–Fisher relation (BTFR) at z ≃ 0 using 153 galaxies from the Spitzer Photometry and Accurate Rotation Curve sample. We consider different definitions of the characteristic velocity from H I and H α rotation curves, as well as H I 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 per cent⁠) and the best-fitting 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 H I line-widths or less extended rotation curves (like H α and CO data). These can be useful to study the BTFR from large H I 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 seven 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