A slippery slope: systematic uncertainties in the line width baryonic Tully-Fisher relation

The baryonic Tully–Fisher relation (BTFR) is both a valuable observational tool and a critical test of galaxy formation theory. We explore the systematic uncertainty in the slope and the scatter of the observed line-width BTFR utilizing homogeneously measured, unresolved H i observations for 930 isolated galaxies. We measure a fiducial relation of ${log}_{10}{M}_{baryon}=3.24{log}_{10}{V}_{rot}+3.21$ with observed scatter of 0.25 dex over a baryonic mass range of 10^7.4 to 10^11.3 $M_{\odot }$ where $V_{rot}$ is measured from 20% H i line widths. We then conservatively vary the definitions of $M_{baryon}$ and $V_{rot}$, the sample definition and the linear fitting algorithm. We obtain slopes ranging from 2.64 to 3.53 and scatter measurements ranging from 0.14 to 0.41 dex, indicating a significant systematic uncertainty of 0.25 in the BTFR slope derived from unresolved H i line widths. We next compare our fiducial slope to literature measurements, where reported slopes range from 3.0 to 4.3 and scatter is either unmeasured, immeasurable, or as large as 0.4 dex. Measurements derived from unresolved H i line widths tend to produce slopes of 3.3, while measurements derived strictly from resolved asymptotic rotation velocities tend to produce slopes of 3.9. The single largest factor affecting the BTFR slope is the definition of rotation velocity. The sample definition, the mass range and the linear fitting algorithm also significantly affect the measured BTFR. We find that galaxies in our sample with $V_{rot}<100$ km s⁻¹ are consistent with the line-width BTFR of more massive galaxies, but these galaxies drive most of the observed scatter. It is critical when comparing predictions to an observed BTFR that the rotation velocity definition, the sample selection and the fitting algorithm are similarly defined. We recommend direct statistical comparisons between data sets with commensurable properties as opposed to simply comparing BTFR power-law fits.