A Slippery Slope: Systematic Uncertainties in the Line Width Baryonic
  Tully-Fisher Relation
  The baryonic Tully-Fisher relation (BTFR) is 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 HI observations for 930 isolated
galaxies. We measure a fiducial relation of $\log_{10}{M_{\rm baryon}} =
3.24\log_{10}{V_{\rm rot}}+3.21$ with observed scatter of 0.25 dex with
$10^{7.4} < M_{\rm baryon} < 10^{11.3}M_{\odot}$ where $V_{\rm rot}$ is
measured from 20\% HI line widths. We vary the definitions of $M_{\rm baryon}$
and $V_{\rm rot}$, the sample selection, 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 systematic uncertainty of 0.25 in the BTFR slope
derived from unresolved HI line widths. We 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 HI line widths tend to produce slopes of 3.3, while
measurements derived from asymptotic rotation curves tend to produce slopes of
3.9. The largest factor affecting the BTFR slope is the definition of $V_{\rm
rot}$. 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 $V_{\rm rot} < 100~\rm{km~s^{-1}}$ 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 $V_{\rm rot}$ 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 comparing BTFR
power-law fits.
