  We use a sample of 97 galaxies selected from the ALFALFA 21cm survey to make
an accurate measurement of the baryonic Tully-Fisher relation (BTFR). These
galaxies are specifically selected to be heavily gas-dominated (Mgas/M* >~ 2.7)
and to be oriented edge-on. The former property ensures that the error on the
galactic baryonic mass is small, despite the large systematic uncertainty
involved in galactic stellar mass estimates. The latter property means that
rotational velocities can be derived directly from the width of the 21cm
emission line, without any need for inclination corrections. We measure a slope
for the linewidth-based BTFR of alpha = 3.75 +- 0.11, a value that is somewhat
steeper than (but in broad agreement with) previous literature results. The
relation is remarkably tight, with almost all galaxies being located within a
perpendicular distance of +- 0.1 dex from the best fit line. The low
observational error budget for our sample enables us to establish that, despite
its tightness, the measured linewidth-based BTFR has some small (i.e.,
non-zero) intrinsic scatter. We furthermore find a systematic difference in the
BTFR of galaxies with "double-horned" 21cm line profiles and those with
"peaked" profiles. When we restrict our sample of galaxies to objects in the
former category, we measure a slightly steeper slope of alpha = 4.13 +- 0.15.
Overall, the high-accuracy measurement of the BTFR presented in this article is
intended as a reliable observational benchmark against which to test
theoretical expectations. Here we consider a representative set of
semi-analytic models and hydrodynamic simulations in the LCDM context, as well
as MOND. In the near future, interferometric follow-up observations of several
sample members will enable us to further refine the BTFR measurement, and make
sharper comparisons with theoretical models.
