  The ratio of baryonic-to-dark matter in present-day galaxies constrains
galaxy formation theories and can be determined empirically via the baryonic
Tully-Fisher relation (BTFR), which compares a galaxy's baryonic mass (Mbary)
to its maximum rotation velocity (Vmax). The BTFR is well-determined at Mbary
>10^8 Msun, but poorly constrained at lower masses due to small samples and the
challenges of measuring rotation velocities in this regime. For 25 galaxies
with high-quality data and Mbary <~10^8 Msun, we estimate Mbary from infrared
and HI observations and Vmax from the HI gas rotation. Many of the Vmax values
are lower limits because the velocities are still rising at the edge of the
detected HI disks (Rmax); consequently, most of our sample has lower velocities
than expected from extrapolations of the BTFR at higher masses. To estimate
Vmax, we map each galaxy to a dark matter halo assuming density profiles with
and without cores. In contrast to non-cored profiles, we find the cored profile
rotation curves are still rising at Rmax values, similar to the data. When we
compare the Vmax values derived from the cored density profiles to our Mbary
measurements, we find a turndown of the BTFR at low masses that is consistent
with LCDM predictions and implying baryon fractions of 1-10% of the cosmic
value. Although we are limited by the sample size and assumptions inherent in
mapping measured rotational velocities to theoretical rotation curves, our
results suggest that galaxy formation efficiency drops at masses below
Mbary~10^8 Msun, corresponding to Mhalo~10^10 Msun.
