Systematically Measuring Ultra Diffuse Galaxies in HI: Results from the
  Pilot Survey
  We present neutral hydrogen (HI) observations using the Robert C. Byrd Green
Bank Telescope (GBT) of 70 optically-detected UDG candidates in the Coma region
from the Systematically Measuring Ultra-Diffuse Galaxies survey (SMUDGes). We
detect HI in 18 targets, confirming 9 to be gas-rich UDGs and the remainder to
be foreground dwarfs. None of our HI-detected UDGs are Coma Cluster members and
all but one are in low-density environments. The HI-detected UDGs are bluer and
have more irregular morphologies than the redder, smoother candidates not
detected in HI, with the combination of optical color and morphology being a
better predictor of gas richness than either parameter alone. There is little
visual difference between the gas-rich UDGs and the foreground dwarfs in the
SMUDGes imaging, and distances are needed to distinguish between them. We find
that the gas richnesses of our HI-confirmed UDGs and those from other samples
scale with their effective radii in two stellar mass bins, possibly providing
clues to their formation. We attempt to place our UDGs on the baryonic
Tully-Fisher relation (BTFR) using optical ellipticities and
turbulence-corrected HI linewidths to estimate rotation velocities, but the
potential systematics associated with fitting smooth $\mathrm{S\acute{e}rsic}$
profiles to clumpy, low-inclination low surface brightness disks precludes a
meaningful analysis of potential BTFR offsets. These observations are a pilot
for a large campaign now underway at the GBT to use the HI properties of
gas-rich UDGs to quantitatively constrain how these galaxies form and evolve.
