Project AMIGA: A Minimal Covering Factor for Optically Thick
  Circumgalactic Gas Around the Andromeda Galaxy
  We present a deep search for HI 21-cm emission from the gaseous halo of
Messier 31 as part of Project AMIGA, a large program Hubble Space Telescope
program to study the circumgalactic medium of the Andromeda galaxy. Our
observations with the Robert C. Byrd Green Bank Telesope target sight lines to
48 background AGNs, more than half of which have been observed in the
ultraviolet with the Cosmic Origins Spectrograph, with impact parameters $25
\lesssim \rho \lesssim 330$ kpc ($0.1 \lesssim \rho / R_{\rm vir} \lesssim
1.1$). We do not detect any 21-cm emission toward these AGNs to limits of
$N({\rm HI}) \approx 4 \times10^{17}$ cm$^{-2}$ ($5\sigma$, per 2 kpc diameter
beam). This column density corresponds to an optical depth of $\sim2.5$ at the
Lyman limit, thus our observations overlap with absorption line studies of
Lyman limit systems at higher redshift. Our non-detections place a limit on the
covering factor of such optically-thick gas around M31 to $f_c < 0.051$ (at
90\% confidence) for $\rho \leq R_{\rm vir}$. While individual clouds have
previously been found in the region between M31 and M33, the covering factor of
strongly optically-thick gas is quite small. Our upper limits on the covering
factor are consistent with expectations from recent cosmological "zoom"
simulations. Recent COS-Halos ultraviolet measurements of \HI\ absorption about
an ensemble of galaxies at $z \approx 0.2$ show significantly higher covering
factors within $\rho \lesssim 0.5 R_{\rm vir}$ at the same $N({\rm H I})$,
although the metal ion-to-H I ratios appear to be consistent with those seen in
M31.
