The covering factor of high redshift damped Lyman-$\alpha$ systems
  We have used the Very Long Baseline Array to image 18 quasars with foreground
damped Lyman-$\alpha$ systems (DLAs) at 327, 610 or 1420 MHz, to measure the
covering factor $f$ of each DLA at or near its redshifted HI 21cm line
frequency. Including six systems from the literature, we find that none of 24
DLAs at $0.09 < z < 3.45$ has an exceptionally low covering factor, with $f
\sim 0.45 - 1$ for the 14 DLAs at $z > 1.5$, $f \sim 0.41 - 1$ for the 10
systems at $z < 1$, and consistent covering factor distributions in the two
sub-samples. The observed paucity of detections of HI 21cm absorption in
high-$z$ DLAs thus cannot be explained by low covering factors and is instead
likely to arise due to a larger fraction of warm HI in these absorbers.
