Intermediate- and high-velocity clouds in the Milky Way I: covering
  factors and vertical heights
  Intermediate- and high-velocity clouds (IVCs, HVCs) are a potential source of
fuel for star formation in the Milky Way (MW), but their origins and fates
depend sensitively on their distances. We search for IVC and HVC in HST
high-resolution ultraviolet spectra of 55 halo stars at vertical heights $|z|
\gtrsim 1$ kpc. We show that IVCs ($40 \leq |v_{\rm LSR}| <90$ km/s) have a
high detection rate - the covering factor, $f_c$ - that is about constant ($f_c
=0.90\pm 0.04$) from $z=1.5$ to $14$ kpc, implying IVCs are essentially
confined to $|z|\lesssim 1.5$ kpc. For the HVCs ($90 \leq |v_{\rm LSR}|
\lesssim 170$ km/s), we find $f_c$ increases from $f_c \simeq 0.14\pm 0.10$ at
$|z|\lesssim 2-3$ kpc to $f_c =0.60\pm 0.15$ at $5\lesssim |z|\lesssim 14$ kpc,
the latter value being similar to that found towards QSOs. In contrast, the
covering factor of very high-velocity clouds (VHVCs, $|v_{\rm LSR}|\gtrsim 170$
km/s) is $f_c<4\%$ in the stellar sample compared to 20\% in a QSO sample,
implying these clouds must be at $d\gtrsim 10-15$ kpc ($|z|\gtrsim 10$ kpc).
Gas clouds with $|v_{\rm LSR}|>40$ km/s at $|b|\gtrsim 15^\circ$ have therefore
$|v_{\rm LSR}|$ decreasing with decreasing $|z|$. Assuming each feature
originates from a single cloud, we derive scale-heights of $1.0 \pm 0.3$ and
$2.8 \pm 0.3$ kpc for the IVCs and HVCs, respectively. Our findings provide
support to the "rain" and galactic fountain models. In the latter scenario,
VHVCs may mostly serve as fuel for the MW halo. In view of their locations and
high covering factors, IVCs and HVCs are good candidates to sustain star
formation in the MW.
