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 IVCs and HVCs in HSThigh-resolution ultraviolet spectra of 55 halo stars at vertical heights vertical bar z vertical bar greater than or similar to 1 kpc. We show that IVCs (40 <= vertical bar v(LSR)vertical bar < 90 km s(-1)) have a high detection rate - the covering factor, f(c) - that is about constant (f(c) = 0.90 +/- 0.04) from z = 1.5 to 14 kpc, implying IVCs are essentially confined to vertical bar z vertical bar less than or similar to 1.5 kpc. For the HVCs (90 <= vertical bar v(LSR)vertical bar less than or similar to 170 km s(-1)), we find f(c) increases from f(c) similar or equal to 0.14 +/- 0.10 at vertical bar z vertical bar less than or similar to 2-3 kpc to f(c) = 0.60 +/- 0.15 at 6 less than or similar to vertical bar z vertical bar less than or similar to 14 kpc, the latter being similar to that found towards QSOs. In contrast, the covering factor of very high-velocity clouds (VHVCs; vertical bar v(LSR)vertical bar greater than or similar to 170 km s(-1)) is f(c) < 0.04 in the stellar sample compared to 20 per cent towards QSOs, implying these clouds must be at d greater than or similar to 10-15 kpc (vertical bar z vertical bar greater than or similar to 10 kpc). Gas clouds with vertical bar v(LSR)vertical bar > 40 km s(-1) at vertical bar b vertical bar greater than or similar to 15 degrees have therefore vertical bar v(LSR)vertical bar decreasing with decreasing vertical bar z vertical bar. Our findings are consistent with a Galactic rain and/or fountain origin for these clouds. In the latter scenario, VHVCs may mostly serve as fuel for the MW halo. In view of their high covering factors and since all the IVCs and some HVCs are found in the thick disc, they appear good candidates as gas reservoirs to help sustain star formation in the MW.