Intermediate- and high-velocity clouds in the Milky Way II: evidence for a Galactic fountain with collimated outflows and diffuse inflows

We model the kinematics of the high- and intermediate- velocity clouds (HVCs and IVCs) observed in absorption towards a sample of 55 Galactic halo stars with accurate distance measurements. We employ a simple model of a thick disc whose main free parameters are the gas azimuthal, radial and vertical velocities ($v_\phi$, $v_{\rm R}$ and $v_{\rm z}$), and apply it to the data by fully accounting for the distribution of the observed features in the distance-velocity space. We find that at least two separate components are required to reproduce the data. A scenario where the HVCs and the IVCs are treated as distinct populations provides only a partial description of the data, which suggests that a pure velocity-based separation may give a biased vision of the gas physics at the Milky Way's disc-halo interface. Instead, the data are best described by a combination of an inflow and an outflow components, both characterised by rotation with $v_\phi$ comparable to that of the disc and $v_{\rm z}$ of 50-100 km/s. Features associated with the inflow appear to be diffused across the sky, while those associated with the outflow are mostly confined within a bi-cone pointing towards ($l\!=\!220^{\circ}$, $b\!=\!+40^{\circ}$) and ($l\!=\!40^{\circ}$, $b\!=\!-40^{\circ}$). Our findings indicate that the lower ($|z|\!\lesssim\!10$ kpc) Galactic halo is populated by a mixture of diffuse inflowing gas and collimated outflowing material, which are likely manifestations of a galaxy-wide gas cycle triggered by stellar feedback, that is, the galactic fountain.