Simulating disk galaxies with a novel sub-grid prescription

I will introduce the problem of numerical galaxy formation in a cosmological context, giving a short review of the current state of the art. I will then show results of cosmological simulations of disk galaxies where star formation and stellar feedback are described using our MUlti Phase Particle Integrator (MUPPI) model. This description is based on a simple multi-phase model of the interstellar medium at unresolved scales, where mass and  energy flows among the components are explicitly followed by solving a system of ordinary differential equations. Thermal energy from SNe is injected into the local hot phase, so as  to avoid that it is promptly radiated away.  A kinetic feedback prescription generates the massive outflows needed to avoid the over-production of stars. We obtain spiral galaxies with small bulge-over-total stellar mass ratios, extended stellar and gas disks, flat rotation curves and realistic values of stellar masses. Star formation rates follow the observed Schmidt-Kennicutt relation. Stars kinematically belonging  to the bulge form early, while disk stars show a clear inside-out formation pattern and mostly form after redshift z=2.   Results are found to be  remarkably stable against resolution. I will then shorty describe the application of our prescription to cosmological volumes, and the future developments of our scheme.