A sub-resolution multiphase interstellar medium model of star formation
  and SNe energy feedback
  We present a new multi-phase sub-resolution model for star formation and
feedback in SPH numerical simulations of galaxy formation. Our model, called
MUPPI (MUlti-Phase Particle Integrator), describes each gas particle as a
multi-phase system, with cold and hot gas phases, coexisting in pressure
equilibrium, and a stellar component. Cooling of the hot tenuous gas phase
feeds the cold gas phase. Stars are formed out of molecular gas with a given
efficiency, which scales with the dynamical time of the cold phase. Our
prescription for star formation is not based on imposing the Schmidt-Kennicutt
relation, which is instead naturally produced by MUPPI. Energy from supernova
explosions is deposited partly into the hot phase of the gas particles, and
partly to that of neighboring particles. Mass and energy flows among the
different phases of each particle are described by a set of ordinary
differential equations which we explicitly integrate for each gas particle,
instead of relying on equilibrium solutions. This system of equations also
includes the response of the multi-phase structure to energy changes associated
to the thermodynamics of the gas. We apply our model to two isolated disk
galaxy simulations and two spherical cooling flows. MUPPI is able to reproduce
the Schmidt-Kennicutt relation for disc galaxies. It also reproduces the basic
properties of the inter-stellar medium in disc galaxies, the surface densities
of cold and molecular gas, of stars and of star formation rate, the vertical
velocity dispersion of cold clouds and the flows connected to the galactic
fountains. Quite remarkably, MUPPI also provides efficient stellar feedback
without the need to include a scheme of kinetic energy feedback. [abridged]
