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We present a new multiphase subresolution model for star formation and feedback in smoothed particle hydrodynamics (SPH) numerical simulations of galaxy formation. Our model, called MUPPI (MUlti‐Phase Particle Integrator), describes each gas particle as a multiphase 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. We compute the cold gas molecular fraction using the phenomenological relation of Blitz &amp; Rosolowsky between this fraction and the external disc pressure, which we identify with the SPH pressure. 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 neighbouring 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 multiphase structure to energy changes associated to the thermodynamics of the gas. Our model has an intrinsically runaway behaviour: energy from supernovae increases gas pressure which increases in turn the star formation rate through the molecular fraction. This runaway is stabilized in simulations by the hydrodynamic response of the gas: when it receives enough energy, it expands thereby decreasing its pressure.  We apply our model to two isolated disc 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 interstellar 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.

A subresolution multiphase interstellar medium model of star formation and supernova energy feedback