Neutrino Processes in Neutron Stars

The aim of these lectures is to introduce basic processes responsible for cooling of neutron stars and to show how to calculate the neutrino production rate in dense strongly interacting nuclear medium. The formalism is presented that treats on equal footing one-nucleon and multiple-nucleon processes and reactions with virtual bosonic modes and condensates. We demonstrate that neutrino emission from dense hadronic component in neutron stars is subject of strong modifications due to collective effects in the nuclear matter. With the most important in-medium processes incorporated in the cooling code an overall agreement with available soft X ray data can be easily achieved. With these findings the so-called “standard” and “non-standard” cooling scenarios are replaced by one general “nuclear medium cooling scenario” which relates slow and rapid neutron star coolings to the star masses (interior densities). The lectures are split in four parts. Part I: After short introduction to the neutron star cooling problem we show how to calculate neutrino reaction rates of the most efficient one-nucleon and two-nucleon processes. No medium effects are taken into account in this instance. The effects of a possible nucleon pairing are discussed. We demonstrate that the data on neutron star cooling cannot be described without inclusion of medium effects. It motivates an assumption that masses of the neutron stars are different and that neutrino reaction rates should be strongly density dependent. Part II: We introduce the Green’s function diagram technique for systems in and out of equilibrium and the optical theorem formalism. The latter allows to perform calculations of production rates with full Green’s functions including all off-mass-shell effects. We demonstrate how this formalism works within the quasiparticle approximation. Part III: The basic concepts of the nuclear Fermi liquid approach are introduced. We show how strong interaction effects can be included within the Green’s function formalism. Softening of the pion mode with an baryon density increase is explicitly incorporated. We show examples of inconsistencies in calculations without inclusion of medium effects. Then we demonstrate calculations of different reaction rates in non-superfluid nuclear matter with taking into account medium effects. Many new reaction channels are open up in the medium and should be analyzed. Part IV: We discuss the neutrino production reactions in superfluid nuclear systems. The reaction rates of processes associated with the pair breaking and formation are calculated. Special attention is focused on the gauge invariance and the exact fulfillment of the Ward identities for the vector current. Finally we present comparison of calculations of neutron star cooling performed within nuclear medium cooling scenario with the available data