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Register a new userNeutrino emission due to electron bremsstrahlung in superfluid neutron-star cores
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We study neutrino energy emission rates (emissivities) due to electron bremsstrahlung produced by $ee$ and $ep$ collisions in the superfluid neutron star cores. The neutrino emission due to $ee$ collisions is shown to be the dominant neutrino reaction at not too high temperatures ($T la 10^8$ K) in dense matter if all other neutrino reactions involving nucleons are strongly suppressed by neutron and proton superfluidity. Simple practical expressions for the $ee$ and $ep$ neutrino emissivities are obtained. The efficiency of various neutrino reactions in the superfluid neutron-star cores is discussed for the cases of standard neutrino energy losses and the losses enhanced by the direct Urca process.
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Mature neutron stars are cold enough to contain a number of superfluid and superconducting components. These systems are distinguished by the presence of additional dynamical degrees of freedom associated with superfluidity. In order to consider models with mixtures of condensates we need to develop a multifluid description that accounts for the presence of rotational neutron vortices and magnetic proton fluxtubes. We also need to model the forces that impede the motion of vortices and fluxtubes, and understand how these forces act on the condensates. This paper concerns the development of such a model for the outer core of a neutron star, where superfluid neutrons co-exist with a type II proton superconductor and an electron gas. We discuss the hydrodynamics of this system, focusing on the role of the entrainment effect, the magnetic field, the vortex/fluxtube tension and the dissipative mutual friction forces. Out final results can be directly applied to a number of interesting astrophysical scenarios, e.g. associated with neutron star oscillations or the evolution of the large scale magnetic field.
Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respects the Ward identity and assures the weak vector current conservation. The systematic expansion of the emissivities for small temperatures and nucleon Fermi velocity, v_{F,i}, i=n,p, is performed. Both neutron and proton processes are mainly controlled by the axial-vector current contributions, which are not strongly changed in the superfluid matter. Thus, compared to earlier calculations the total emissivity of processes on neutrons paired in the 1S_0 state is suppressed by a factor ~(0.9-1.2) v_{F,n}^2. A similar suppression factor (~v_{F,p}^2) arises for processes on protons.
The bulk viscosity of the neutron star matter due to the direct Urca processes involving nucleons, electrons and muons is studied taking into account possible superfluidity of nucleons in the neutron star cores. The cases of singlet-state pairing or triplet-state pairing (without and with nodes of the superfluid gap at the Fermi surface) of nucleons are considered. It is shown that the superfluidity may strongly reduce the bulk viscosity. The practical expressions for the superfluid reduction factors are obtained. For illustration, the bulk viscosity is calculated for two models of dense matter composed of neutrons, protons,electrons and muons. The presence of muons affects the bulk viscosity due to the direct Urca reactions involving electrons and produces additional comparable contribution due to the direct Urca reactions involving muons. The results can be useful for studying damping of vibrations of neutron stars with superfluid cores.
We calculate the shear viscosity $eta = eta_{emu}+eta_{n}$ in a neutron star core composed of nucleons, electrons and muons ($eta_{emu}$ being the electron-muon viscosity, mediated by collisions of electrons and muons with charged particles, and $eta_{n}$ the neutron viscosity, mediated by neutron-neutron and neutron-proton collisions). Deriving $eta_{emu}$, we take into account the Landau damping in collisions of electrons and muons with charged particles via the exchange of transverse plasmons. It lowers $eta_{emu}$ and leads to the non-standard temperature behavior $eta_{emu}propto T^{-5/3}$. The viscosity $eta_{n}$ is calculated taking into account that in-medium effects modify nucleon effective masses in dense matter. Both viscosities, $eta_{emu}$ and $eta_{n}$, can be important, and both are calculated including the effects of proton superfluidity. They are presented in the form valid for any equation of state of nucleon dense matter. We analyze the density and temperature dependence of $eta$ for different equations of state in neutron star cores, and compare $eta$ with the bulk viscosity in the core and with the shear viscosity in the crust.
Neutrino emissivities in a neutron star are computed for the neutrino bremsstrahlung process. In the first part the electro-weak nucleon-nucleon bremsstrahlung is calculated in free space in terms of a on-shell $T$-matrix using a generalized Low energy theorem. In the second part the emissivities are calculated in terms of the hadronic polarization at the two-loop level. Various medium effects, such as finite particle width, Pauli blocking in the $T$-matrix are considered. Compared to the pioneering work of Friman and Maxwell in terms of (anti-symmetrized) one-pion exchange the resulting emissivity is about a factor 4 smaller at saturation density.
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