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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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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.
We calculate the neutrino production cross-section through the direct URCA process in proto-neutron star matter in the presence of a strong magnetic field. We assume isoentropic conditions and introduce a new equation of state parameter-set in the relativistic mean-field approach that can reproduce neutron stars with $M > 1.96$ M$_odot$ as required by observations. We find that the production process increases the flux of emitted neutrinos along the direction parallel to the magnetic field and decreases the flux in the opposite direction. This means that the neutrino flux asymmetry due to the neutrino absorption and scattering processes in a magnetic field becomes larger by the inclusion of the neutrino production process.
We use a recently developed model of relativistic meson-exchange currents to compute the neutron-proton and proton-proton yields in $( u_mu,mu^-)$ scattering from $^{12}$C in the 2p-2h channel. We compute the response functions and cross sections with the relativistic Fermi gas model for different kinematics from intermediate to high momentum transfers. We find a large contribution of neutron-proton configurations in the initial state, as compared to proton-proton pairs. In the case of charge-changing neutrino scattering the 2p-2h cross section of proton-proton emission ({it i.e.,} np in the initial state) is much larger than for neutron-proton emission ({it i.e.,} two neutrons in the initial state) by a $(omega,q)$-dependent factor. The different emission probabilities of distinct species of nucleon pairs are produced in our model only by meson-exchange currents, mainly by the $Delta$ isobar current. We also analyze other effects including exchange contributions and the effect of the axial and vector currents.
Numerous theoretical studies using various equation of state models have shown that quark matter may exist at the extreme densities in the cores of high-mass neutron stars. It has also been shown that a phase transition from hadronic matter to quark matter would result in an extended mixed phase region that would segregate phases by net charge to minimize the total energy of the phase, leading to the formation of a crystalline lattice. The existence of quark matter in the core of a neutron star may have significant consequences for its thermal evolution, which for thousands of years is facilitated primarily by neutrino emission. In this work we investigate the effect a crystalline quark-hadron mixed phase can have on the neutrino emissivity from the core. To this end we calculate the equation of state using the relativistic mean-field approximation to model hadronic matter and a nonlocal extension of the three-flavor Nambu-Jona-Lasinio model for quark matter. Next we determine the extent of the quark-hadron mixed phase and its crystalline structure using the Glendenning construction, allowing for the formation of spherical blob, rod, and slab rare phase geometries. Finally we calculate the neutrino emissivity due to electron-lattice interactions utilizing the formalism developed for the analogous process in neutron star crusts. We find that the contribution to the neutrino emissivity due to the presence of a crystalline quark-hadron mixed phase is substantial compared to other mechanisms at fairly low temperatures ($lesssim 10^9$ K) and quark fractions ($lesssim 30%$), and that contributions due to lattice vibrations are insignificant compared to static-lattice contributions.
Magnetars are a subclass of neutron stars whose intense soft-gamma-ray bursts and quiescent X-ray emission are believed to be powered by the decay of a strong internal magnetic field. We reanalyze neutrino emission in such stars in the plausibly relevant regime in which the Landau band spacing of both protons and electrons is much larger than kT (where k is the Boltzmann constant and T is the temperature), but still much smaller than the Fermi energies. Focusing on the direct Urca process, we find that the emissivity oscillates as a function of density or magnetic field, peaking when the Fermi level of the protons or electrons lies about 3kT above the bottom of any of their Landau bands. The oscillation amplitude is comparable to the average emissivity when the Landau band spacing mentioned above is roughly the geometric mean of kT and the Fermi energy (excluding mass), i. e., at fields much weaker than required to confine all particles to the lowest Landau band. Since the density and magnetic field strength vary continuously inside the neutron star, there will be alternating surfaces of high and low emissivity. Globally, these oscillations tend to average out, making it unclear whether there will be any observable effects.
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