We propose a general method to self-consistently study the quasistationary evolution of the magnetic field in the cores of neutron stars. The traditional approach to this problem is critically revised. Our results are illustrated by calculation of the typical timescales for the magnetic field dissipation as functions of temperature and the magnetic field strength.

The central compact object in the supernova remnant HESS J1731-347 appears to be the hottest observed isolated cooling neutron star. The cooling theory of neutron stars enables one to explain observations of this star by assuming the presence of strong proton superfluidity in the stellar core and the existence of the surface heat blanketing envelope which almost fully consists of carbon. The cooling model of this star is elaborated to take proper account of the neutrino emission due to neutron-neutron collisions which is not suppressed by proton superfluidity. Using the results of spectral fits of observed thermal spectra for the distance of 3.2 kpc and the cooling theory for the neutron star of age 27 kyr, new constraints on the stellar mass and radius are obtained which are more stringent than those derived from the spectral fits alone.

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.

In [Gusakov et al. PRD, 96, 103012, (2017)], we proposed a self-consistent method to study the quasistationary evolution of the magnetic field in neutron-star cores. Here we apply it to calculate the instantaneous particle velocities and other parameters of interest, which are fixed by specifying the magnetic field configuration. Interestingly, we found that the magnetic field can lead to generation of a macroscopic fluid motion with the velocity, significantly exceeding the diffusion particle velocities. This result calls into question the standard view on the magnetic field evolution in neutron stars and suggests a new, shorter timescale for such evolution.

It is well-known that r-mode oscillations of rotating neutron stars may be unstable with respect to the gravitational wave emission. It is highly unlikely to observe a neutron star with the parameters within the instability window, a domain where this instability is not suppressed. But if one adopts the 'minimal' (nucleonic) composition of the stellar interior, a lot of observed stars appear to be within the r-mode instability window. One of the possible solutions to this problem is to account for hyperons in the neutron star core. The presence of hyperons allows for a set of powerful (leptonfree) non-equilibrium weak processes, which increase the bulk viscosity, and thus suppress the r-mode instability. Existing calculations of the instability windows for hyperon NSs generally use reaction rates calculated for the Σ − Λ hyperonic composition via the contact W boson exchange interaction. In contrast, here we employ hyperonic equations of state where the Λ and Ξ − are the first hyperons to appear (the Σ − 's, if they are present, appear at much larger densities), and consider the meson exchange channel, which is more effective for the lepton-free weak processes. We calculate the bulk viscosity for the non-paired npeµΛΞ − matter using the meson exchange weak interaction. A number of viscosity-generating non-equilibrium processes is considered (some of them for the first time in the neutron-star context). The calculated reaction rates and bulk viscosity are approximated by simple analytic formulas, easy-to-use in applications. Applying our results to calculation of the instability window, we argue that accounting for hyperons may be a viable solution to the r-mode problem.PACS numbers:

The self-consistent approach to the magnetic field evolution in neutron star cores, developed recently, is generalised to the case of superfluid and superconducting neutron stars. Applying this approach to the cold matter of neutron star cores composed of neutrons, protons, electrons, and muons we find that, similarly to the case of normal matter, an arbitrary configuration of the magnetic field may result in generation of macroscopic particle velocities, strongly exceeding their diffusive (relative) velocities. This effect substantially accelerates evolution of the magnetic field in the stellar core. An hierarchy of timescales of such evolution at different stages of neutron star life is proposed and discussed. It is argued that the magnetic field in the core cannot be considered as frozen or vanishing and that its temporal evolution should affect the observational properties of neutron stars.

The solution of the system of Boltzmann equation for plasma in magnetic field, with arbitrary degenerate electrons and nondegenerate nuclei, is obtained by Chapman-Enskog method. Three functions, generalising Sonin polynomials are used for obtaining an approximal solution. Fully ionized plasma is considered. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulae are obtained, which are compared with different results of previous authors. Due to kinetic approach, our results are more exact than usually used coefficients, obtained by a simplified approach for the thermal conductivity in a plasma of a neutron star crust.

PACS 13.15.+g -Neutrino interactions PACS 97.60.-s -Late stages of stellar evolution (including black holes) PACS 21.65.Cd -Nuclear matter: Asymmetric matter, neutron matter Abstract -Based on the formalism by Kaminker et al. (Astron. Astrophys. 343 (1999) 1009) we derive an analytic approximation for neutrino-pair bremsstrahlung emissivity due to scattering of electrons by atomic nuclei in the neutron star crust of any realistic composition. The emissivity is expressed through generalized Coulomb logarithm which we fit by introducing an effective potential of electron-nucleus scattering. In addition, we study the conditions at which the neutrino bremsstrahlung in the crust is affected by strong magnetic fields. The results can be applied for modelling of many phenomena in neutron stars, such as thermal relaxation in young isolated neutron stars and in accreting neutron stars with overheated crust in soft X-ray transients.p-1