Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter
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Calculation of Thermal Conductivity Coefficients of Electrons in Magnetized Dense Matter1 G. S. Bisnovatyi-Kogana, b* and M. V. Glushikhinaa** a
Space Research Institute, Russian Academy of Sciences, Moscow, 117997 Russia bNational Research Nuclear University “MEPhI,” Moscow, 115409 Russia *e-mail: [email protected] **e-mail: [email protected] Received August 11, 2017; in final form, October 19, 2017
Abstract—The solution of Boltzmann equation for plasma in magnetic field with arbitrarily degenerate electrons and nondegenerate nuclei is obtained by Chapman−Enskog method. Functions generalizing Sonine polynomials are used for obtaining an approximate solution. Fully ionized plasma is considered. The tensor of the heat conductivity coefficients in nonquantized magnetic field is calculated. For nondegenerate and strongly degenerate plasma the asymptotic analytic formulas are obtained and compared with results of previous authors. The Lorentz approximation with neglecting of electron−electron encounters is asymptotically exact for strongly degenerate plasma. For the first time, analytical expressions for the heat conductivity tensor for nondegenerate electrons in the presence of a magnetic field are obtained in the three-polynomial approximation with account of electron−electron collisions. Account of the third polynomial improved substantially the precision of results. In the two-polynomial approximation, the obtained solution coincides with the published results. For strongly degenerate electrons, an asymptotically exact analytical solution for the heat conductivity tensor in the presence of a magnetic field is obtained for the first time. This solution has a considerably more complicated dependence on the magnetic field than those in previous publications and gives a several times smaller relative value of the thermal conductivity across the magnetic field at ωτ * 0.8 . DOI: 10.1134/S1063780X18040013
1. INTRODUCTION Observations of thermal emission from neutron stars provides information about the magnetic field strength and configuration, temperature, and chemical composition of the outer regions, as well as about the properties of matter at higher densities, deeper inside the star (see [1, 2]). To derive this information, we need to calculate the structure and evolution of the star and compare theoretical models with observational data. X-ray observations of thermal emission show periodic variabilities in single neutron stars [3], indicating an anisotropic temperature distribution. It is produced at the low- and intermediate-density regions, such as the solid crust, where a complicated magnetic field geometry could cause a coupled magnetothermal evolution. In some extreme cases with a very high magnetic field, this anisotropy may even be present in the poorly known interior, where neutrino processes are responsible for the energy removal [4]. The spectrum of these neutron stars in a broad range from optics to X-ray band cannot be reproduced by a spectrum of the surface with a unique temperatur
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