arXiv subjects
Publications and source records attributed to A. Y. Potekhin.
Recent calculations indicate that in the outer parts of neutron stars nuclei are rod-like or slab-like, rather than roughly spherical. We consider the elastic properties of these phases, and argue that they behave as liquid crystals, rather than rigid solids. We estimate elastic constants and discuss implications of our results for neutron star behavior.
The relationships between the effective surface (T_e) and internal temperatures of neutron stars (NSs) with and without accreted envelopes are calculated for T_e > 5\times10^4 K using new data on the equation of state and opacities in the outer NS layers. We examine various models of accreted layers (H, He, C, O shells produced by nuclear transformations in accreted matter). We employ new Opacity Library (OPAL) radiative opacities for H, He, and Fe. In the outermost NS layers, we implement the modern OPAL equation of state for Fe, and the Saumon-Chabrier equation of state for H and He. The updated thermal conductivities of degenerate electrons include the Debye-Waller factor for the electron-phonon scattering in solidified matter, while in liquid matter they include the contributions from electron-ion collisions (evaluated with non-Born corrections and with the ion structure factors in responsive electron background) and from the electron-electron collisions. For T_e < 10^{5.5} K, the electron conduction in non-degenerate layers of the envelope becomes important, reducing noticeably the temperature gradient. The accreted matter further decreases this gradient at T_e > 10^5 K. Even a small amount of accreted matter (with mass > 10^{-16} Msun) affects appreciably the NS cooling, leading to higher T_e at the neutrino cooling stage and to lower T_e at the subsequent photon stage.
Analytical approximations are constructed for binding energies of hydrogen atoms arbitrarily moving in magnetic fields 7\times10^{11} G to 2\times10^{13} G, typical of magnetic neutron stars.
Transport properties of degenerate relativistic electrons along quantizing magnetic fields in neutron star crusts are considered. A kinetic equation is derived for the spin polarization density matrix of electrons. Its solution does not depend on the choice of basic electron wave functions unlike previous solutions of the traditional kinetic equation for the distribution function. The density matrix formalism shows that one can always reach high accuracy with the traditional method by a proper choice of the basic functions. Electron Coulomb scattering on ions is considered in liquid matter, and on high-temperature phonons or on charged impurities in solid matter. In the solid regime, the Debye -- Waller reduction of phonon scattering can strongly enhance the longitudinal thermal or electric conductivity. An efficient numerical method is proposed for calculating the transport properties of electron gas at any magnetic field of practical interest.
Practical expressions are derived for a rapid and accurate evaluation of electric and thermal conductivities and thermopower of degenerate relativistic electrons along quantizing magnetic fields in outer neutron star crusts. The electron Coulomb scattering on ions is considered in liquid matter, and on high-temperature phonons or charged impurities in solid matter. A semi-quantitative treatment of low-temperature phonons is also proposed. The transport properties are expressed through the energy dependent effective electron relaxation time, which is calculated using the theoretical formalism of the previous work (astro-ph/9603133). Accurate fitting expressions for the relaxation time are obtained, and an efficient energy averaging procedure proposed. A Fortran code, which calculates the longitudinal transport properties of degenerate electrons in strong magnetic fields for any parameters of dense stellar matter of practical interest, is available from the authors upon request.
The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K_\perp of its generalized momentum. In particular, the photoionization process is modified substantially: (i) threshold energies are decreased as compared with those for an atom at rest, (ii) cross section values are changed significantly, and (iii) selection rules valid for atoms at rest are violated by the motion so that new photoionization channels become allowed. To calculate the photoionization cross sections, we, for the first time, employ exact numerical treatment of both initial and final atomic states. This enables us to take into account the quasi-bound (autoionizing) atomic states as well as coupling of different ionization channels. We extend the previous consideration, restricted to the so-called centered states corresponding to relatively small values of K_\perp, to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over K. For typical temperatures of neutron star atmospheres, the averaged cross sections differ substantially from those of atoms at rest. In particular, the photoionization edges are strongly broadened by the thermal motion of atoms; this "magnetic broadening" exceeds the usual Doppler broadening by orders of magnitude. The decentered states of the atoms give rise to the low-energy component of the photoionization cross section. This new component grows significantly with increasing temperature above 10^{5.5} K and decreasing density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.
Contemporary multidimensional cosmological theories predict different variations of fundamental physical constants in course of the cosmological evolution. On the basis of the QSO spectra analysis, we show that the fine-structure constant α=e^2/(\hbar c) and the proton-to-electron mass ratio μ=m_p/m_e reveal no statistically significant variation over the last 90% of the lifetime of the Universe. At the 2σsignificance level, the following upper bounds are obtained for the epoch corresponding to the cosmological redshifts z ~ 3 (i.e., ~ 10 Gyr ago): |Δα/α| < 0.00016 and |Δμ/μ| < 0.00022. The corresponding upper limits to the time-average rates of the constant variations are |dα/(αdt)| < 1.6\times 10^{-14} yr^{-1} and |dμ/(μdt)| < 2.2\times10^{-14} yr^{-1}. These limits serve as criteria for selection of those theoretical models which predict αand μvariation with the cosmological time. In addition, we test a possible anisotropy of the high-redshift fine splitting over the celestial sphere, which might reveal a non-equality of αvalues in causally disconnected areas of the Universe.
The hydrogen plasma is studied at temperatures T ~ 10^4 - 10^6 K using the free energy minimization method. A simple analytic free energy model is proposed which is accurate at densities up to 1 g/cc and yields convergent internal partition function of atoms. The occupation probability formalism is modified for solving the ionization equilibrium problem. The ionization degree and equation of state are calculated and compared with the results of other models.
High magnetic fields in neutron stars, B ~ 10^{11} - 10^{13} G, substantially modify the properties of atoms and their interaction with radiation. In particular, the photoionization cross section becomes anisotropic and strongly polarization dependent. In a number of previous works based on the adiabatic approximation the conclusion was drawn that the transverse cross section vanishes for frequencies smaller than the electron cyclotron frequency. In other works (which employed a different form of the interaction operator) appreciable finite values were obtained. An adequate interpretation of the neutron star thermal-like radiation requires a resolution of this controversy. In this work the atomic wave functions for both discrete and continuum states are calculated by solving the coupled channel equations allowing the admixture between different Landau levels, which provides much higher accuracy than the adiabatic approximation. This enables to resolve the above contradiction in favour of the finite transverse cross sections. The non-adiabatic treatment of the continuum includes coupling between closed and open channels, which leads to the autoionization of quasi-bound energy levels associated with the electron cyclotron excitations and gives rise to Beutler - Fano resonances of the photoionization cross section. Autoionization widths of these quasi-bound levels are calculated and compared with the radiative widths. The results are important for investigations of the radiation emergent from the surface layers of neutron stars.