Thermodynamic functions of degenerate magnetized electron gas

The Fermi energy, pressure, internal energy, entropy, and heat capacity of completely degenerate relativistic electron gas are calculated by numerical methods. It is shown that the maximum admissible magnetic field on the order of 10⁹ G in white dwarfs increases the pressure by a factor of 1.06 in the central region, where the electron concentration is ∼10³³ cm⁻³, while the equilibrium radius increases by approximately a factor of 1.03, which obviously cannot be observed experimentally. A magnetic field of ∼10⁸ G or lower has no effect on the pressure and other thermodynamic functions. It is also shown that the contribution of degenerate electron gas to the total pressure in neutron stars is negligible compared to that of neutron gas even in magnetic fields with a maximum induction ∼10¹⁷ G possible in neutron stars. The neutron beta-decay forbiddeness conditions in a superstrong magnetic field are formulated. It is assumed that small neutron stars have such magnetic fields and that pulsars with small periods are the most probable objects that can have super-strong magnetic fields.     

Neutronization and Protonization of Nuclei: Two Possible Ways of the Evolution of Astrophysical Objects and the Laboratory Electron-Nucleus Collapse

We consider the peculiarities of the fundamental nuclear transformations running both in the shell of a heavy star compressed by the strong gravitational field and during the laboratory electron-nucleus collapse where the compression occurs at the expense of the electron-nucleus interaction in a volume occupied by a degenerate electron gas, define their analogs, and analyze the differences. It is shown that the account of relativistic and nonlinear corrections to the Coulomb electron-nucleus interaction gives the possibility to realize two alternative ways for the evolution of the star matter which depend on both the rate of compression upon the gravitational collapse and the initial isotope composition of a star on the stage preceding the collapse. Upon the relatively slow compression of a heavy star in the process of gravitational collapse after the attainment of the threshold electron density, there occur the stage-by-stage neutronization of nuclei and the formation of a neutron star with a great concentration of neutrons and a low concentration of protons and electrons. This process is characterized by the presence of a bounded interval of the density of a relativistic degenerate gas of electrons (“the neutronization corridor”), in the scope of which the neutronization runs with a decrease in the Fermi energy and the release of energy in the form of fast neutrinos. At a higher electron density, the process of protonization becomes energy-gained. In this case, an increase in both the charge of nuclei and the concentration of degenerate electrons causes the continuous increase in the binding energy of electrons and nuclei which turns out to be more significant than the increase in the Fermi energy of electrons. The transition of nuclei through “the neutronization corridor” into “the protonization zone”, which ranges up to the nuclear density of a substance, is possible only in the case of a very fast compression of a heavy star. Such a process leads to the possibility of the formation of proton stars with a very small residual concentration of neutrons and a great (nuclear) concentration of protons and electrons. It is shown that analogous effects can be realized during the laboratory electron-nucleus collapse. Due to a microscopic size of the collapse zone, a great velocity of its formation, and a relatively low rate of neutronization, the passage of the electron-nucleus substance through “the neutronization corridor” weakly affects its state. In this case, the main mechanism of transformations is the process of protonization with a simultaneous increase in the concentration of degenerate electrons.     

Exchange of transverse plasmons and electrical conductivity of neutron star cores

We study the electrical conductivity in magnetized neutron star cores produced by collisions between charged particles. We take into account the ordinary exchange of longitudinal plasmons and the exchange of transverse plasmons in collisions between particles. The exchange of transverse plasmons is important for collisions between relativistic particles, but it has been disregarded previously when calculating the electrical conductivity. We show that taking this exchange into account changes the electrical conductivity, including its temperature dependence (thus, for example, the temperature dependence of the electrical resistivity along the magnetic field in the low-temperature limit takes the form ?_‖ ∝ T ^5/3 instead of the standard dependence ?_‖ ∝ T ² for degenerate Fermi systems). We briefly describe the effect of possible neutron and proton superfluidity in neutron star cores on the electrical conductivity and discuss various scenarios for the evolution of neutron star magnetic fields.     

Structure of Rotating Neutron Stars in Uniform Strong Magnetic Field

Properties and deformations of the rotating neutron stars in uniform strong magnetic field are calculated. The magnetic field will soften the equation of state of the neutron star matters and make an obvious effect on the structure of the rotating neutron star. If the magnetic field is superstrong （B=10^17 T）, the mass, radius, and the deformation will become smaller effectively.     

Magnetism of a relativistic degenerate electron gas in a strong magnetic field

The magnetization and magnetic susceptibility of a degenerate electron gas in a strong magnetic field in which electrons are located on the ground Landau level and the electron gas has the properties of a nonlinear paramagnet have been calculated. The paradoxical properties of the electron gas under these conditions??a decrease in the magnetization with the field and an increase in the magnetization with the temperature??have been revealed. It has been shown that matter under the corresponding conditions of neutron stars is a paramagnet with a magnetic susceptibility of ?? ?? 0.001.     

Frame Dragging Effect on Properties of Rotating Neutron Stars with Strong Magnetic Field

The general relativistic frame dragging effect on the properties, such as the moments of inertia and the radii of gyration of fast rotating neutron stars with a uniform strong magnetic field, is calculated accurate to the first order in the uniform angular velocity. The results show that compared with the corresponding non-rotating static spherical symmetric neutron star with a weaker magnetic field, a fast rotating neutron star (millisecond pulsar) with a stronger magnetic field has a relative smaller moment of inertia and radius of gyration.     

High-energy approximations to nuclear scattering: W. E. Frahn and B. Schürmann. Physics Department,University of Cape Town,Rondebosch (Cape), South Africa

The effect of slow rotation on the dipole magnetic field of neutron stars is studied. It is shown that the differential rotation of inertial frames produced by the effect of “dragging of inertial frames” induces an additional component of electric field outside the star. This new component, as well as the usual electromagnetic components, vanishes as in the limit of collapse of a star to its Schwarzschild radius. For typical neutron stars, the electric quadrupole moment is about half that obtainable from a flat space analysis.     

Magnetic collapse of a neutron gas: Can magnetars indeed be formed?

A relativistic degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular to than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas. Taking this as a model for neutron stars, the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable neutron star pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and a meson condensate, a strange star, or a highly distorted black hole or black ”cigar”, but not a magnetar, if viewed as a superstrongly magnetized neutron star. However, we do not exclude the possibility of superstrong magnetic fields arising in supernova explosions which lead directly to strange stars. In other words, if any magnetars exist, they cannot be neutron stars. Received: 25 November 2002 / Revised version: 25 February 2003 / Published online: 5 May 2003     

Neutron star matter superfluidity and superconductivity

The possibility of superfluidity or superconductivity in neutron or proton subsystems in the nuclear-matter region in neutron stars is investigated. The energy gap and corresponding critical temperature and critical magnetic field is calculated or estimated as function of density or Fermi momentum. In the calculations are used reaction matrix elements calculated earlier by means of Brueckner theory by the author. The final results indicate that neutron superfluidity, corresponding specifically toS-state pairing, may exist in a low-density shell in the nuclear-matter region of a neutron star. There is probably anisotropic neutron superfluidity, corresponding to the³ P ₂ or the singletD state, for higher densities. Superfluidity or superconductivity, corresponding toS-state pairing for the proton subsystem, is quite likely in most of the nuclear-matter region. The expected temperatures and magnetic fields in neutron stars seem to be well below the estimated critical temperatures or critical magnetic fields corresponding to the calculated values of the energy gap. However, similar methods have earlier predicted a much too high critical temperature for liquid³He.     

Determination of the final equilibrium radius and the increase in the emittance of a nonequilibrium relativistic electron beam during transport along an external magnetic field in a gas-plasma scattering medium

An equation describing the evolution of the transverse energy of a segment of a paraxial axisymmetric relativistic electron beam (REB) propagating in a gas-plasma scattering medium along an external magnetic field is used to find the equation relating the final equilibrium radius of the beam to its initial nonequilibrium value. An analytical expression for the increase in the mean-square emittance of an REB during transport up to achievement of the equilibrium state is found for the case considered. The dependence of the final equilibrium radius and the corresponding increase in the mean-square emittance on the density of the scattering medium and the induction of the external magnetic field is investigated. Pis’ma Zh. Tekh. Fiz. 67, 108–111 (July 1997)     

Symmetry energy impact in simulations of core-collapse supernovae

In this work we study the effect of the symmetry energy on several properties of neutron stars. First, we discuss its effect on the density, proton fraction and pressure of the neutron star crust-core transition. We show that whereas the first two quantities present a clear correlation with the slope parameter L of the symmetry energy, no satisfactory correlation is seen between the transition pressure and L . However, a linear combination of the slope and curvature parameters at ρ = 0.1 fm^?3 is well correlated with the transition pressure. In the second part we analyze the effect of the symmetry energy on the pasta phase. It is shown that the size of the pasta clusters, number of nucleons and the cluster proton fraction depend on the density dependence of the symmetry energy: a small L gives rise to larger clusters. The influence of the equation of state at subsaturation densities on the extension of the inner crust of the neutron star is also discussed. Finally, the effect of the density dependence of the symmetry energy on the strangeness content of neutron stars is studied in the last part of the work. It is found that charged (neutral) hyperons appear at smaller (larger) densities for smaller values of the slope parameter L. A linear correlation between the radius and the strangeness content of a star with a fixed mass is also found.     

Field Angular Momentum

We examine the possible role played by field angular momentum in two systems of vastly different sizes: (i) the nucleon and (ii) highly magnetic white dwarf stars. For the nucleon we study the restrictions on the nucleon's structure that arise from the requirement that the total field angular (spin, orbital and field angular momentum) should satisfy the standard angular momentum commutation relationship. For the magnetic white dwarfs we argue that the magnetic field may alter the statistics of some fraction of the white dwarf's electrons from fermionic to bosonic. This would effect the stars structure, giving it a smaller than expected radius, and a lower than expected temperature. In some extreme cases one could imagine that this effect could lead to the collapse of the white dwarf into a neutron star despite being below the Chandreshekar limit.     

Axion emission from a magnetized neutron gas

By using the polarization density matrix for a neutron in a magnetic field, the axion luminosity of magnetic neutron stars that is associated with the flip of the anomalous magnetic moment of degenerate nonrelativistic neutrons is calculated. It is shown that, at values of the magnetic-field induction in the region B ≳ 10¹⁸ G, this mechanism of axion emission is dominant in “young” neutron stars of temperature about a few tens of MeV units. At B ∼ 10¹⁷ G, it is one of the basic mechanisms. The Fermi energy of a degenerate neutron gas in a magnetic field is found, and it is shown that there is no such mechanism of axion emission in the degenerate case.     

Evidence for heating of neutron stars by magnetic-field decay

We show the existence of a strong trend between neutron star (NS) surface temperature and the dipolar component of the magnetic field extending through three orders of field magnitude, a range that includes magnetars, radio-quiet isolated neutron stars, and many ordinary radio pulsars. We suggest that this trend can be explained by the decay of currents in the crust over a time scale of approximately 10(6) yr. We estimate the minimum temperature that a NS with a given magnetic field can reach in this interpretation.     

Nuclear and neutron star radii

We investigate the correlation between nuclear neutron radii and the radius of neutron stars. We use a well-established hadronic SU(3) model based on chiral symmetry that naturally includes nonlinear vector meson and scalar meson–vector meson couplings. The relative strengths of the couplings modify the nuclear isospin-dependent interactions. We study the dependence of nuclear and neutron star radii on the coupling strengths. The relevance of the results for parity-violating electron–nucleus scattering is discussed.     

超强磁场对中子星外壳层核素56Fe,56Co,56Ni,56Mn和56Cr电子俘获过程中微子能量损失的影响

研究了超强磁场对中子星外壳层核素⁵⁶Fe,⁵⁶Co,⁵⁶Ni,⁵⁶Mn和⁵⁶Cr电子俘获过程中微子能量损失的影响.结果表明,就大部分中子星表面的磁场B<10¹³G,超强磁场对中微子能量损失率的影响很小.对于一些磁场范围为10¹³—10¹⁵G的超磁星,超强磁场可使中微子能量损失率大大降低,甚至超过5个数量级.     

Stationary Electromagnetic Fields of a Slowly Rotating Magnetized Neutron Star in General Relativity

Following the general formalism presented by Rezzolla, Ahmedov and Miller, ⁽¹⁾ we here derive analytic solutions of the electromagnetic fields equations in the internal and external background spacetime of a slowly rotating highly conducting magnetized neutron star. The star is assumed to be isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. Our results indicate that the electromagnetic fields of a slowly rotating neutron star are modified by general relativistic effects arising from both the monopolar and the dipolar parts of the gravitational field. The results presented here differ from the ones discussed by Rezzolla, Ahmedov and Miller ⁽¹⁾ mainly in that we here consider the interior magnetic field to be dipolar with the same radial dependence as the external one. While this assumption might not be a realistic one, it should be seen as the application of our formalism to a case often discussed in the literature.     

Magic ultramagnetized nuclei in explosive nucleosynthesis

Direct evidence of the presence of ⁴⁴Ti and content of the isotope in the supernova remnant Cassiopeia A are obtained from the analysis of gamma-ray spectrum of the remnant. A significant excess of observational ⁴⁴Ti volume on predictions of supernova models can be explained as the magnetization effect in the process of explosive nucleosynthesis. The formation of chemical elements is considered accounting for superstrong magnetic fields predicted for supernovae and neutron stars. Using the arguments of nuclear statistical equilibrium, a significant effect of magnetic field on the nuclear shell energy is demonstrated. The magnetic shift of the most tightly ??bound?? nuclei from the transition metals of iron series to titanium leads to an exponential increase in the portion of ⁴⁴Ti and, accordingly to a significant excess of the yield of these products of nucleosynthesis.     

The lead nucleus as a miniature surrogate for a neutron star

The nucleus of ²⁰⁸Pb, a system 18 orders of magnitude smaller and 55 orders of magnitude lighter than a neutron star, may be used as a miniature surrogate to establish important correlations between its neutron skin and several neutron-star properties. Indeed, models with a thicker neutron skin in ²⁰⁸Pb generate larger neutron stars that have a lower liquid-to-solid transition density. Further, we illustrate how the correlation between the neutron skin in ²⁰⁸Pb and the radius of a 1.4 solar-mass neutron star may be used to place important constraints on the equation of state of neutron-rich matter and how it may help elucidate the existence of a phase transition at the core of the star.