Evolution of the multipolar magnetic field in isolated neutron stars

The evolution of the multipolar structure of the magnetic field of isolated neutron stars is studied assuming the currents to be confined to the crust. We find that, except for multipoles of very high order ( l ≳25), the evolution is similar to that of a dipole. Therefore no significant evolution is expected in the pulse shape of isolated radio pulsars because of the evolution of the multipole structure of the magnetic field.     

Diamagnetic screening of the magnetic field in accreting neutron stars

A possible mechanism for screening of the surface magnetic field of an accreting neutron star, by the accreted material, is investigated. We model the material flow in the surface layers of the star by an assumed two-dimensional velocity field satisfying all the physical requirements. Using this model velocity we find that, in the absence of magnetic buoyancy, the surface field is screened (i.e. there is submergence of the field by advection) within the time-scale of material flow of the top layers. On the other hand, if magnetic buoyancy is present, the screening happens over a time-scale that is characteristic of the slower flow of the deeper (and hence, denser) layers. For accreting neutron stars, this longer time-scale turns out to be about 10⁵ yr, which is of a similar order of magnitude to the accretion time-scale of most massive X-ray binaries.     

Generation of a toroidal magnetic field in rotating neutron stars

The electromagnetic properties of neutron stars (pulsars) are studied. It is shown that taking the presence of two angular rotation velocities of the components of neutron stars and the first corrections to the general theory of relativity into account in the equations of hydrodynamic equilibrium for the plasma and in Maxwell’s equations leads to the generation of toroidal magnetic fields in the depths of a neutron star. __________ Translated from Astrofizika, Vol. 49, No. 1, pp. 97–101 (February 2006).     

Emergence of magnetic field due to spin-polarized baryon matter in neutron stars

A model of the ferromagnetic origin of magnetic fields of neutron stars is considered. In this model, the magnetic phase transition occurs inside the core of neutron stars soon after formation. However, owing to the high electrical conductivity the core magnetic field is initially fully screened. We study how this magnetic field emerges for an outside observer. After some time, the induced field that screens the ferromagnetic field decays enough to uncover a detectable fraction of the ferromagnetic field. We calculate the time-scale of decay of the screening field and study how it depends on the size of the ferromagnetic core. We find that the same fractional decay of the screening field occurs earlier for larger cores. We conjecture that weak fields of millisecond pulsars, B ∼10⁸–10⁹ G, could be identified with ferromagnetic fields of unshielded fraction ε ∼10⁻⁴–10⁻³ resulting from the decay of screening fields by a factor 1− ε in ∼10⁸ yr since their birth.     

Gravitational collapse of magnetic neutron stars

Pulsars are presently believed to be rotating neutron stars with frozen-in magnetic fields. Because of the high density of neutron stars, general relativistic effects are important since they effect both the structure and stability of such stars. Besides this, the magnetic field outside the star is also affected. Instead of falling of asr ^(2+l) as in flat space, it is shown that each magnetic multipole varies as a hypergeometric function of radius. A closed form of these hypergeometric functions is given in terms of Legendre functions of the second kind. If the mass of a neutron star exceeds about 2.4m , the star becomes unstable and coliapses. For a quasistatically collapsing body, it is shown that the magnetic field seen by a distant observer vanishes as the radius approaches the gravitational radius.This work was supported in part by the Air Force Office of Scientific Research, Office of Aerospace Research under AFOSR Grant 70-1866.     

Surface composition of magnetic neutron stars

The relative abundances of seven constitutent nuclei, He⁴, C¹², O¹⁶, Ne²⁰, Mg²⁴, Si²⁸ and Fe⁵⁶, are calculated as a function of time for neutron star atmospheres within which exist magnetic fields of the order of 10¹³G. The opacity, equation of state of the electrons, and cooling rate of the magnetic star are discussed, and it is shown to be a reasonable approximation to assume an atmosphere to be isothermal. The effects of particle diffusion are included in the nuclear reaction network. Computations are performed both for a constant mass atmosphere and for an atmosphere in which mass is being ejected. It is found that the final abundances are model independent as long as the initial model contains predominantly He⁴. The relative abundances are compared to the cosmic ray spectrum. For both the constant mass and mass loss atmospheres, nucleosynthesis proceeds virtually completely to Fe⁵⁶. However the outermost layers of the envelope, in which no mass is being ejected, are composed almost entirely of He⁴ with trace amounts of Fe⁵⁶. After the loss of about 10²¹ g, only Fe⁵⁶ is ejected from atmospheres expelling mass.A portion of the research on which this paper was based was performed while L. C. Rosen was present at the Lawrence Radiation Laboratory, Livermore, California.     

The simulation of the magnetic field and spin period evolution of accreting neutron stars

By means of the Monte Carlo method, we simulate the evolutionary distribution of accreting neutron stars (NSs) in the magnetic field versus spin period (B‐P) diagram where the accretion induced magnetic‐field decay model is exploited. The simulated results show that by mass accretion the B‐P distribution of the accreting NS would evolve along the equilibrium period line to a region with low field and short period. The B‐P distributions of the simulated accreting NSs are consistent with those of the observed millisecond pulsars (MSPs) after accretion of ∼ 0.1–0.2 M⊙. We also test the effects of the initial magnetic field and the spin period on the evolved B‐P distribution of the accreting NSs. It is shown that the evolved distributions of the simulated samples are independent of the selection of the initial condition when the NS magnetic field decays to a value less than ∼10¹⁰ G. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Superconducting critical field in cold magnetic white dwarfs and in neutron stars

For an evaluation of the superconducting critical fieldH _c as a function of the mass-density in the external layers of cold magnetic white dwarfs and in the superconducting proton fluid in neutron stars, we use the solution of a differential equation involvingH _c as a function of the pressure. The differential equation and its solution are obtained by pure thermodynamic way.Finally other thermodynamic quantities are calculated for the above superconducting astrophysical systems.     

Disk accretion onto magnetic neutron stars

The magnetic torque contributed by field-threading disk takes on a significant role in the total torque exerted on the magnetic neutron stars in X-ray binaries. In previous works, the toroidal field generated by rotational shear is estimated from the Faraday induction law. It is re-evaluated in this paper with the electrodynamical boundary conditions across the surface of the disk in an axisymmetric case. The dependence of the resistivity of disk plasma on radius is also estimated based on the standard disk theory. A more realistic expression of the disk torque is then derived. The applications to several disk-accreted X-ray pulsars are briefly discussed.Project supported by the National Nature Science Foundation of China and the funds from the State Education Commission for the training of Ph.D.'s     

Magnetic field evolution in neutron stars

Neutron stars contain persistent, ordered magnetic fields that are the strongest known in the Universe. However, their magnetic fluxes are similar to those in magnetic A and B stars and white dwarfs, suggesting that flux conservation during gravitational collapse may play an important role in establishing the field, although it might also be modified substantially by early convection, differential rotation, and magnetic instabilities. The equilibrium field configuration, established within hours (at most) of the formation of the star, is likely to be roughly axisymmetric, involving both poloidal and toroidal components. The stable stratification of the neutron star matter (due to its radial composition gradient) probably plays a crucial role in holding this magnetic structure inside the star. The field can evolve on long time scales by processes that overcome the stable stratification, such as weak interactions changing the relative abundances and ambipolar diffusion of charged particles with respect to neutrons. These processes become more effective for stronger magnetic fields, thus naturally explaining the magnetic energy dissipation expected in magnetars, at the same time as the longer-lived, weaker fields in classical and millisecond pulsars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radiative heat transfer in surface layers of neutron stars with a magnetic field

Thermal conductivity due to Thomson scattering and free-free absorption of photons is numerically evaluated for a non-relativistic non-degenerate plasma in a magnetic field for a number of values ofb =_B/kT 1000. In the case of pure scattering, simple fitting formulae are derived. Atb6, the magnetic field is shown to decrease (by about one order) the characteristic densities above which heat transfer is mainly determined by free-free transitions.     

Partially degenerate nonrelativistic isothermal gas spheres in the presence of a magnetic field

The effect of a weak poloidal magnetic field on the equilibrium structure of a partially degenerate nonrelativistic isothermal gas sphere has been studied. Models have been computed for varying degrees of central degeneracy and the effect of the magnetic field on the various parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been looked into. It is found that as the central degeneracy parameter is increased, the central condensation in general decreases and, hence, the eccentricity of the configuration decreases.     

The evolution of the magnetic fields of neutron stars

Observational evidence, and theoretical models of the magnetic field evolution of neutron stars is discussed. Observational data indicates that the magnetic field of a neutron star decays significantly only if it has been a member of a close interacting binary. Theoretically, the magnetic field evolution has been related to the processing of a neutron star in a binary system through the spin evolution of the neutron star, and also through the accretion of matter on the neutron star surface. I describe two specific models, one in which magnetic flux is expelled from the superconducting core during spin-down, via a copuling between Abrikosov fluxoids and Onsager-Feynman vortices; and another in which the compression and heating of the stellar crust by the accreted mass drastically reduces the ohmic decay time scale of a magnetic field configuration confined entirely to the crust. General remarks about the behaviour of the crustal field under ohmic diffusion are also made.     

The radiation of a hot magnetized plasma accreted by degenerate stars with a strong magnetic field

The absorption coefficients for extraordinary and ordinary electromagnetic modes are found for a tenuous hot magnetized plasma, taking into account the collisions between plasma particles and the scattering of photons. An approach is suggested which generalizes collisionless and cold-plasma approximations. The simple formulae obtained are valid both near, and at a distance from, the cyclotron harmonics. In particular, the ordinary mode is shown to have resonance at the cyclotron frequency. The number of noticeable reasonances of absorption coefficient at cyclotron harmonics is estimated for both modes.Using the coefficients obtained, the intensity, Stokes parameters and polarization of radiation of a homogeneous plasma slab are calculated for conditions which may be realized in the heated regions of accreted plasma in an AM Herculis-type system. The large difference between the absorption coefficient of extra-ordinary and ordinary modes near the cyclotron harmonics may result in the emission of the broad polarized continuum together with the narrow cyclotron lines. The polarization of these lines has a complicated spectral dependence.The results obtained are shown to be useful for explaining the main properties of AM Herculistype objects.     

Thermal and electrical conductivities of crystals in neutron stars and degenerate dwarfs

Thermal and electrical conductivities due to electron scattering on phonons are calculated for degenerate cores of white dwarfs and envelopes of neutron stars for wide ranges of density, temperature and ion charge. In the stellar zones, in which T _pi(Z^1/3e²/_F) (_piis the ion plasma frequency and _F the Fermi velocity of electrons), the main contribution into scattering comes from the Umklapp processes. In the zones with lowerT, the Umklapp processes are frozen out, that results in a sharp growth of electrical and thermal conductivities. This, for instance, should make nuclear burning more stable in such zones.     

Describing neutron stars by the relativistic mean field theory

Neutron stars are studied in the framework of the relativistic mean field theory of interacting nucleons, hyperons, and mesons. Within the hadronic freedom, the cores of neutron stars are found to be dominated by hyperons when the density is sufficiently high. The influence of hyperon coupling constants on the transition from a neutron star to a hyperon-dominated strange neutron star is also investigated. It is found that the transition density gets its minimum value when the ratio of hyperon coupling constant to nucleon's takes the value of 0.65, and the calculated maximum mass of the neutron star is 1.4 M which lies within the range of the observational results.     

Pulsar radio luminosities and the magnetic moments of neutron stars

Using equations from the theory of pulsar radio emission, the radio luminosities of pulsars and the magnetic moments of neutron stars are calculated from existing observational data. Translated from Astrofizika, Vol. 42, No. 3, pp. 433–437, July–September, 1999.