The evolution of the core and surface magnetic fields in isolated neutron stars

We apply the model of flux expulsion from the superfluid and superconductive core of a neutron star, developed by Konenkov & Geppert, both to neutron star models based on different equations of state and to different initial magnetic field structures. Initially, when the core and the surface magnetic field are of the same order of magnitude, the rate of flux expulsion from the core is almost independent of the equation of state, and the evolution of the surface field decouples from the core field evolution with increasing stiffness. When the surface field is initially much stronger than the core field, the magnetic and rotational evolution resembles that of a neutron star with a purely crustal field configuration; the only difference is the occurrence of a residual field. In the case of an initially submerged field, significant differences from the standard evolution only occur during the early period of the life of a neutron star, until the field has been re-diffused to the surface. The reminder of the episode of submergence is a correlation of the residual field strength with the submergence depth of the initial field. We discuss the effect of the re-diffusion of the magnetic field on the difference between the real and the active age of young pulsars and on their braking indices. Finally, we estimate the shear stresses built up by the moving fluxoids at the crust–core interface and show that these stresses may cause crust cracking, preferentially in neutron stars with a soft equation of state.     

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 physics of strong magnetic fields in neutron stars

In this paper we present a new result, namely that the primal magnetic field of the collapsed core during a supernova explosion will, as a result of the conservation of magnetic flux, receive a massive boost to more than 90 times its original value by the Pauli paramagnetization of the highly degenerate relativistic electron gas just after the formation of the neutron star. Thus, the observed super-strong magnetic field of neutron stars may originate from the induced Pauli paramagnetization of the highly degenerate relativistic electron gas in the interior of the neutron star. We therefore have an apparently natural explanation for the surface magnetic field of a neutron star.     

Thermal evolution of neutron stars with decaying magnetic fields

Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field(108G) could have a lower temperature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature,except millisecond pulsar J0437–4715.     

Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Isolated neutron stars: magnetic fields, distances,and spectra

We present timing measurements, astrometry, and high-resolution spectra of a number of nearby, thermally emitting, isolated neutron stars. We use these to infer magnetic field strengths and distances, but also encounter a number of puzzles. We discuss three specific ones in detail: (i) For RX J0720.4-3125 and RX J1308.6+2127, the characteristic ages are in excess of 1 Myr, while their temperatures and kinematic ages indicate that they are much younger; (ii) For RX J1856.5-3754, the brightness temperature for the optical emission is in excess of that measured at X-ray wavelengths for reasonable neutron-star radii; (iii) For RX J0720.4-3125, the spectrum changed from an initially featureless state to one with an absorption feature, yet there was only a relatively small change in T _eff. Furthermore, we attempt to see whether the spectra of all seven sources, in six of which absorption features have now been found, can be understood in the context of strongly magnetised hydrogen atmospheres. We find that the energies of the absorption features can be reproduced, but that it remains puzzling that, for J0720.4-3125 specifically, the spectrum was featureless in one state, and that, generally, the spectra do not have high-energy tails that are harder than the Wien-like ones obseved.      

The influence of Hall drift on the magnetic fields of neutron stars

We consider the evolution of magnetic fields under the influence of Hall drift and Ohmic decay. The governing equation is solved numerically, in a spherical shell with   r _i / r _o = 0.75  . Starting with simple free-decay modes as initial conditions, we then consider the subsequent evolution. The Hall effect induces so-called helicoidal oscillations, in which energy is redistributed among the different modes. We find that the amplitude of these oscillations can be quite substantial, with some of the higher harmonics becoming comparable with the original field. Nevertheless, this transfer of energy to the higher harmonics is not sufficient to accelerate significantly the decay of the original field, at least not at the   R _B = O (100)  parameter values accessible to us, where this Hall parameter   R _B   measures the ratio of the Ohmic time-scale to the Hall time-scale. We do find clear evidence though of increasingly fine structures developing for increasingly large   R _B   , suggesting that perhaps this Hall-induced cascade to ever-shorter length-scales is eventually sufficiently vigorous to enhance the decay of the original field. Finally, the implications for the evolution of neutron star magnetic fields are discussed.     

Tunnel effect in molecules in strong magnetic fields of neutron stars

It is shown that, in the strong magnetic field of the neutron starB=10¹²–10¹³ G, the probability of the tunnel effect in the molecules increases significantly. It is quite probable that this effect can catalyze nuclear reactions at the neutron star surface.     

Magnetic fields in axisymmetric neutron stars

We derive general equations for axisymmetric Newtonian magnetohydrodynamics and use these as the basis of a code for calculating equilibrium configurations of rotating magnetized neutron stars in a stationary state. We investigate the field configurations that result from our formalism, which include purely poloidal, purely toroidal and mixed fields. For the mixed-field formalism, the toroidal component appears to be bounded at less than 7 per cent. We calculate distortions induced both by magnetic fields and by rotation. From our non-linear work, we are able to look at the realm of validity of perturbative work: we find for our results that perturbative-regime formulae for magnetic distortions agree to within 10 per cent of the non-linear results if the ellipticity is less than 0.15 or the average field strength is less than 10¹⁷ G. We also consider how magnetized equilibrium structures vary for different polytropic indices.     

Vibrational damping by quark matter inside neutron stars

Free quark state may exist in the central region of massive neutron stars. We discuss the damping of the vibration of such neutron stars through the quark weak interaction. The damping time scale may be as short as tens of milliseconds. Damping with such short time constant may possibly be reflected in some γ-ray burst phenomena. An attempt is made to explain the γ burst of 1979 March 5 by this mechanism.     

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.     

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     

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.     

Magnetic fields and rotation in white dwarfs and neutron stars

Recent spectropolarimetric observations of Ap and Bp stars with improved sensitivity have suggested that most Ap and Bp stars are magnetic with dipolar fields of at least a few hundred gauss. These new estimates suggest that the range of magnetic fluxes found for the majority of magnetic white dwarfs is similar to that of main-sequence Ap–Bp stars, thus strengthening the empirical evidence for an evolutionary link between magnetism on the main sequence and magnetism in white dwarfs. We draw parallels between the magnetic white dwarfs and the magnetic neutron stars and argue that the observed range of magnetic fields in isolated neutron stars  ( B_p ∼ 10¹¹–10¹⁵ G)  could also be explained if their mainly O-type progenitors have effective dipolar fields in the range of a few gauss to a few kilogauss, assuming approximate magnetic flux conservation with the upper limit being consistent with the recent measurement of a field of   B_p ∼ 1100 G  for θ Orion C.
In the magnetic field–rotation diagram, the magnetic white dwarfs can be divided into three groups of different origin: a significant group of strongly magnetized slow rotators  ( P _rot∼ 50 –100 yr)  that have originated from single-star evolution, a group of strongly magnetized fast rotators  ( P _rot∼ 700 s)  , typified by EUVE J0317–853, that have originated from a merger, and a group of modest rotators ( P _rot∼ hours–days) of mixed origin (single-star and CV-type binary evolution). We propose that the neutron stars may similarly divide into distinct classes at birth , and suggest that the magnetars may be the counterparts of the slowly rotating high-field magnetic white dwarfs.