The evolution of core and surface magnetic field 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 (2000), both to neutron star models based on different equations of state and to different initial magnetic field structures. When initially 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 to those of a neutron star with a purely crustal field configuration; the only difference is the occurence of a residual field. In case of an initially submerged field significant differences from the standard evolution occur only during the early period of neutron star's life, until the field has been rediffused 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 rediffusion of the magnetic field on to 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 preferentially in neutron stars with a soft equation of state these stresses may cause crust cracking.Comment: 10 pages with 5 figures. accepted by MNRA

Magnetic and spin evolution of neutron stars in close binaries

The evolution of neutron stars in close binary systems with a low-mass companion is considered assuming the magnetic field to be confined within the solid crust. We adopt the standard scenario of the evolution in a close binary system in accordance with which the neutron star passes throughout four evolutionary phases ("isolated pulsar" -- "propeller" -- accretion from the wind of a companion -- accretion due to Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties both of the neutron star and low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period being processed in low-mass binaries can evolve to low-field rapidly rotating pulsars. Even if the main-sequence life of a companion is as long as $10^{10}$ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The considered model can well account for the origin of millisecond pulsars.Comment: 18 pages + 10 figures, uses epsf.sty. Accepted by MNRA

Magnetic and spin evolution of isolated neutron stars with the crustal magnetic field

We consider the magnetic and spin evolution of isolated neutron stars assuming that the magnetic field is initially confined to the crust. The evolution of the crustal field is determined by the conductive properties of the crust which, in its turn, depend on the thermal history of the neutron star. Due to this fact, a study of the magnetic field decay may be a powerful diagnostic of the properties of matter in the core where the density is above the nuclear density. We treat the evolution of neutron stars for different possible equations of state and cooling scenarios (standard and, so called, accelerated cooling). The spin evolution is strongly influenced by the behaviour of the magnetic field. Assuming that the spin-down rate of the neutron star is determined by the magnetodipole radiation, we calculated the evolutionary tracks of isolated pulsars in the $B - \tau$ and $B-P$ planes, where $B$ and $P$ are the magnetic field and period, respectively, and $\tau$ is the spin-down age. The calculated tracks are compared with observational data on the magnetic field and period of pulsars. This comparison allows to infer the most suitable equations of state of nuclear matter and cooling model and to determine the range of parameters of the original magnetic configurations of pulsars.Comment: 13 pages + 5 figures, uses epsf.st

ROSAT X-ray sources and exponential field decay in isolated neutron stars

In this paper we semianalyticaly evaluate influence of the exponential decay of magnetic field on the fate of isolated neutron stars. The fact of ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars gives us an opportunity to put some limits on the parameters of the exponential decay. We argue, that, if most part of neutron stars have approximately the same decay and initial parameters, then the combinations of the bottom magnetic momentum, $\mu_b$, in the range $\sim 10^{28}-10^{29.5} {\rm G} {\rm cm}^3$ and characteristic time scale, $t_d$, in the range $\sim 10^7-10^8 {\rm yrs}$ for standard initial magnetic momentum, $\mu_0=10^{30} {\rm G} {\rm cm}^3$, can be excluded, because for that sets of parameters neutron stars never come to the stage when accretion of the interstellar medium on their surfaces is possible even for low velocity of neutron stars and relatively high density of the interstellar medium. The region of excluded parameters increases with $\mu_0$ decreasing.Comment: 5 pages, 4 PostScript figures (uses A&A style

RX J0720.4--3125 as a Possible Example of the Magnetic Field Decay of Neutron Stars

We studied possible evolution of the rotational period and the magnetic field of the X-ray source RX J0720.4-3125 assuming this source to be an isolated neutron star accreting interstellar medium. Magnetic field of the source is estimated to be $10^6 - 10^9$ G, and it is difficult to explain observed rotational period 8.38 s without invoking hypothesis of the magnetic field decay. We used the model of ohmic decay of the crustal magnetic field. The estimates of accretion rate ($10^{-14} - 10^{-16} M_\odot/yr$), velocity of the source relative to interstellar medium ($10 - 50$ km/s), neutron star age ($2\cdot 10^9 - 10^{10}$ yrs) are obtained.Comment: 12 pages (LATEX), 2 PostScript figures. Also available at http://xray.sai.msu.su/~polar/ (with the Russian variant of the article

A Numerical Approach for Calculation of Characteristics of Edge Waves in Three-Dimensional Plates

© 2020 World Scientific Publishing CompanySurface waves have been extensively studied in earthquake seismology. Surface waves are trapped near an infinitely large surface. The displacements decay exponentially with depth. These waves are also named Rayleigh and Love waves. Surface waves are also used for nondestructive testing of surface defects. Similar waves exist in finite width three-dimensional plates. In this case, displacements are no longer constant in the direction perpendicular to the wave propagation plane. Wave energy could still be trapped near the edge of the three-dimensional plate, and hence the term edge waves. These waves are thus different to the two-dimensional Rayleigh and Love waves. This paper presents a numerical model to study dispersion properties of edge waves in plates. A two-dimensional semi-analytical finite element method is developed, and the problem is closed by a perfectly matched layer adjacent to the edge. The numerical model is validated by comparing with available analytical and numerical solutions in the literature. On this basis, higher order edge waves and mode shapes are presented for a three-dimensional plate. The characteristics of the presented edge wave modes could be used in nondestructive testing applications.Peer reviewe

SGRs and AXPs proposed as ancestors of the Magnificent seven

The recently suggested correlation between the surface temperature and the magnetic field in isolated neutron stars does not seem to work well for SGRs, AXPs and X-ray dim isolated neutron stars (XDINs; specifically the Magnificent Seven or M7). Instead by appealing to a Color-Flavor Locked Quark Star (CFLQS) we find a more natural explanation. In this picture, the heating is provided by magnetic flux expulsion from a crust-less superconducting quark star. Combined with our previous studies concerning the possibility of SGRs, AXPs, and XDINs as CFLQSs, this provides another piece of evidence that these objects are all related. Specifically, we propose that XDINs are the descendants of SGRs and AXPs.Comment: submitted to A&A letters to the edito

Evolution of isolated neutron stars in globular clusters: number of Accretors

With a simple model from the point of view of population synthesis we try to verify an interesting suggestion made by Pfahl & Rappaport (2001) that dim sources in globular clusters (GCs) can be isolated accreting neutron stars (NSs). Simple estimates show, that we can expect about 0.5-1 accreting isolated NS per typical GC with $M=10^5 M_{\odot}$ in correspondence with observations. Properties of old accreting isolated NSs in GCs are briefly discussed. We suggest that accreting NSs in GCs experienced significant magnetic field decay.Comment: 6 pages, no figures. Submitted to Astronomical and Astrophysical Transactions (style included

Constrains on parameters of magnetic field decay for accreting isolated neutron stars

The influence of exponential magnetic field decay (MFD) on the spin evolution of isolated neutron stars is studied. The ROSAT observations of several X-ray sources, which can be accreting old isolated neutron stars, are used to constrain the exponential and power-law decay parameters. We show that for the exponential decay the ranges of minimum value of magnetic moment, $\mu_b$, and the characteristic decay time, $t_d$, $\sim 10^{29.5}\ge \mu_b \ge 10^{28} {\rm G} {\rm cm}^3$, $\sim 10^8\ge t_d \ge 10^7 {\rm yrs}$ are excluded assuming the standard initial magnetic moment, $\mu_0=10^{30} {\rm G} {\rm cm}^3$. For these parameters, neutron stars would never reach the stage of accretion from the interstellar medium even for a low space velocity of the stars and a high density of the ambient plasma. The range of excluded parameters increases for lower values of $\mu_0$. We also show, that, contrary to exponential MFD, no significant restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations. Isolated neutron stars with constant magnetic fields and initial values of them less than $\mu_0 \sim 10^{29} {\rm G} {\rm cm}^3$ never come to the stage of accretion. We briefly discuss the fate of old magnetars with and without MFD, and describe parameters of old accreting magnetars.Comment: 18 pages, 6 PostScript figures, to be published in the Proceedings of the XXVIII ITEP Winter Schoo