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 Physics , 1998, DOI: 10.1046/j.1365-8711.1999.02781.x Abstract: The evolutionary scenario of the neutron star magnetic field is examined assuming a spindown-induced expulsion of magnetic flux originally confined to the core, in which case the expelled flux undergoes ohmic decay. The nature of field evolution, for accreting neutron stars, is investigated incorporating the crustal microphysics and material movement due to accretion. This scenario may explain the observed field strengths of neutron stars but only if the crustal lattice contains a large amount of impurity which is in direct contrast to the models that assume an original crustal field.
 Physics , 1998, DOI: 10.1046/j.1365-8711.1999.02287.x Abstract: We investigate the evolution of the magnetic field of isolated pulsars and of neutron stars in different kinds of binary systems, assuming the field to be originally confined to the crust. Our results for the field evolution in isolated neutron stars helps us to constrain the physical parameters of the crust. Modelling the full evolution of a neutron star in a binary system through several stages of interaction we compare the resulting final field strength with that observed in neutron stars in various types of binary systems. One of the interesting aspects of our result is a positive correlation between the rate of accretion and the final field strength, for which some observational indication already exists. Our results also match the overall picture of the field evolution in neutron stars derived from observations.
 Physics , 2000, Abstract: Based on the accretion induced magnetic a field decay model, in which a frozen field and an incompressible fluid are assumed, we obtain the following results. (1) An analytic relation between the magnetic field and spin period, if the fastness parameter of the accretion disk is neglected. The evolutionary tracks of accreting neutron stars in the P-B diagram in our model are different from the equilibrium period lines when the influence of the fastness parameter is taken into account. (2) The theoretical minimum spin period of an accreting neutron star is $\max (1.1{\rm ms}(\frac{\Delta M}{M_{\odot}})^{-1} R^{-5/14}_6 I_{45}(\frac{M}{M_{\odot}})^{-1/2}, 1.1{\rm ms} (\frac{M}{M_{\odot}})^{-1/2} R^{17/14}_6)$, independent of the accretion rate (X-ray luminosity) but dependent on the total accretion mass $\Delta M$. However, the minimum magnetic field depends on the accretion rate. (3) The magnetic field strength decreases faster with time than the period.
 Sushan Konar Physics , 2000, DOI: 10.1046/j.1365-8711.2002.05449.x Abstract: The evolution of the magnetic field in an accreting neutron star is investigated using a fully general relativistic treatment and assuming that initially the currents supporting the field are completely confined to the crust. We find that the field decay slows down due to the inclusion of the curvature of space-time but the final results do not differ significantly from those obtained assuming a flat space-time. We also find that such modifications are small compared to the uncertainties introduced by a lack of precise knowledge of the neutron star micro-physics.
 Physics , 2001, DOI: 10.1086/321658 Abstract: We investigate whether the magnetic field of an accreting neutron star may be diamagnetically screened by the accreted matter. We assume the freshly accumulated material is unmagnetized, and calculate the rate at which the intrinsic stellar magnetic flux is transported into it by Ohmic diffusion. We calculate the one-dimensional steady-state magnetic field profiles, and show that the magnetic field strength decreases as one moves up through the outer crust and ocean by roughly (Mdot/0.02 Mdot_Edd) orders of magnitude, where Mdot is the accretion rate and Mdot_Edd the Eddington accretion rate. We show that buoyancy instabilities set a limit to the strength of any buried field of roughly 10^10-10^11 G. Our results show that magnetic screening is ineffective for Mdot<0.01 Mdot_Edd, so that, no matter how the accreted material joins onto the star, the underlying stellar field should always be evident. In this respect, we point out the only known persistently-pulsing accreting X-ray millisecond pulsar, SAX J1808.4-3658, has an accretion rate of 10^-3 Mdot_Edd, far below the regime where magnetic screening can play a role. Most steadily accreting neutron stars in low-mass X-ray binaries in our Galaxy accrete at rates where screening would be effective if the simplified magnetic and accretion geometry we adopt were correct. If screened, then the underlying field will emerge after accretion halts, on a timescale of only 100--1000 years, set by the Ohmic diffusion time across the outer crust. It thus seems unlikely that screening alone can explain the low magnetic fields of the millisecond radio pulsars.
 Physics , 2000, DOI: 10.1080/10556790108221135 Abstract: In this short note we discuss the influence of power-law magnetic field decay on the evolution of old accreting isolated neutron stars. We show, that, contrary to exponential field decay (Popov & Prokhorov 2000), no additional restrictions can be made for the parameters of power-law decay from the statistics of isolated neutron star candidates in ROSAT observations. We also briefly discuss the fate of old magnetars with and without field decay, and describe parameters of old accreting magnetars.
 Physics , 2000, DOI: 10.1080/01422410108228807 Abstract: 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.
 Physics , 2010, DOI: 10.1111/j.1365-2966.2010.16910.x Abstract: We study evolution of isolated neutron stars on long time scale and calculate distribution of these sources in the main evolutionary stages: Ejector, Propeller, Accretor, and Georotator. We compare different initial magnetic field distributions taking into account a possibility of magnetic field decay, and include in our calculations the stage of subsonic Propeller. It is shown that though the subsonic propeller stage can be relatively long, initially highly magnetized neutron stars ($B_0\ga 10^{13}$ G) reach the accretion regime within the Galactic lifetime if their kick velocities are not too large. The fact that in previous studies made $>$10 years ago, such objects were not considered results in a slight increase of the Accretor fraction in comparison with earlier conclusions. Most of the neutron stars similar to the Magnificent seven are expected to become accreting from the interstellar medium after few billion years of their evolution. They are the main predecestors of accreting isolated neutron stars.
 Physics , 2002, Abstract: A possible mechanism for screening of the surface magnetic field of an accreting neutron star, by the accreted material, is investigated. In particular, we investigate the nature of the evolution of the internal field configuration in the case of a) a polar cap accretion and b) a spherical accretion.
 Physics , 2012, DOI: 10.1103/PhysRevD.86.044004 Abstract: Differential rotation induced by the r-mode instability can generate very strong toroidal fields in the core of accreting, millisecond spinning neutron stars. We introduce explicitly the magnetic damping term in the evolution equations of the r-modes and solve them numerically in the Newtonian limit, to follow the development and growth of the internal magnetic field. We show that the strength of the latter can reach large values, $B \sim 10^{14}$ G, in the core of the fastest accreting neutron stars. This is strong enough to induce a significant quadrupole moment of the neutron star mass distribution, corresponding to an ellipticity $|\epsilon_B}| \sim 10^{-8}$. If the symmetry axis of the induced magnetic field is not aligned with the spin axis, the neutron star radiates gravitational waves. We suggest that this mechanism may explain the upper limit of the spin frequencies observed in accreting neutron stars in Low Mass X-Ray Binaries. We discuss the relevance of our results for the search of gravitational waves.
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