Vortex–interface interactions and generation of glitches in pulsars

We show that the crust–core interface in neutron stars acts as a potential barrier to the peripheral neutron vortices approaching the interface in the model in which these are coupled to the proton vortex clusters. This elementary barrier arises because of the interaction of vortex magnetic flux with the Meissner currents set up by the crustal magnetic field at the interface. The dominant part of the force is derived from the cluster–interface interaction. As a result of the stopping of the continuous neutron vortex current through the interface, angular momentum is stored in the superfluid layers in the vicinity of the crust–core interface during the interglitch period. Discontinuous annihilation of proton vortices at the boundary restores the neutron vortex current and spins up the observable crust on short time-scales, leading to a glitch in the spin characteristics of a pulsar.     

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.     

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 for the evolution in a close binary system, in which the neutron star passes through four evolutionary phases ('isolated pulsar'–'propeller'– accretion from the wind of a companion – accretion resulting from Roche-lobe overflow). Calculations have been performed for a great variety of parameters characterizing the properties of both the neutron star and the low-mass companion. We find that neutron stars with more or less standard magnetic field and spin period that are 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 10¹⁰ yr, the neutron star can maintain a relatively strong magnetic field to the end of the accretion phase. The model that is considered can account well for the origin of millisecond pulsars.     

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.     

Nuclear physics of reverse electron flow at pulsar polar caps

Protons produced in electromagnetic showers formed by the reverse electron flux are usually the largest component of the time-averaged polar cap open magnetic flux line current in neutron stars with positive corotational charge density. Although the electric field boundary conditions in the corotating frame are time independent, instabilities on both medium and short time-scales cause the current to alternate between states in which either protons or positrons and ions form the major component. These properties are briefly discussed in relation to nulling and microstructure in radio pulsars, pair production in an outer gap and neutron stars with high surface temperatures.     

Evolution of neutron stars in high-mass X-ray binaries

We consider the evolution of neutron stars during the X-ray phase of high-mass binaries. Calculations are performed assuming a crustal origin of the magnetic field. A strong wind from the companion can significantly influence the magnetic and spin behaviour of a neutron star even during the main-sequence life of the companion. In the course of evolution, the neutron star passes through four evolutionary phases ('isolated pulsar', propeller, wind accretion, and Roche lobe overflow). The model considered can naturally account for the observed magnetic fields and spin periods of neutron stars, as well as the existence of pulsating and non-pulsating X-ray sources in high-mass binaries. Calculations also predict the existence of a particular sort of high-mass binary with a secondary that fills its Roche lobe and a neutron star that does not accrete the overflowing matter because of fast spin.     

The effect of the neutron-star crust on the evolution of a core magnetic field

We consider the expulsion of the magnetic field from the super-conducting core of a neutron star and its subsequent decay in the crust. Particular attention is paid to a strong feedback of the distortion of magnetic field lines in the crust on the expulsion of the flux from the core. This causes a considerable delay in the core flux expulsion if the initial field strength is larger than 10¹¹ G. It is shown that the hypothesis on the magnetic field expulsion induced by the neutron-star spin-down is adequate only for a relatively weak initial magnetic field B ≈10¹¹ G. The expulsion time-scale depends not only on the conductivity of the crust, but also on the initial magnetic field strength itself. Our model of the field evolution naturally explains the existence of the residual magnetic field of neutron stars. Its strength is correlated with the impurity concentration in neutron-star crusts and anticorrelated with the initial field strengths.     

Evolution of neutron star magnetic fields

This paper reviews the current status of the theoretical models of the evolution of the magnetic fields of neutron stars other than magnetars. It appears that the magnetic fields of neutron stars decay significantly only if they are in binary systems. Three major physical models for this, namely spindown-induced flux expulsion, ohmic evolution of crustal field and diamagnetic screening of the field by accreted plasma, are reviewed.     

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.     

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.     

Type I and two-gap superconductivity in neutron star magnetism

Neutron star inner cores with several charged baryonic components are likely to be analogues of the two-gap superconductor which is of current interest in condensed-matter physics. Consequently, type I superconductivity is less probable than type II but may nevertheless be present in some intervals of matter density. The intermediate-state structure formed at finite magnetic flux densities after the superconducting transitions is subject to buoyancy, frictional and neutron vortex interaction forces. These are estimated and it is shown that the most important frictional force is that produced by the stable stratification of neutron star matter, the irreversible process being diffusion in the normal, finite magnetic flux density, parts of the structure. The length-scale of the structure, in directions perpendicular to the local magnetic field is of crucial importance. For small scales, the flux comoves with the neutron vortices, as do the proton vortices of a type II superconductor. But for much larger length-scales, flux movement tends to that expected for normal charged Fermi systems.     

中子星的热演化和磁衰减

本文研究了中子星的热演化、自转演化和磁场演化的相互影响．考虑了一个自洽模型：中子星因磁偶极辐射而自转减慢，在内部产生某些加热过程，中子星磁场通过壳层的欧姆耗散来衰减．结果表明，磁场衰减提高了加热过程的重要性；相反，加热效应减慢了磁衰减．因此可以得出，中子星的热、自转和磁场也许不是独立演化的．不仅如此，这些演化与初始条件有关，因此，人们也许可以从射电和Ｘ射线观测对脉冲星年龄、初始磁场和周期给出某些限制．     

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.     

Can a slowly rotating neutron star be a radio pulsar?

It is shown that the radius of curvature of magnetic field lines in the polar region of a rotating magnetized neutron star can be significantly less than the usual radius of curvature of the dipole magnetic field. The magnetic field in the polar cap is distorted by toroidal electric currents flowing in the neutron star crust. These currents close up the magnetospheric currents driven by the electron–positron plasma generation process in the pulsar magnetosphere. Owing to the decrease in the radius of curvature, electron–positron plasma generation becomes possible even for slowly rotating neutron stars, with   PB ^−2/3₁₂ < 10 s  , where P is the period of star rotation and   B ₁₂= B /10¹² G  is the magnitude of the magnetic field on the star surface.     

Fermion zero-mode influence on neutron-star magnetic field evolution

The quantum phenomenon of spectral flow which has been observed in laboratory superfluids, such as ³He-B, controls the drift velocity of proton type II superconductor vortices in the liquid core of a neutron star and so determines the rate at which magnetic flux can be expelled from the core to the crust. In the earliest and most active phases of the anomalous X-ray pulsars and soft-gamma repeaters, the rates are low and consistent with a large fraction of the active crustal flux not linking the core. If normal neutrons are present in an appreciable core matter-density interval, the spectral flow force limits flux expulsion in cases of rapid spin-down, such as in the Crab pulsar or in the propeller phase of binary systems.     

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.     

Activation of the Blandford–Znajek mechanism in collapsing stars

The collapse of massive stars may result in the formation of accreting black holes in their interiors. The accreting stellar matter may advect substantial magnetic flux on to the black hole and promote the release of its rotational energy via magnetic stresses (the Blandford–Znajek mechanism). In this paper we explore whether this process can explain the stellar explosions and relativistic jets associated with long gamma-ray bursts. In particular, we show that the Blandford–Znajek mechanism is activated when the rest mass–energy density of matter drops below the energy density of the magnetic field in the near vicinity of the black hole (within its ergosphere). We also discuss whether such a strong magnetic field is in conflict with the rapid rotation of the stellar core required in the collapsar model, and suggest that the conflict can be avoided if the progenitor star is a component of a close binary. In this case the stellar rotation can be sustained via spin-orbital interaction. In an alternative scenario the magnetic field is generated in the accretion disc, but in this case the magnetic flux through the black hole ergosphere is not expected to be sufficiently high to explain the energetics of hypernovae by the BZ mechanism alone. However, this energy deficit can be recovered via the additional power provided by the disc.     

Model pulsar magnetospheres: the perpendicular rotator

The simplest model illustrating the effect of the magnetospheric charge-current field on the structure of a pulsar magnetic field has the region within the light-cylinder filled with the GoldreichJulian charge density which corotates with the neutron star, but has no electric currents along the magnetic field lines. This model has previously been studied for the axisymmetric case, with the rotation and magnetic dipolar axes aligned. The analogous problem is now solved with the two axes mutually perpendicular, so that not only the material current arising from the rotating charges but also the displacement current contributes. Again, the constructed magnetic field B ₀ crosses the light-cylinder normally, and there is no energy flux to infinity. However, in a more realistic model there is a flow of current along B ₀, generating a field B ₁ which has a non-vanishing toroidal component at the light-cylinder, so yielding a finite integrated Poynting flux.     

年轻脉冲星周期-磁场分类及演化

年轻脉冲星多处于超新星遗迹(Supernova Remnant, SNR)中, 其分为转动供能脉冲星(Rotation-powered SNR-PSR)、磁星(Magnetar)和中心致密天体(Central Compact Object, CCO), 这3类年轻脉冲星有着不同的自旋周期及磁场强度分布. % 其中, 遗迹磁星(SNR-Magnetar)的平均自旋周期比转动供能遗迹脉冲星大近一个量级, 平均磁场强度高近两个量级. % 同时, 中心致密天体比转动供能遗迹脉冲星的平均磁场强度低近两个量级. % 这3类年轻脉冲星不同的物理性质, 可能源于其不同的前身星或不同的超新星爆发过程, 也可能源于其中子星诞生后的不同演化过程. % 此外, 转动供能遗迹脉冲星比年轻的转动供能非遗迹脉冲星具有更快的平均自旋周期、更大的平均磁场强度和更短的平均特征年龄. % 这暗示新诞生的中子星经时间约为$10^5$--$10^6$yr的演化过程, 其自旋速度将减小近一半, 同时其磁场强度也将衰减近一半.     

A comment on the colour–colour diagrams of low-mass X-ray binaries

Disc-accreting neutron stars come in two distinct varieties, atolls and Z sources, named after their differently shaped tracks on a colour–colour diagram as the source luminosity changes. Here we present analysis of three transient atoll sources showing that there is an additional branch in the colour–colour diagram of atoll sources which appears at very low luminosities. This new branch connects to the top of previously known C-shaped (atoll) path, forming a horizontal track where the average source flux decrease from right to left. This turns the C-shape into a Z. Thus both atolls and Z sources share the same topology on the colour–colour diagram and evolve in similar way, as a function of increasing averaged mass accretion rate. This strongly favours models in which the underlying geometry of these sources changes in similar ways. A possible scenario is one where the truncated disc approaches the neutron star when the accretion rate increases, but in the atolls the disc is truncated by evaporation (similarly to black holes), and in the Z sources it is truncated by the magnetic field.