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1.
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.  相似文献   

2.
We discuss the nature of the various modes of pulsation of superfluid neutron stars using comparatively simple Newtonian models and the Cowling approximation. The matter in these stars is described in terms of a two-fluid model, where one fluid is the neutron superfluid, which is believed to exist in the core and inner crust of mature neutron stars, and the other fluid represents a conglomerate of all other constituents (crust nuclei, protons, electrons, etc.). In our model, we incorporate the non-dissipative interaction known as the entrainment effect, whereby the momentum of one constituent (e.g. the neutrons) carries along part of the mass of the other constituent. We show that there is no independent set of pulsating g-modes in a non-rotating superfluid neutron star core, even though the linearized superfluid equations contain a well-defined (and real-valued) analogue to the so-called Brunt–Väisälä frequency. Instead, what we find are two sets of spheroidal perturbations whose nature is predominately acoustic. In addition, an analysis of the zero-frequency subspace (i.e. the space of time-independent perturbations) reveals two sets of degenerate spheroidal perturbations, which we interpret to be the missing g-modes, and two sets of toroidal perturbations. We anticipate that the degeneracy of all these zero-frequency modes will be broken by the Coriolis force in the case of rotating stars. To illustrate this we consider the toroidal pulsation modes of a slowly rotating superfluid star. This analysis shows that the superfluid equations support a new class of r-modes, in addition to those familiar from, for example, geophysical fluid dynamics. Finally, the role of the entrainment effect on the superfluid mode frequencies is shown explicitly via solutions to dispersion relations that follow from a 'local' analysis of the linearized superfluid equations.  相似文献   

3.
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.  相似文献   

4.
Using time evolutions of the relevant linearized equations, we study non-axisymmetric oscillations of rapidly rotating and superfluid neutron stars. We consider perturbations of Newtonian axisymmetric background configurations and account for the presence of superfluid components via the standard two-fluid model. Within the Cowling approximation, we are able to carry out evolutions for uniformly rotating stars up to the mass-shedding limit. This leads to the first detailed analysis of superfluid neutron star oscillations in the fast rotation regime, where the star is significantly deformed by the centrifugal force. For simplicity, we focus on background models where the two fluids (superfluid neutrons and protons) corotate, are in β-equilibrium and co-exist throughout the volume of the star. We construct sequences of rotating stars for two analytical model equations of state. These models represent relatively simple generalizations of single fluid, polytropic stars. We study the effects of entrainment, rotation and symmetry energy on non-radial oscillations of these models. Our results show that entrainment and symmetry energy can have a significant effect on the rotational splitting of non-axisymmetric modes. In particular, the symmetry energy modifies the inertial mode frequencies considerably in the regime of fast rotation.  相似文献   

5.
Just as a rotating magnetized neutron star has material pulled away from its surface to populate a magnetosphere, a similar process can occur as a result of neutron-star pulsations rather than rotation. This is of interest in connection with the overall study of neutron star oscillation modes but with a particular focus on the situation for magnetars. Following a previous Newtonian analysis of the production of a force-free magnetosphere in this way Timokhin et al., we present here a corresponding general-relativistic analysis. We give a derivation of the general relativistic Maxwell equations for small-amplitude arbitrary oscillations of a non-rotating neutron star with a generic magnetic field and show that these can be solved analytically under the assumption of low current density in the magnetosphere. We apply our formalism to toroidal oscillations of a neutron star with a dipole magnetic field and find that the low current density approximation is valid for at least half of the oscillation modes, similarly to the Newtonian case. Using an improved formula for the determination of the last closed field line, we calculate the energy losses resulting from toroidal stellar oscillations for all of the modes for which the size of the polar cap is small. We find that general relativistic effects lead to shrinking of the size of the polar cap and an increase in the energy density of the outflowing plasma. These effects act in opposite directions but the net result is that the energy loss from the neutron star is significantly smaller than suggested by the Newtonian treatment.  相似文献   

6.
The gravitational radiation from millisecond pulsars owing to glitches in their angular velocity is examined. It is assumed that the energy transferred from interior superfluid regions to the crust of a neutron star is converted into gravitational wave energy by damping oscillations of the matter in the star. The gravitational wave intensity and amplitude are calculated for fourteen millisecond pulsars. Gravitational radiation can explain the observed spin-down of millisecond pulsars and an estimate is given for the magnetic field at which the proposed mechanism predominates in the spin-down of these pulsars. __________ Translated from Astrofizika, Vol. 51, No. 3, pp. 479–486 (August 2008).  相似文献   

7.
We study the effect of the magnetic field geometry on the oscillation spectra of strongly magnetized stars. We construct a configuration of magnetic field where a toroidal component is added to the standard poloidal one. We consider a star with a type I superconductor core so that both components of the magnetic field are expelled from the core and confined in the crust. Our results show that the toroidal contribution does not influence significantly the torsional oscillations of the crust. On the contrary, the confinement of the magnetic field in the crust drastically affects the torsional oscillation spectrum. A comparison with estimations for the magnetic field strength, from observations, excludes the possibility that magnetars will have a magnetic field solely confined in the crust, that is, our results suggest that the magnetic field in whatever geometry has to permeate the whole star.  相似文献   

8.
The presence of a magnetic field in a neutron star interior results in a dynamical coupling between the fluid core and the elastic crust. We consider a simple toy-model where this coupling is taken into account and compute the system’s mode oscillations. Our results suggest that the notion of pure torsional crust modes is not useful for the coupled system, instead all modes excite Alfvén waves in the core. However, we also show that among a rich spectrum of global MHD modes the ones most likely to be excited by a fractured crust are those for which the crust and the core oscillate in concert. For our simple model, the frequencies of these modes are similar to the “pure crustal” frequencies. We advocate the significant implications of these results for the attempted theoretical interpretation of QPOs during magnetar flares in terms of neutron star oscillations.   相似文献   

9.
Minimal models of cooling neutron stars with accreted envelopes   总被引：1，自引：0，他引：1  
We study the 'minimal' cooling scenario of superfluid neutron stars with nucleon cores, where the direct Urca process is forbidden and enhanced cooling is produced by neutrino emission due to the Cooper pairing of neutrons. Extending our recent previous work, we include the effects of surface accreted envelopes of light elements. We employ the phenomenological density-dependent critical temperatures   T cp(ρ)  and   T cnt(ρ)  of singlet-state proton and triplet-state neutron pairing in a stellar core, as well as the critical temperature   T cns(ρ)  of singlet-state neutron pairing in a stellar crust. We show that the presence of accreted envelopes simplifies the interpretation of observations of thermal radiation from isolated neutron stars in the scenario of our recent previous work and widens the class of models for nucleon superfluidity in neutron star interiors consistent with the observations.  相似文献   

10.
Strong magnetic fields in relativistic stars can be a cause of crust fracturing, resulting in the excitation of global torsional oscillations. Such oscillations could become observable in gravitational waves or in high-energy radiation, thus becoming a tool for probing the equation of state of relativistic stars. As the eigenfrequency of torsional oscillation modes is affected by the presence of a strong magnetic field, we study torsional modes in magnetized relativistic stars. We derive the linearized perturbation equations that govern torsional oscillations coupled to the oscillations of a magnetic field, when variations in the metric are neglected (Cowling approximation). The oscillations are described by a single two-dimensional wave equation, which can be solved as a boundary-value problem to obtain eigenfrequencies. We find that, in the non-magnetized case, typical oscillation periods of the fundamental     torsional modes can be nearly a factor of 2 larger for relativistic stars than previously computed in the Newtonian limit. For magnetized stars, we show that the influence of the magnetic field is highly dependent on the assumed magnetic field configuration, and simple estimates obtained previously in the literature cannot be used for identifying normal modes observationally.  相似文献   

11.
We present a model of a freely precessing neutron star, which is then compared against pulsar observations. The aim is to draw conclusions regarding the structure of the star, and to test theoretical ideas of crust–core coupling and superfluidity. We argue that, on theoretical grounds, it is likely that the core neutron superfluid does not participate in the free precession of the crust. We apply our model to the handful of proposed observations of free precession that have appeared in the literature. Assuming crust-only precession, we find that all but one of the observations are consistent with there being no pinned crustal superfluid at all; the maximum amount of pinned superfluid consistent with the observations is about 10−10 of the total stellar moment of inertia. However, the observations do not rule out the possibility that the crust and neutron superfluid core precess as a single unit. In this case the maximum amount of pinned superfluid consistent with the observations is about 10−8 of the total stellar moment of inertia. Both of these values are many orders of magnitude less than the 10−2 value predicted by many theories of pulsar glitches. We conclude that superfluid pinning, at least as it affects free precession, needs to be reconsidered.  相似文献   

12.
It is shown how to set up a mathematically elegant and fully relativistic superfluid model that can provide a realistic approximation (neglecting small anisotropies due to crust solidity, magnetic fields, etc., but allowing for the regions with vortex pinning) of the global structure of a rotating neutron star, in terms of just two independently moving constituents. One of these represents the differentially rotating neutron superfluid, while the other part represents the combination of all the other ingredients, including the degenerate electrons, the superfluid protons in the core, and the ions in the crust, the electromagnetic interactions of which will tend to keep them locked together in a state of approximately rigid rotation. Order of magnitude estimates are provided for relevant parameters such as the resistive drag coefficient.  相似文献   

13.
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.  相似文献   

14.
Formation enthalpies are calculated for a number of point-defect structures in solid neutron star matter at densities above the neutron-drip threshold. The enthalpies obtained show that an amorphous heterogeneous solid phase is formed at temperatures in a glass transition region, and is likely to persist as the star cools. Its structural differences from the homogeneous body-centred cubic lattice previously assumed make it necessary to reconsider predictions of neutron-star magnetic field evolution, and severely limit the role of conventional superfluid neutron vortex pinning in the interpretation of pulsar glitch phenomena.  相似文献   

15.
There is a 3P2 neutron superfluid region in NS (neutron star) interior. For a rotating NS the 3P2 superfluid region is like a system of rotating magnetic dipoles. It will give out electromagnetic radiation, which may provide a new heating mechanism of NSs. This mechanism plus some cooling agent may give a sound explanation to NS glitches.  相似文献   

16.
A recent laboratory experiment suggests that a Kelvin–Helmholtz (KH) instability at the interface between two superfluids – one rotating and anisotropic, the other stationary and isotropic – may trigger sudden spin-up of the stationary superfluid. This result suggests that a KH instability at the crust–core (  1 S0–3 P2  –superfluid) boundary of a neutron star may provide a trigger mechanism for pulsar glitches. We calculate the dispersion relation of the KH instability involving two different superfluids including the normal fluid components and their effects on stability, particularly entropy transport. We show that an entropy difference between the core and crust superfluids reduces the threshold differential shear velocity and threshold crust–core density ratio. We evaluate the wavelength of maximum growth of the instability for neutron star parameters and find the resultant circulation transfer to be within the range observed in pulsar glitches.  相似文献   

17.
We find numerical solutions of the coupled system of Einstein–Maxwell equations with a linear approach, in which the magnetic field acts as a perturbation of a spherical neutron star. In our study, magnetic fields having both poloidal and toroidal components are considered, and higher order multipoles are also included. We evaluate the deformations induced by different field configurations, paying special attention to those for which the star has a prolate shape. We also explore the dependence of the stellar deformation on the particular choice of the equation of state and on the mass of the star. Our results show that, for neutron stars with mass   M = 1.4 M⊙  and surface magnetic fields of the order of 1015 G, a quadrupole ellipticity of the order of 10−6 to 10−5 should be expected. Low-mass neutron stars are in principle subject to larger deformations (quadrupole ellipticities up to 10−3 in the most extreme case). The effect of quadrupolar magnetic fields is comparable to that of dipolar components. A magnetic field permeating the whole star is normally needed to obtain negative quadrupole ellipticities, while fields confined to the crust typically produce positive quadrupole ellipticities.  相似文献   

18.
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.  相似文献   

19.
We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l , the fundamental mode (without radial nodes) has a frequency of ∼300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies ≳20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (having approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.  相似文献   

20.
The internal properties of the neutron star crust can be probed by observing the epoch of thermal relaxation. After the supernova explosion, powerful neutrino emission quickly cools the stellar core, while the crust stays hot. The cooling wave then propagates through the crust, as a result of its finite thermal conductivity. When the cooling wave reaches the surface (age 10–100 yr) , the effective temperature drops sharply from 250 eV to 30 or 100 eV, depending on the cooling model. The crust relaxation time is sensitive to the (poorly known) microscopic properties of matter of subnuclear density, such as the heat capacity, thermal conductivity, and superfluidity of free neutrons. We calculate the cooling models with the new values of the electron thermal conductivity in the inner crust, based on a realistic treatment of the shapes of atomic nuclei. Superfluid effects may shorten the relaxation time by a factor of 4. The comparison of theoretical cooling curves with observations provides a potentially powerful method of studying the properties of the neutron superfluid and highly unusual atomic nuclei in the inner crust.  相似文献   

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