The magnetosphere of oscillating neutron stars in general relativity

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.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – II. Solution of the induction equations

We have solved numerically the general relativistic induction equations in the interior background space–time of a slowly rotating magnetized neutron star. The analytic form of these equations was discussed recently (Paper I), where corrections due to both the space–time curvature and the dragging of reference frames were shown to be present. Through a number of calculations we have investigated the evolution of the magnetic field with different rates of stellar rotation, different inclination angles between the magnetic moment and the rotation axis, as well as different values of the electrical conductivity. All of these calculations have been performed for a constant-temperature relativistic polytropic star and make use of a consistent solution of the initial-value problem which avoids the use of artificial analytic functions. Our results show that there exist general relativistic effects introduced by the rotation of the space–time which tend to decrease the decay rate of the magnetic field. The rotation-induced corrections are however generally hidden by the high electrical conductivity of the neutron star matter, and when realistic values for the electrical conductivity are considered, these corrections become negligible even for the fastest known pulsar.     

Relativistic Correction of Neutrino Emission in Neutron Stars

By the relativistic mean field theory and relevant weak-interactional cooling theory, the relativistic cooling properties in the conventional and hyperonic neutron star matter are studied. Also a comparison between the relativistic and non-relativistic results after taking consideration of the gravity correction is performed. The results show that the relativistic effect of neutrino emission reduces the neutrino emissivity, luminosity, and the cooling rate of stellar objects, in comparison with the non-relativistic case. In the neutron star matter without hyperon, the amplitude of the cooling rate reduction caused by the relativistic effect is maximal after taking the gravity correction into consideration, it attains 56% for a 2 M_⊙ neutron star composed of conventional neutron star matter, and in the hyperonic matter the amplitude of reduction is minimal, about 38%.     

Magnetic Neutron Stars. I. Static Field Configurations

The paper is the first in a series dealing with the structure of magnetic and rotating neutron stars including general relativistic effects. The geometry of fossile magnetic fields frozen in the highly conductive neutron star matter in a non-rotating (or weakly rotating) star is studied. § 2 treats the general poloidal field in a vacuum outside the star. The geometry of magnetic fields within the star — whose matter is governed by a barytropic equation of state — is restricted by the condition that the magnetic force density should be curl-free to maintain equilibrium (§ 3). Numerical results are obtained for a poloidal and a toroidal dipole field (§ 4).     

Evolution of neutron star magnetic fields

During the evolution of the neutron star its magnetic field first decays exponentially with the time and then may becomes quasi-stationary. The non-decaying magnetic field of the neutron star is generated by a degenerate electron gas which is in the Landau orbital ferromagnetism (LOFER) state. Possibly, due to the neutron star transition into the LOFER state, magnetic fields remained sufficiently strong in the case of such old magnetic neutron stars as powerful X-ray sources (e.g., Her X-1), millisecond pulsars and the binary pulsar PSR 0655+64.     

Transport properties of the degenerate electron gas of neutron stars along the quantizing magnetic field

The expressions are derived for thermal and electric conductivities as well as thermopower of a degenerate relativistic electron gas in the surface layers of neutron stars along the magnetic fieldB=4×10¹¹–10¹⁴G for two scattering mechanisms of electrons, namely, for Coulomb scattering on ions in the ion-liquid regime and on high-temperature phonons in the solid regime. The results may be of use to study neutron star cooling rates, nuclear burning of the matter in the surface layers, diffusion of the magnetic field, etc.     

Impact of small bodies on to discs around compact objects — II. Interaction with the disc

We consider a system consisting of a neutron star surrounded by a disc of dense degenerate matter, and study the sequence of events following the impact of comets on to the disc. The direct signature of the impact event is a short burst of high-energy radiation (X-rays to UV, depending on the impact location) emitted from the bubble of hot gas created at the impact site. We assume that the bubble is confined by the magnetic field of the central neutron star. Part of the bubble matter may be channelled along magnetic field lines and rain down on the polar caps. The surface density at the neutron star surface may be sufficient to initiate a runaway thermonuclear reaction. These X-rays or the direct effect of the transferred plasma crossing charge-depleted regions in the outer magnetosphere may re-ignite an otherwise dead pulsar.     

The γ-ray burst phenomenon treated as the collapse of a QED magnetized vacuum bubble: analogy with sonoluminescence

We treat the phenomenon of a γ -ray burst as the non-linear collapse of a magnetic cavity surrounding a neutron star with extremely large magnetic field B ∼10¹⁵–10¹⁶ G due to the process of bubble shape instability in the resonant MHD field of an accreting plasma or on a neutron star surface. The QED effect of vacuum polarizability by a strong magnetic field is taken into a consideration. We develop an analogy with the phenomenon of sonoluminescence in which the gas bubble is located in a surrounding liquid with a driven sound intensity.     

A General Relativistic Calculation of Boundary Layer and Disc Luminosity for Accreting Non-magnetic Neutron Stars in Rapid Rotation

We calculate the disc and boundary layer luminosities for accreting rapidly rotating neutron stars with low magnetic fields in a fully general relativistic manner. Rotation increases the disc luminosity and decreases the boundary layer luminosity. A rapid rotation of the neutron star substantially modifies these quantities as compared with the static limit. For a neutron star rotating close to the centrifugal mass shed limit, the total luminosity has contribution only from the extended disc. For such maximal rotation rates, we find that well before the maximum stable gravitational mass configuration is reached, there exists a limiting central density, for which particles in the innermost stable orbit will be more tightly bound than those at the surface of the neutron star. We also calculate the angular velocity profiles of particles in Keplerian orbits around the rapidly rotating neutron star. The results are illustrated for a representative set of equation of state models of neutron star matter.     

A magnetically driven origin for the low luminosity GRB 170817A associated with GW170817

The gamma-ray burst GR170817 A associated with GW170817 is subluminous and subenergetic compared with other typical short gamma-ray bursts. It may be due to a relativistic jet viewed off-axis, or a structured jet or cocoon emission. Giant flares from magnetars may possibly be ruled out.However, the luminosity and energetics of GRB 170817 A are coincident with those of magnetar giant flares. After the coalescence of a binary neutron star, a hypermassive neutron star may be formed. The hypermassive neutron star may have a magnetar-strength magnetic field. During the collapse of this hypermassive neutron star, magnetic field energy will also be released. This giant-flare-like event may explain the luminosity and energetics of GRB 170817 A. Bursts with similar luminosity and energetics are expected in future neutron star-neutron star or neutron star-black hole mergers.     

强磁场下中子星外壳的组分和状态方程

本文计算和讨论了强磁场下由冷的催化物质组成的中子星外壳的组份和状态方程。文中考虑了晶格能和强磁场下均匀电子气体的交换能的贡献.得出结论:(1)强磁场使低密度区的状态方程变软;(2)强磁场对高密度区的状态方程几乎没有影响;(3)核质量公式对外壳的组份影响较明显.     

The Lifshitz-Kosevich-Shoenberg theory of relativistic electronic gas in neutron stars

Similar to the de Haas-van Alphen magnetic oscillatory in some normal metals when the Landau quantization is predominant, the magnetic oscillation can also occur in highly degenerate and relativistic electron gas in neutron stars. At large Landau quantum number (Landau quantum number r≥2), we generalize the Lifshitz-Kosevich-Shoenberg theory in non-relativistic electron gas to relativistic gas. At small Landau quantum number (r<2), we expand the grand potential into Fourier series and get similar harmonic oscillatory formula of magnetization. These results indicate that magnetic phase transition similar as Condon transition observed in metals can appear in neutron stars when the differential susceptibility exceeds 1/4π.     

A new approximation for the high magnetic field Compton cross-section

A midly relativistic quantum-mechanical treatment of the Compton scattering cross-section in a strong magnetic field regime appropriate to observed electron temperature and field strengths in a neutron star magnetosphere is provided. The approximations used in the evaluation of the electron propagator are different from those employed previously and lead finally to simpler and more usable expressions for the cross-section.Various conceptual difficulties with the quantum cyclotron line mechanism are also discussed and the problem of the translational invariance of the Hamiltonian commonly used is addressed.     

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.     

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.     

中子星的相对论平均场描述

从相对论平均场理沦出发,考虑核子、超子和介子的相互作用,研究了中子星的结构和性质以及超子耦合常数对中子星性质的影响.发现当密度较高时,中子星的核心区主要由超子组成,即中子星转变成以超子为主要成分的奇异中子星,并且这种转变受到超子相互作用的影响.当超子耦合常数与核子耦合常数的比值为0.65时,中子星转变为奇异中子星所对应的密度最小,此时计算的中子星的最大质量为1.4 M⊙,与天文观测结果较好符合.     

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.     

General relativistic electromagnetic fields of a slowly rotating magnetized neutron star – I. Formulation of the equations

We present analytic solutions of Maxwell equations in the internal and external background space–time of a slowly rotating magnetized neutron star. The star is considered isolated and in vacuum, with a dipolar magnetic field not aligned with the axis of rotation. With respect to a flat space–time solution, general relativity introduces corrections related both to the monopolar and the dipolar parts of the gravitational field. In particular, we show that in the case of infinite electrical conductivity general relativistic corrections resulting from the dragging of reference frames are present, but only in the expression for the electric field. In the case of finite electrical conductivity, however, corrections resulting from both the space–time curvature and the dragging of reference frames are shown to be present in the induction equation. These corrections could be relevant for the evolution of the magnetic fields of pulsars and magnetars. The solutions found, while obtained through some simplifying assumption, reflect a rather general physical configuration and could therefore be used in a variety of astrophysical situations.     

Two-fluid models of superfluid neutron star cores

Both relativistic and non-relativistic two-fluid models of neutron star cores are constructed, using the constrained variational formalism developed by Brandon Carter and co-workers. We consider a mixture of superfluid neutrons and superconducting protons at zero temperature, taking into account mutual entrainment effects. Leptons, which affect the interior composition of the neutron star and contribute to the pressure, are also included. We provide the analytic expression of the Lagrangian density of the system, the so-called master function, from which the dynamical equations can be obtained. All the microscopic parameters of the models are calculated consistently using the non-relativistic nuclear energy density functional theory. For comparison, we have also considered relativistic mean field models. The correspondence between relativistic and non-relativistic hydrodynamical models is discussed in the framework of the recently developed 4D covariant formalism of Newtonian multifluid hydrodynamics. We have shown that entrainment effects can be interpreted in terms of dynamical effective masses that are larger in the relativistic case than in the Newtonian case. With the nuclear models considered in this work, we have found that the neutron relativistic effective mass is even greater than the bare neutron mass in the liquid core of neutron stars.