Hydrogen molecular ion in the magnetic field of a neutron star

A two-dimensional potential energy surface of an H ₂ ⁺ molecular ion is calculated for the case of the strong magnetic field of the neutron starB=10¹¹–10¹³ G. It is shown that the dependence of the potential energy from the angle between the magnetic field direction and the internuclear axis becomes very sharp as the magnetic field increases. The obtained potential energy surfaces can be used for studying the vibrational-rotational structure of the H ₂ ⁺ spectrum in a strong magnetic field and the development of the observational methods for the determination of the magnetic field of a neutron star.     

Hydrogen molecular ion in the magnetic field of a neutron star

The paper discusses the structure and energies of rotational-vibrational levels of a molecular ion H ₂ ⁺ in a strong magnetic field typical of neutron stars,B=10¹²–10¹³ G. The study is based on the calculations of the potential energy surface of this molecular ion presented in the paper by Khersonskii (1984a). The energies of the rovibrational levels are calculated with the aid of the perturbation theory. The number of levels in a H ₂ ⁺ potential hole is determined at different magnetic intensities. In particular, it is ascertained that the number of levels decreases as the strength of the magnetic field increases. The effect of nuclear spins on the structure of the rotational levels is considered.     

Gravitational radiation of a differentially rotating superfluid neutron star

The gravitational radiation of a neutron star with a weakly coupled superfluid component is considered. It is assumed that regions can exist in the star's core which rotate at substantially higher angular velocities than the observed angular velocities of pulsars. A star of this sort has a quadrupole moment on the order of the maximum value for the neutron star configurations that have been discussed, so it could be a powerful source of gravitational radiation for the planned Advanced LIGO detector. Translated from Astrofizika, Vol. 51, No. 4, pp. 647–652 (November 2008).     

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.     

Relaxation time of the superfluid core of a neutron star

The superconducting proton condensate in the “npe” phase of a neutron star is considered. It is shown to be a type II superconductor in the outer layer of the “npe” phase and a type I superconductor in the inner layer. Relaxation times are found for elastic scattering of normal relativistic electrons from the magnetic fields of proton vortex clusters in the case of a type II superconductor and elastic scattering from the magnetic field at the center of a neutron vortex in the case of a superconductor of the first kind. The dynamical relaxation times obtained for the angular velocity of the pulsar PSR 0833—45 vary, as a function of the density of the layers taking part in the relaxation process, within a fairly wide range: from several hours to l0⁹ years. This means that the characteristic times of variation of pulsar angular velocity may be observed to lie in the indicated time range. Translated from Astrofizika, Vol. 40, No. 4, op. 497–506, October–December, 1997.     

On the dynamics of superfluid neutron star cores

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.     

Electrical conductivity of neutron star cores in the presence of a magnetic field

General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities ₀, where ₀ = 2.8×10¹⁴ g cm^–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of ^–-hyperons at > _c , where _c 4₀. The electric resistivities along and acrossB, and , and the Hall resistivity _H are calculated and fitted by simple analytical formulae at _c and > _c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If _c , one has = [1 + (B/B ₀)²] for the normal neutrons, and for the superfluid neutrons, while _H = B/B _e for both cases. HereB _e 10⁹ T ₈ ² G,B ₀10¹¹ T ₈ ² G, andT ₈ is temperature in units of 10⁸ K. Accordingly for the normal neutrons atBB ₀, the transverse resistivity suffers an enhancement, _{1/4 1}. When 5₀ andB varies from 0 toBB _p 10¹³ T ₈ ² G, increases by a factor of about 10³–10⁴ and _H changes sign. WhenBB _p , remains constant for the superfluid neutrons, and _H B ² for the normal neutrons, while _H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.     

Toroidal magnetic field in pulsars

The differential rotation of plasma in the core of pulsars (Ω_s ≠ Ω_e) generates convective currents increasing with time which in turn generates the toroidal magnetic field. To avoid difficulties of physical interpretation inherent to the theory of general relativity we have adopted the tetrad approach to discuss the generation of the magnetic field in the core of the neutron stars. The results which we have obtained are in agreement with those obtained earlier. Published in Astrofizika, Vol. 49, No. 4, pp. 613–620 (August 2006).     

On the electron cap shape of a rotating neutron star with a strong magnetic field

Numerical calculations of the electron cap shape of a rapidly rotating neutron star with a strong magnetic field have been provided. It is supposed that the magnetic dipole axis is aligned, and ejection of positive charged particles from the star's surface absent. The total charge of the star has been calculated. Estimation of the character of charged-particle motion in the electromagnetic field of the star has been obtained. It is shown that two streams of charged particles escape from the star surface. The electron stream moves along the magnetic axis. The electron stream is enveloped by proton-positron stream, which is generated by returning hard electrons accelerated by electromagnetic field of the star.     

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.     

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.     

Spin-driven changes in neutron star magnetic fields

Interactions among a neutron star’s superfluid neutrons, superconducting protons, and solid crust cause predictable spin-down and spin-up driven crustal motion and magnetic field changes. Applications and unsolved problems are discussed for millisecond pulsar evolution and properties, glitches and post-glitch responses, and transcient gamma-ray emission.     

The bottom magnetic field and magnetosphere evolution of neutron star in low-mass X-ray binary

The accretion-induced neutron star (NS) magnetic field evolution is studied through considering the accretion flow to drag the field lines aside and dilute the polar-field strength, and as a result the equatorial field strength increases, which is buried inside the crust on account of the accretion-induced global compression of star crust. The main conclusions of model are as follows: (i) the polar field decays with increase in the accreted mass; (ii) the bottom magnetic field strength of about 10⁸ G can occur when the NS magnetosphere radius approaches the star radius, and it depends on the accretion rate as     ; and (iii) the NS magnetosphere radius decreases with accretion until it reaches the star radius, and its evolution is little influenced by the initial field and the accretion rate after accreting  ∼0.01 M_⊙  , which implies that the magnetosphere radii of NSs in low-mass X-ray binaries would be homogeneous if they accreted the comparable masses. As an extension, the physical effects of the possible strong magnetic zone in the X-ray NSs and recycled pulsars are discussed. Moreover, the strong magnetic fields in the binary pulsars PSR 1831−00 and PSR 1718−19 after accreting about  0.5 M_⊙  in the binary-accretion phase,  8.7 × 10¹⁰  and  1.28 × 10¹² G  , respectively, can be explained through considering the incomplete frozen flow in the polar zone. As an expectation of the model, the existence of the low magnetic field  (∼3 × 10⁷ G)  NSs or millisecond pulsars is suggested.     

Dense matter in strong gravitational field of neutron star

Mass, radius and moment of inertia are direct probes of compositions and Equation of State (EoS) of dense matter in neutron star interior. These are computed for novel phases of dense matter involving hyperons and antikaon condensate and their observable consequences are discussed in this article. Furthermore, the relationship between moment of inertia and quadrupole moment is also explored.     

Magnetic field of a neutron star with a superconducting quark core in the CFL-phase

The Ginzburg-Landau equations are derived for the magnetic and gluomagnetic gauge fields in the color superconducting core of a neutron star containing a CFL-condensate of diquarks. The interaction of the diquark CFL-condensate with the magnetic and gluomagnetic gauge fields is taken into account. The behavior of the magnetic field in a neutron star is studied by solving the Ginzburg-Landau equations taking correct account of the boundary conditions, including the gluon confinement conditions. The magnetic field distribution in the quark and hadronic phases of a neutron star is found. It is shown that a magnetic field generated in the hadronic phase by the entrainment effect penetrates into the quark core in the form of quark vortex filaments because of the presence of screening Meissner currents. __________ Translated from Astrofizika, Vol. 50, No. 1, pp. 87–98 (February 2007).     

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons (E _F (e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: E _F (e) is related to density ρ, the mean electron number per baryon Y _e and magnetic field strength B.     

Kelvin–Helmholtz instability and circulation transfer at an isotropic–anisotropic superfluid interface in a neutron star

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.