Model neutron stars with a constant scalar field in the bimetric scalar-tensor theory of gravitation. Different versions of the equation of state

In our preceding paper we found solutions for the equations of the bimetric scalar—tensor theory of gravitation for neutron stars, in which the scalar field is constant while the metric tensor satisfies the equations of the general theory of relativity. In the present paper we find analogous solutions for different versions of the equation of state of the matter of a neutron star. Translated from Astrofizika, Vol. 41, No. 2, pp. 297–301. April-June, 1998.     

Pulsar radio luminosities and the magnetic moments of neutron stars

Using equations from the theory of pulsar radio emission, the radio luminosities of pulsars and the magnetic moments of neutron stars are calculated from existing observational data. Translated from Astrofizika, Vol. 42, No. 3, pp. 433–437, July–September, 1999.     

Universality in quasi-normal modes of neutron stars

We study universality in gravitational waves emitted from non-rotating neutron stars characterized by different equations of state (EOSs). We find that the quasi-normal mode frequencies of such waves, including the w -modes and the f -mode, display similar universal scaling behaviours that hold for most EOSs. Such behaviours are shown to stem from the mathematical structure of the axial and the polar gravitational wave equations, and the fact that the mass distribution function can be approximated by a cubic–quintic polynomial in the radius. As a benchmark for other realistic neutron stars, a simple model of neutron stars is adopted here to reproduce the pulsation frequencies and the generic scaling behaviours mentioned above with good accuracy.     

Neutron Stars With a Quark Core

Models of neutron stars with a quark core are calculated on the basis of an extensive set of equations of state for superdense matter. The possible existence of a new branch of stable layered neutron stars is revealed for some realistic equations of state of neutron matter.     

Relaxation of the Vela pulsar’s angular velocity following its jumps

The dynamics of the vortex lattice in the inner crust of a neutron star is considered. A general equation of motion is obtained and solved under the assumption that there are regions of pinned and of free vortices. By comparing these solutions with observational data for the Vela pulsar, the relative moments of inertia of regions of relaxation with the corresponding characteristic times are calculated for two model stars with different equations of state. It is shown that the theory can be reconciled with observations of the relaxation of pulsar angular velocity only for model stars with extremely stiff equations of state. Translated from Astrofizika, Vol. 40, No. 1, pp. 67–76, January–March, 1997.     

Statified model of a neutron star

Evolutionary calculations based on realistic equations of state indicate the stratified nature of the distribution of hadron matter in the interiors of neutron stars. In the proposed model, the stratified structure of a neutron star is treated as a rigid inert core surrounded by a dynamical layer. The physical basis for the model is the concept of the stellar matter of the peripheral envelope as an elastic Fermi continuum, the motions of which are described by the equations of nuclear elastodynamics, proposed in the macroscopic theory of collective processes in laboratory nuclear physics. It is shown that the vibrational dynamics of a neutron star is characterized by two branches of gravitational—elastic, spheroidal (s-mode) and torsional (t-mode) nonradial eigenvibrations. Estimates obtained for the periods of global, gravitational nonradial modes suggest that variations in the intensity of micropulses observed in the millisecond range of the spectra of C-pulsars may be ascribed to these vibrations. The proposed two-component model of a neutron star enables one to consider a glitch in a pulsar’s radio emission as a starquake due to the passage of the companion through periastron of the binary system. Translated from Astrofizika, Vol. 42, No. 2, pp. 235–252, April–June, 1999     

A numerical study of the r-mode instability of rapidly rotating nascent neutron stars

The first results of numerical analysis of classical r-modes of rapidly rotating compressible stellar models are reported. The full set of linear perturbation equations of rotating stars in Newtonian gravity is solved numerically without the slow rotation approximation. A critical curve of gravitational wave emission induced instability, which restricts the rotational frequencies of hot young neutron stars, is obtained. Taking the standard cooling mechanisms of neutron stars into account, we also show the 'evolutionary curves' along which neutron stars are supposed to evolve as cooling and spinning down proceed. Rotational frequencies of 1.4-M_⊙ stars suffering from this instability decrease to around 100 Hz when the standard cooling mechanism of neutron stars is employed. This result confirms the results of other authors, who adopted the slow rotation approximation.     

Rotating superdense configurations: pulsars and their astrophysical manifestations

This paper is a discussion of some results from papers by followers of V. A. Ambartsumyan, whose fundamental articles serve as the beginning of research on superdense stars: white dwarfs and neutron stars. Solutions of the Einstein equations are given for the case of axial symmetry and are used to determine the integral parameters of rotating neutron stars and white dwarfs. A theory of magnetic field generation in neutron stars has been developed and is consistent with the existence of high, nonuniform magnetic fields on the order of 10¹⁴ G in pulsars. A theory has been proposed for the dynamics of neutron vortices and used to explain the observed relaxation of the angular velocity of pulsars following glitches.     

Disk luminosity and angular momentum for accreting,weak field neutron stars in the ‘Slow’ rotation approximation

For accretion on to neutron stars possessing weak surface magnetic fields and substantial rotation rates (corresponding to the secular instability limit), we calculate the disk and surface layer luminosities general relativistically using the Hartle & Thorne formalism, and illustrate these quantities for a set of representative neutron star equations of state. We also discuss the related problem of the angular momentum evolution of such neutron stars and give a quantitative estimate for this accretion driven change in angular momentum. Rotation always increases the disk luminosity and reduces the rate of angular momentum evolution. These effects have relevance for observations of low-mass X-ray binaries.     

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.     

Radio-Loud and Radio-Quiet Gamma-Ray Pulsars from the Galaxy and the Gould Belt

We present results of a population synthesis study of radio-loud and radio-quiet γ-ray pulsars from the Galactic plane and the Gould Belt. The simulation includes the Parkes multibeam pulsar survey, realistic beam geometries for radio and γ-ray emission from neutron stars and the new electron density model of Cordes and Lazio. Normalizing to the number of radio pulsars observed by a set of nine radio surveys, the simulation suggests a neutron star birth rate of 1.4 neutron stars per century in the Galactic plane. In addition, the simulation predicts 19 radio-loud and 7 radio-quiet γ-ray pulsars from the plane that EGRET should have observed as point sources. Assuming that during the last 5 Myr the Gould Belt produced 100 neutron stars, only 10 of these would be observed as radio pulsars with three radio-loud and four radio-quiet γ-ray pulsars observed by EGRET. These results are in general agreement with the recent number of about 25 EGRET error boxes that contain Parkes radio pulsars. Since the Gould Belt pulsars are relatively close by, the selection of EGRET radio-quiet γ-ray pulsars strongly favors large impact angles, β, in the viewing geometry where the off-beam emission from curvature radiation provides the γ-ray flux. Therefore, the simulated EGRET radio-quiet γ-ray pulsars, being young and nearby, most closely reflect the current shape of the Gould Belt suggesting that such sources may significantly contribute to the EGRET unidentified γ-ray sources correlated with the Gould Belt.     

Evolution of massive binary stars in the LMC and its implications for radio pulsar population

The Hertzsprung-Russell diagram of the Large Magellanic Cloud compiled recently by Fitzpatrick & Garmany (1990) shows that there are a number of supergiant stars immediately redward of the main sequence although theoretical models of massive stars with normal hydrogen abundance predict that the region 4.5 ≤ logT _eff ≤ 4.3 should be un-populated (“gap”). Supergiants having surface enrichment of helium acquired for example from a previous phase of accretion from a binary companion, however, evolve in a way so that the evolved models and observed data are consistent — an observation first made by Tuchman & Wheeler (1990). We compare the available optical data on OB supergiants with computed evolutionary tracks of massive stars of metallicity relevant to the LMC with and without helium-enriched envelopes and conclude that a large fraction (≈ 60 per cent) of supergiant stars may occur in binaries. As these less evolved binaries will later evolve into massive X-ray binaries, the observed number and orbital period distribution of the latter can constrain the evolutionary scenarios of the supergiant binaries. The distributions of post main sequence binaries and closely related systems like WR + O stars are bimodal-consisting of close and wide binaries in which the latter type is numerically dominating. When the primary star explodes as a supernova leaving behind a neutron star, the system receives a kick and in some cases can lead to runaway O-stars. We calculate the expected space velocity distribution for these systems. After the second supernova explosion, the binaries in most cases, will be disrupted leading to two runaway neutron stars. In between the two explosions, the first born neutron star’s spin evolution will be affected by accretion of mass from the companion star. We determine the steady-state spin and radio luminosity distributions of single pulsars born from the massive stars under some simple assumptions. Due to their great distance, only the brightest radio pulsars may be detected in a flux-limited survey of the LMC. A small but significant number of observable single radio pulsars arising out of the disrupted massive binaries may appear in the short spin period range. Most pulsars will have a low velocity of ejection and therefore may cluster around the OB associations in the LMC.     

Low-Mass Quark Stars

More and more observational hints of quark stars are proposed these years though pulsars are considered conventionally to be normal neutron stars. The existence of low-mass quark stars is a direct consequence of the possibility that pulsar-like stars are actually quark stars, because of the ability that quark matter can confine itself by color interaction. After a brief introduction to the study of quark stars, the various astrophysical implications of low-mass quark stars are investigated. It is addressed that some of the transient unidentified γ -ray sources are probably merging quark stars. The observability of low-mass quark stars is discussed.     

Magnetic field evolution in OBA stars

The applications of the spectral analysis methods discovered by Kirchhoff for the investigation of stellar magnetic fields are considered. The statistical properties of the mean magnetic fields for OBA stars have been investigated by analyzing data from two catalogs of magnetic fields. It is shown that the mean effective magnetic field ℬ of a star can be used as a statistically significant characteristic of its magnetic field. The magnetic field distribution functions F(ℬ) have been constructed for B-type and chemically peculiar (CP) stars, which exhibit a power-law dependence on ℬ. A sharp decrease in F(ℬ) in the range of weak magnetic fields has been found. The statistical properties of the magnetic fluxes for main-sequence stars, white dwarfs, and neutron stars are analyzed.     

Natural MHD oscillations of a neutron star

Natural, low-frequency, hydromagnetic oscillations of an isolated, nonrotating neutron star, which are localized in the peripheral crust, the structure of which is determined by the electron-nuclear plasma (the Ae phase), are studied. The plasma medium of the outer crust is treated as a homogeneous, infinitely conducting, incompressible continuum, the motions of which are determined by the equations of magnetohydrodynamics. In the approximation of a constant magnetic field inside the crust (the magnetic field outside the star is assumed to have a dipole structure), the spectrum of normal poloidal and toroidal hydromagnetic oscillations, due to presumed residual fluctuations of flow and their associated fluctuations in magnetic field strength, is calculated. Numerical estimates given for the periods of MHD oscillations fall in the range of periods of radio pulsar emission, indicating a close connection between the residual hydromagnetic oscillations and the electromagnetic activity of neutron stars. Translated from Astrofizika, Vol. 40, No. 1, pp. 77–86, January–March, 1997.     

Merging strangeon stars

The state of supranuclear matter in compact stars remains puzzling, and it is argued that pulsars could be strangeon stars. What would happen if binary strangeon stars merge? This kind of merger could result in the formation of a hyper-massive strangeon star, accompanied by bursts of gravitational waves and electromagnetic radiation(and even a strangeon kilonova explained in the paper). The tidal polarizability of binary strangeon stars is different from that of binary neutron stars, because a strangeon star is self-bound on the surface by the fundamental strong force while a neutron star by the gravity, and their equations of state are different. Our calculation shows that the tidal polarizability of merging binary strangeon stars is favored by GW170817. Three kinds of kilonovae(i.e., of neutron, quark and strangeon) are discussed, and the light curve of the kilonova AT 2017 gfo following GW170817 could be explained by considering the decaying strangeon nuggets and remnant star spin-down. Additionally,the energy ejected to the fireball around the nascent remnant strangeon star, being manifested as a gamma-ray burst, is calculated. It is found that, after a prompt burst, an X-ray plateau could follow in a timescale of 10~2-10~3 s. Certainly, the results could be tested also by further observational synergies between gravitational wave detectors(e.g., Advanced LIGO) and X-ray telescopes(e.g., the Chinese HXMT satellite and e XTP mission), and especially if the detected gravitational wave form is checked by peculiar equations of state provided by the numerical relativistical simulation.     

Accretion by isolated neutron stars

Accretion of interstellar material by an isolated neutron star is discussed. The point I address here is the interaction between the accretion flow and the stellar magnetosphere. I show that the interchange instabilities of the magnetospheric boundary under the conditions of interest are basically suppressed. The entry of the material into the magnetosphere is governed by diffusion. Due to this reason the persistent accretion luminosity of isolated neutron stars is limited to <4×10²⁶ erg s⁻¹. These objects can also appear as X-ray bursters with the burst durations of ∼30 min and repetition time of ∼10⁵ yr. This indicates that the number of the accreting isolated neutron stars which could be observed with recent and modern X-ray missions is a few orders of magnitude smaller than that previously estimated.      

Massive compact dwarf stars and C-field

The effect of C-field in high density matter has been studied. We find that the negative energy and negative pressure of the C-field helps in formation of massive compact stable neutron stars of mass ∼ 0.5 solar mass which is in the range of 0.01 to 1.0 solar mass of recently observed dwarf stars.     

The Crust Properties and Cooling of Strange Stars

We investigate the influence of the following parameters on the crust properties of strange stars: the strange quark mass (m _s), the strong coupling constant (α_c) and the vacuum energy density (B). It is found that the mass density at the crust base of strange stars cannot reach the neutron drip density. For a conventional parameter set of m _s=200 MeV, B ^1/4 = 145 MeV and α_c = 0.3, the maximum density at the crust base of a typical strange star is only 5.5 × 10¹⁰ gcm^-3, and correspondingly the maximum crust mass is 1.4 ×10^-6 M_⊙. Subsequently, we present the thermal structure and the cooling behavior of strange stars with crusts of different thickness, and under different diquark pairing gaps. Our work might provide important clues for distinguishing strange stars from neutron stars.     

Oscillations of rapidly rotating superfluid stars

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.