Spontaneous magnetization of solid quark-cluster stars

Pulsar-like compact stars usually have strong magnetic fields, with strengths from ~10~8 to ~10~(12) G on the surface. How such strong magnetic fields can be generated and maintained is still an unsolved problem,which is, in principle, related to the interior structure of compact stars, i.e., the equation of state of cold matter at supra-nuclear density. In this paper we are trying to solve the problem in the regime of solid quark-cluster stars.Inside quark-cluster stars, the extremely low ratio of number density of electrons to that of baryons n_e /n_b and the screening effect from quark-clusters could reduce the long-range Coulomb interaction between electrons to short-range interaction. In this case, Stoner's model could apply, and we find that the condition for ferromagnetism is consistent with that for the validity of Stoner's model. Under the screened Coulomb repulsion, the electrons inside the stars could be spontaneously magnetized and become ferromagnetic, and hence would contribute non-zero net magnetic momentum to the whole star. We conclude that, for most cases in solid quark-cluster stars, the amount of net magnetic momentum, which is proportional to the amount of unbalanced spins ξ =(n_+- n_-)/ne and depends on the number density of electrons n_e =n_+ + n_-, could be significant with non-zero ξ. The net magnetic moments of electron system in solid quark-cluster stars could be large enough to induce the observed magnetic fields for pulsars with B ~ 10~(11) to ~ 10~(13) G.     

A corresponding-state approach to quark-cluster matter

The state of super-dense matter is essential for us to understand the nature of pulsars; however, non- perturbative quantum chromodynamics makes it very difficult to make direct calculations of the state of cold matter at realistic baryon number densities inside compact stars. Nevertheless, from an observational point of view, it is conjectured that pulsars could be made up of quark clusters since the strong coupling between quarks might render the quarks to be grouped in clusters. In this paper, we attempt to find an equation of state of condensed quark-cluster matter in a phenomenological way. Supposing that the quark-clusters could be analogized to inert gases, we apply here the corresponding-state approach to derive the equation of state of quark-cluster matter, as was similarly demonstrated for nuclear and neutron-star matter in the 1970s. According to the calculations that we have presented, the quark-cluster stars, which are composed of quark-cluster matter, could have a high maximum mass that is consistent with observations and, in turn, further observations of pulsar mass could also place a constraint on the properties of quark-cluster matter. We will also briefly discuss the melting heat during the solid-liquid phase conversion and its related astrophysical consequences.     

A corresponding-state approach to quark-cluster matter~

The state of super-dense matter is essential for us to understand the nature of pulsars; however, non-perturbative quantum chromodynamics makes it very difficult to make direct calculations of the state of cold matter at realistic baryon number densities inside compact stars. Nevertheless, from an observational point of view, it is conjectured that pulsars could be made up of quark clusters since the strong coupling between quarks might render the quarks to be grouped in clusters. In this paper, we attempt to find an equation of state of condensed quark-cluster matter in a phenomenological way. Supposing that the quark-clusters could be analogized to inert gases, we apply here the corresponding-state approach to derive the equation of state of quark-cluster matter, as was similarly demonstrated for nuclear and neutron-star matter in the 1970s. According to the calculations that we have presented, the quark-cluster stars, which are composed of quark-cluster matter, could have a high maximum mass that is consistent with observations and, in turn, further observations of pulsar mass could also place a constraint on the properties of quark-cluster matter. We will also briefly discuss the melting heat during the solid-liquid phase conversion and its related astrophysical consequences.     

Evolving into Magnetars from Normal Pulsars with a Low Braking Index

Anomalous x-ray pulsars （AXPs） and soft gamma-ray repeaters （SCRs） are believed to be candidates for magnetars, and they are powered by the decay of ultra-strong magnetic fields of〉 1014 C. From the modified spin-down relation of pulsars P ∝P^2-n, we find that the Vela pulsar would evolve into the classes of magnetars under some assumptions that pulsars lose their rotational energy only by magnetic dipole radiation and the braking index is a constant. Our rough calculation indicates that only pulsars with n - 1.3 - 1.6 can evolve into magnetars. Pulsars like Vela with a low braking index may be the progenitors of AXPs and SCRs. Regarding the mechanism evolved into magnetars, we suggest that pulsars＇ surface magnetic field component may be increased by frequent glitches.     

Coalescence of heteroclusters Au767 and Ag767: a molecular-dynamics study

This paper studies the coalescence of heteroclusters Au767 and Ag767 by using molecular dynamics with the embedded atom method, where layer atomic energy is employed to describe the potential energy variation of per atom in different layers along radial direction. The results show that the coalescence is driven by releasing the atomic energy of the coalesced zone. The deformation, which is induced by substitutional and vacancy diffusion during the coalescence, makes the coalesced cluster disorder. If the summation of the thermal energy and the released atomic energy is large enough to keep the disorder state, the clusters form a metastable liquid droplet; otherwise, the clusters coalesce into a solid cluster when the coalesced cluster reaches the equilibrium state, and the coalesced cluster experiences liquid to solid ordering changes during the coalescence of a solid Au767 with a liquid Ag767 and a liquid Au767 with a liquid Ag767. The centre of figure of the cluster system is shifted during the coalescence process, and higher coalescence temperature causes larger shift degree.     

Neutrino Emission and Cooling of Dark-Matter-Admixed Neutron Stars

The GW170817 binary neutron star merger event in 2017 has raised great interest in the theoretical research f neutron stars. The structure and cooling properties of dark-matter-admixed neutron stars are studied here using relativistic mean field theory and cooling theories. The non-self-annihilating dark matter(DM) component is assumed to be ideal fermions, among which the weak interaction is considered. The results show that pulsars J1614-2230, J0348+0432 and EXO 0748-676 may all contain DM with the particle mass of 0.2–0.4 GeV. However,it is found that the effect of DM on neutron star cooling is complicated. Light DM particles favor the fast cooling of neutron stars, and the case is converse for middle massive DM. However, high massive DM particles, around1.0 GeV, make the low mass(around solar mass) neutron star still undergo direct Urca process of nucleons at the core, which leads the DM-admixed stars cool much more quickly than the normal neutron star, and cannot support the direct Urca process with a mass lower than 1.1 times solar mass. Thus, we may conjecture that if small(around solar mass) and super cold(at least surface temperature 5–10 times lower than that of the usual observed data) pulsars are observed, then the star may contain fermionic DM with weak self-interaction.     

K0 Condensation in Hyperonic Neutron Star Matter

In the framework of the relativistic mean field theory, we investigate K^0 condensation along with K^- condensation in neutron star matter including the baryon octet. The results show that both K^0 and K^- condensations can occur well in the core of the maximum mass stars for relatively shallow optical potentials of K^- in the range of-100 MeV～ -160 MeV. With the increasing optical potential of K^-, the critical densities of K^- decrease and the species of baryons appearing in neutron stars become fewer. The main role of K^0 condensation is to make the abundances of particles become identical leading to isospin saturated symmetric matter including antikaons, nucleons and hyperons. K^- condensation is chiefly responsible for the softening of the corresponding equation of state, which leads to a large reduction in the maximum masses of neutron stars. In the core of massive neutron stars, neutron star matter including rich particle species, such as antikaons, nucleons and hyperons, may exist.     

Investigating the abundance enrichment pattern of heavy elements in the only observed CEMP-r/s star J004441.04-732136.4 of the SMC

The post-AGB star J004441 is the first and the only one CEMP-r/s star found in SMC.Herein,we investigate the observed abundance pattern of the heavy elements using our parametric model.A consistent fitting results was obtained for the sample star.Based on the low r=0.08,the s-process nucleosynthesis occurred in the interior is supposed to belong to the single neutron-exposure event.The median value ofτ0=0.44(T90.348)1/2mbarn-1supports a higher efficiency of the s-process nucleosynthesis relative to J004441 than that of the solar system,however,the value is not sufficiently high to favor the formation of a lead star.Thus,J004441does not belong to lead star group.The large Csvalue of J004441 supports the intrinsic characteristic of the s-enrichment.The Crvalue is similar with that found in halo CEMP-r/s stars,which indicates that the r-process contributions is critical during heavy element enrichment.This star has a metallicity of[Fe/H]=-1.34,which is larger than that of Galaxy halo CEMP-r/s stars.The reason may be because of the different history of metallicity enrichment between the SMC and the Galaxy halo.     

Effects of the density dependence of the symmetry energy on neutron stars

In this paper,we include the density dependence behavior of the symmetry energy in the improved quark mass density dependent （IQMDD） model.Under the mean field approximation,this model is applied to investigate neutron star matter and neutron stars successfully.Effects of the density dependence of the symmetry energy on neutron stars are described.     

Energy of Gravitational Field of Static Spherically Symmetric Neutron Stars

By using the Einstein-Tolman expression of the energy-momentum pseudo-tensor, the energy density of the gravitational field of the static spherically symmetric neutron stars is calculated in the Cartesian coordinate system.It is exciting that the energy density of gravitational field is positive and rational The xmmerical results of the energy density of gravitational field of neutron stars are calculated. For neutron stars with M=2M, the ratio of the energy density of gravitational field to the energy density of pure matters would be up to 0.54 at the surface.     

Maximum elastic deformations of compact stars with exotic equations of state

I make the first estimates of maximum elastic quadrupole deformations sustainable by alternatives to conventional neutron stars. Solid strange quark stars might sustain maximum ellipticities (dimensionless quadrupoles) up to a few times rather than a few times for conventional neutron stars, and hybrid quark-baryon or meson-condensate stars might sustain up to . Most of the difference is due to the shear modulus, which can be up to rather than in the inner crust of a conventional neutron star. Maximum solid strange star ellipticities are comparable to upper limits obtained for several known pulsars in a recent gravitational-wave search by LIGO. Maximum ellipticities of the more robust hybrid model will be detectable by LIGO at initial design sensitivity. A large shear modulus also strengthens the case for starquakes as an explanation for frequent pulsar glitches.     

Slowly rotating neutron stars and hadronic stars in the chiral SU(3) quark mean-field model

The equations of state for neutron matter, strange and non-strange hadronic matter in the chiral SU(3) quark mean-field model are applied in the study of slowly rotating neutron stars and hadronic stars. The radius, mass, moment of inertia, and other physical quantities are carefully examined. The effect of the nucleon crust for the strange hadronic star is exhibited. Our results show that the rotation can increase the maximum mass of compact stars significantly. For a big enough mass of pulsars which cannot be explained as strange hadronic stars, theoretical approaches to increase the maximum mass are addressed.     

Constraints on the symmetry energy from observational probes of the neutron star crust

A number of observed phenomena associated with individual neutron star systems or neutron star populations find explanations in models in which the neutron star crust plays an important role. We review recent work examining the sensitivity to the slope of the symmetry energy L of such models, and constraints extracted on L from confronting them with observations. We focus on six sets of observations and proposed explanations: i) The cooling rate of the neutron star in Cassiopeia A, confronting cooling models which include enhanced cooling in the nuclear pasta regions of the inner crust; ii) the upper limit of the observed periods of young X-ray pulsars, confronting models of magnetic field decay in the crust caused by the high resistivity of the nuclear pasta layer; iii) glitches from the Vela pulsar, confronting the paradigm that they arise due to a sudden recoupling of the crustal neutron superfluid to the crustal lattice after a period during which they were decoupled due to vortex pinning; iv) the frequencies of quasi-periodic oscillations in the X-ray tail of light curves from giant flares from soft gamma-ray repeaters, confronting models of torsional crust oscillations; v) the upper limit on the frequency to which millisecond pulsars can be spun-up due to accretion from a binary companion, confronting models of the r-mode instability arising above a threshold frequency determined in part by the viscous dissipation timescale at the crust-core boundary; and vi) the observations of precursor electromagnetic flares a few seconds before short gamma-ray bursts, confronting a model of crust shattering caused by resonant excitation of a crustal oscillation mode by the tidal gravitational field of a companion neutron star just before merger.     

Do Neutron Star Gravitational Waves Carry Superfluid Imprints?

Isolated neutron stars undergoing non-radial oscillations are expected to emit gravitational waves in the kilohertz frequency range. To date, radio astronomers have located about 1,300 pulsars, and can estimate that there are about 2×10⁸ neutron stars in the galaxy. Many of these are surely old and cold enough that their interiors will contain matter in the superfluid or superconducting state. In fact, the so-called glitch phenomenon in pulsars (a sudden spin-up of the pulsar's crust) is best described by assuming the presence of superfluid neutrons and superconducting protons in the inner crusts and cores of the pulsars. Recently there has been much progress on modelling the dynamics of superfluid neutron stars in both the Newtonian and general relativistic regimes. We will discuss some of the main results of this recent work, perhaps the most important being that superfluidity should affect the gravitational waves from neutron stars (emitted, for instance, during a glitch) by modifying both the rotational properties of the background star and the modes of oscillation of the perturbed configuration. Finally, we present an analysis of the so-called zero-frequency subspace (i.e., the space of time-independent perturbations) and determine that it is spanned by two sets of polar (or spheroidal) and two sets of axial (or toroidal) degenerate perturbations for the general relativistic system. As in the Newtonian case, the polar perturbations are the g-modes which are missing from the pulsation spectrum of a non-rotating configuration, and the axial perturbations should lead to two sets of r-modes when the degeneracy of the frequencies is broken by having the background rotate.     

Remote quantum mechanical detection of gravitational radiation

The presumed existence of atomic hydrogen in the vicinity of sources of gravitational radiation suggests its use as a radiation detector. Curvature-induced atomic energy level shifts carry a unique signature and could thus provide for remote detection of gravitational radiation. We investigate the shifts induced by space-time curvature arising from gravitational waves. The effect is studied for both low-lying and highly excited states of atomic hydrogen. Numerical results are quoted for radiation from various sources, including binary star systems, binary neutron stars, binary black holes, collapsing stars, and pulsars. In addition, we provide a theoretical upper limit to the magnitude of the effect. For completeness, we examine the shifts induced in a harmonic oscillator as well as a rigid rotator.     

Thermal properties and detectability of neutron stars - I cooling and heating of neutron stars

In this report, we first review earlier and recent developments in some of thermodynamic problems of neutron stars, especially those involving cooling mechanisms and theoretical predictions of surface temperatures of neutron stars. Emphasis is placed particularly on: the effect of equations of state and hence that of nuclear and strong interactions; the effect of better treatment of various neutrino cooling mechanisms, especially those involving pion condensates; and implication of these better and more detailed theoretical estimates on the prospect of directly observing thermal radiation from the surface of neutron stars. In connection with the last problem, we briefly review recent developments on the observational side — the HEAO-B and other programs already existing or expected to be planned for near future, which are directly related to the above problem. In connection with the possibilities of observing older neutron stars we briefly summarise various heating mechanisms.From these studies, we see that exciting possibilities exist through the HEAO-B and some other programs which may be realised in the 1980's, that we may observe radiation directly from neutron star surfaces if they are ? (3?5) × 10⁵°K. If such radiation is detected, the observed surface temperatures and further spectral studies may give invaluable insight into various important problems, such as magnetic properties of dense matter, equations of state, pion condensates, and other fundamental problems in nuclear, particle and high energy physics. If the surface temperatures of younger members of these stars (? 10⁴ years) are observationally found to be less than ≈ (5?10) × 10⁵°K (depending on the individual objects), we note that at the moment only pion coolings are consistent with observations, and the outcome may be equally far reaching. Among various observed neutron stars (pulsars) and neutron star candidates (e.g. supernova remnants), the Vela pulsar may prove to be the most rewarding one. If regular pulsar-like periodicities are discovered in radiations from any of supernova remnants, we can assume the presence of neutron stars in these objects. In that case, some supernova remnants, such as SN 1006, may also turn out to be promising. If we defect surface radiations from older pulsars (? 10⁵ years), that may support some of heating theories. At the end, we point out that there may be many point sources of very soft weak thermal X-rays across the sky (as old neutron stars accrete interstellar matter) and some of the closest ones may be detectable through the HEAO-B and similar devices.     

R-mode Instability of Neutron Star with Non-Newtonian Gravity

The Chandrasekhar-Friedmann-Schutz(CFS) instabilities of r-modes for canonical neutron stars(1.4 M ⊙) with rigid crusts are investigated by using an equation of state of asymmetric nuclear matter with super-soft symmetry energy,where the non-Newtonian gravity proposed in the grand unification theories is also considered.Constrained by the observations of the masses and the spin frequencies for neutron stars,the boundary of the r-mode instability window for a canonical neutron star is obtained,and the results show that the observed neutron stars are all outside the instability window,which is consistent with the theoretical expectation.In addition,an upper limit of the non-Newtonian gravity parameters is also given.     

Magnetic collapse of a neutron gas: Can magnetars indeed be formed?

A relativistic degenerate neutron gas in equilibrium with a background of electrons and protons in a magnetic field exerts its pressure anisotropically, having a smaller value perpendicular to than along the magnetic field. For critical fields the magnetic pressure may produce the vanishing of the equatorial pressure of the neutron gas. Taking this as a model for neutron stars, the outcome could be a transverse collapse of the star. This fixes a limit to the fields to be observable in stable neutron star pulsars as a function of their density. The final structure left over after the implosion might be a mixed phase of nucleons and a meson condensate, a strange star, or a highly distorted black hole or black ”cigar”, but not a magnetar, if viewed as a superstrongly magnetized neutron star. However, we do not exclude the possibility of superstrong magnetic fields arising in supernova explosions which lead directly to strange stars. In other words, if any magnetars exist, they cannot be neutron stars. Received: 25 November 2002 / Revised version: 25 February 2003 / Published online: 5 May 2003