The EOSs and the Blatant Discrepancy in Modelling Massive Neutron Stars: Origin and a Possible Solution Method

Exploring the state of ultra-cold supranuclear dense matter that makes up the cores of massive neutron stars is one of the greatest unresolved problems in modern physics. In this letter, we show that when the interiors of pulsars are made of compressible and dissipative normal matter, the commonly used solution procedures combined with the known EOSs yield widely scattered solutions and poorly determined radii. A remarkable agreement emerges, however, if pulsars harbour cores that are made of incompressible entropy-free superfluids (SuSu-matter) embedded in flat spacetimes. Such supranuclear dense matter should condensate to form false vacua as predicated by non-perterbative QCD vacuum. The solutions here are found to be physically consistent and mathematically elegant, irrespective of the object’s mass. Based thereon, we conclude that the true masses of massive NSs may differ significantly from those revealed by direct observation.

From Finite Nuclei to Neutron Stars: The Essential Role of High-Order Density Dependence in Effective Forces

A unified description of finite nuclei and equation of state of neutron stars presents both a major challenge and also opportunities for understanding nuclear interactions.Inspired by the Lee-Huang-Yang formula of hardsphere gases,we develop effective nuclear interactions with an additional high-order density dependent term.While the original Skyrme force SLy4 is widely used in studies of neutron stars,there are not satisfactory global descriptions of finite nuclei.The refitted SLy4' force can improve descriptions of finite nuclei but slightly reduces the radius of neutron star of 1.4 M_☉ with M_☉ being the solar mass.We find that the extended SLy4 force with a higher-order density dependence can properly describe properties of both finite nuclei and GW170817 binary neutron stars,including the mass-radius relation and the tidal deformability.This demonstrates the essential role of high-order density dependence at ultrahigh densities.Our work provides a unified and predictive model for neutron stars,as well as new insights for the future development of effective interactions.

Systematic comparison of initial velocities for neutron stars in different models

I have studied the initial velocity（Maxwellian and exponential distributions） and the scale height of isolated old（aged≥10^9yr） neutron stars（NSs） at different Galactocentric distances R in three population models. The smooth time-independent 3-D axisymmetric gravitational potentials（MiyamotoNagai and Paczy n′ski models） were also used. The correlation between these quantities significantly affects the shapes of the profiles and distributions of the simulated sample, because the differences in the initial kick can arise from differences in the formation and evolution of NSs with other physical parameters. The scale height of the density distribution increases systematically with R. I have also shown that the distribution of old NSs in these population models agrees with the observed structure of the Galaxy in terms of initial velocities（1-D and 3-D）, as well as the scale height distributions. These distributions tend to have an asymptotic behavior at the point R = 2.75 kpc. This means that the quality of the models can be described in terms of a mean of the fitted Gaussian, and this could also give an overall perspective of the phase space properties of nearby old NSs on a given gravitational potential.

Hyperon Effects on the Spin Parameter of Rotating Neutron Stars

Based on the equations of state from the relativistic mean field theory without and with the inclusion of strangeness-bearing hyperons, we study the dimensionless spin parameter j = cJ/（GM2） of uniformly rotat- ing neutron stars. It is shown that the maximum value of the spin parameter jmax of a neutron star rotating at the Keplerian frequency fK is .jmax - 0.7 when the star mass M 〉 0.SM⊙, which is sustained for various versions of equations of state without and with hyperons. The relationship between j and the scaled rotation frequency f /fK is found to be insensitive to the star mass or the adopted equation of state in the models without hyperons. However, the emergence of byperons in neutron stars will lead to an uncertainty of the spin parameter j, which in turn could generate a complexity in the theoretical study of the quasi-periodic oscillations observed in disk-accreting compact-star systems.

Effects of Gravitational Correction on Neutrino Emission from Neutron Stars

Considering the gravitational correction through introduction of weakly interacting light vector U bosons, not only the equation of state （EoS） of the neutron star matter, but also the cooling properties of neutron stars may be changed. In this work, effects of gravitational correction on neutrino emission and cooling of neutron stars in the matter with neutrons, protons, electrons, muons, △- and △0 are studied by the relativistic mean field theory and the related cooling theory. The results show that the effects are sensitive to the ratio of coupling strength to mass squared of U bosons, defined as gu. With increasing gu, the radial region where direct Urca process of nucleons can be allowed in a neutron star with the fixed mass becomes narrower, while the neutrino emissivity is somewhat higher. Moreover, the gravitational correction suppresses the effects of △- on neutrino emission. The gravitational correction leads the star to cool faster, and the higher the gu is, the faster the star cools.

Influence of strong magnetic field on β decay in the crusts of neutron stars

β decay in the strong magnetic field of the crusts of neutron stars is analysed by an improved method. The reactions ^67Ni（β-）^67Cu and ^62Mn（β-）^62Fe are investigated as examples. The results show that a weak magnetic field has little effect on β decay but a strong magnetic field （B 〉 10^12G） increases β decay rates obviously. The conclusion derived may be crucial to the research of late evolution of neutron stars and nucleosynthesis in r-process.

R-mode instability of strange stars and observations of neutron stars in LMXBs

Using a realistic equation of state （EOS） of strange quark matter, namely, the modified bag model, and considering the constraints on the parameters of EOS by the observational mass limit of neutron stars, we investigate the r-mode instability window of strange stars, and find the same result as in the brief study of Haskell, Degenaar and Ho in 2012 that these instability windows are not consistent with the spin frequency and temperature observations of neutron stars in low mass X-ray binaries.

Long-term evolution and gravitational wave radiation of neutron stars with differential rotation induced by r-modes

In a second-order r-mode theory, Sa and Tome found that the r-mode oscillation in neutron stars （NSs） could induce stellar differential rotation, which naturally leads to a saturated state of the oscillation. Based on a consideration of the coupling of the r-modes and the stellar spin and thermal evolution, we carefully investigate the influences of the differential rotation on the long-term evolution of isolated NSs and NSs in low-mass X-ray binaries, where the viscous damping of the r-modes and its resultant effects are taken into account. The numerical results show that, for both kinds of NSs, the differential rotation can significantly prolong the duration of the r-modes. As a result, the stars can keep nearly a constant temperature and constant angular velocity for over a thousand years. Moreover, the persistent radiation of a quasi-monochromatic gravitational wave would also be predicted due to the long-term steady r-mode oscillation and stellar rotation. This increases the detectability of gravitational waves from both young isolated and old accreting NSs.

Influence of a scalar-isovector δ-meson field on the quark phase structure in neutron stars

The deconfinement phase transition from hadronic matter to quark matter in the interior of compact stars is investigated. The hadronic phase is described in the framework of relativistic mean-field theory, where the scalar-isovector 6-meson effec- tive field is also taken into account. The MIT bag model for describing a quark phase is used. The changes of the parameters of phase transition caused by the presence of a δ-meson field are explored. Finally, alterations in the integral and structural parameters of hybrid stars due to both a deconfinement phase transition and inclusion of a δ-meson field are discussed.

^3PF2 neutron superfluidity in neutron stars and three-body force effect

We investigate the ^3PF2 neutron superfluidity in H-stable neutron star matter and neutron stars by using the BCS theory and the Brueckner-Hartree-Fock approach. We adopt the Argonne V18 potential supplemented with a microscopic three-body force as the realistic nucleon-nucleon interaction. We have concentrated on studying the threebody force effect on the ^3PF2 neutron pairing gap. It is found that the three-body force effect is to enhance remarkably the ^3PF2 neutron superfluidity in neutron star matter and neutron stars.

Phases of Dense Matter in Supernovae and Neutron Stars

We study the properties of dense matter at finite temperature with various proton fractions for use in supernova simulations. The relativistic mean-field theory is used to describe homogeneous nuclear matter, while the Thomas-Fermi approximation is adopted to describe inhomogeneous matter. We also discuss the equation of state of neutron star matter at zero temperature in a wide density range. The equation of state at high densities can be significantly softened by the inclusion of hyperons.

Effects of the symmetry energy slope on the axial oscillations of neutron stars

The impact of symmetry energy slope L on the axial w-mode oscillations is explored, where the range of the con- strained slope L of symmetry energy at saturation density is adopted from 25 MeV to 115 MeV while keeping the equation of state （EOS） of symmetric nuclear matter fixed. Based on the range of the symmetry energy slope, a constraint on the frequency and damping time of the wi-mode of the neutron star is given. It is found that there is a perfect linear relation between the frequency and the stellar mass for a fixed slope L, and the softer symmetry energy corresponds to a higher frequency. Moreover, it is confirmed that both the frequencies and damping times have a perfect universal scaling behavior for the EOSs with different symmetry energy slopes at saturation density.

Effect of strong magnetic field on electron capture of iron group nuclei in crusts of neutron stars

In this paper electron capture on iron group nuclei in crusts of neutron stars in a strong magnetic field is investigated. The results show that the magnetic fields have only a slight effect on electron capture rates in a range of 10^5 - 10^13g on surfaces of most neutron stars, whereas for some magnetars the magnetic fields range from 10^13 to 10^18 G. The electron capture rates of most iron group nuclei are greatly decreased, reduced by even four orders of magnitude due to the strong magnetic field.

Effect of superstrong magnetic field on electron screening at the crusts of neutron stars

The influences of electron screening （ES） and electron energy correction （EEC） are investigated by superstrong magnetic field （SMF）. We also discuss in detail the discrepant factor between our results and those of Fushiki, Gudmundsson and Pethick （FGP） in SMF. The results show that SMF has only a slight effect on ES when B 〈 10^9 T on the surfaces of most neutron stars. Whereas for some magnetars, SMF influence ES greatly when B 〉 10^9 T . For instance, due to SMF the ES potential may be increased about 23.6% and the EEC may be increased about 4 orders of magnitude at ρ/μe = 1.0 × 10^6 mol/cm^3 and T9 = 1. On the other hand, the discrepant factor shows that our results are in good agreement with FGP＇s when B 〈 10^9 T . But the difference will be increased with increasing SMF.

Neutron stars:a relativistic study

We study the inner structure of a neutron star from a theoretical point of view and the outcome results are compared with observed data. We propose a stiff equation of state relating pressure with matter density. From our study we calculate mass（M）,compactness（u） and surface redshift（Zs） for two binary millisecond pulsars,namely PSR J1614–2230 and PSR J1903＋327,and four X-ray binaries,namely Cen X-3,SMC X-1,Vela X-1 and Her X-1,and compare them with recent observational data.Finally,we examine the stability for such a type of theoretical structure.

Observational Constraints on Quark Matter in Neutron Stars

We study the observational constraints of mass and redshift on the properties of the equation of state （EOS） for quark matter in compact stars based on the quasi-particle description. We discuss two scenarios; strange stars and hybrid stars. We construct the equations of state utilizing an extended MIT bag model taking the medium effect into account for quark matter and the relativistic mean field theory for hadron matter. We show that quark matter may exist in strange stars and in the interior of neutron stars. The bag constant is a key parameter that affects strongly the mass of strange stars. The medium effect can lead to the stiffer hybrid-star EOS approaching the pure hadronic EOS, due to the reduction of quark matter, and hence the existence of heavy hybrid stars. We find that a middle range coupling constant may be the best choice for the hybrid stars being compatible with the observational constraints.

Transient Phenomena from Gas Erupting Neutron Stars

Starquakes probably occur in rapidly spinning or ultra high field neutron stars. In this article, we argue that highly compressed gas containing electron–positron pairs could evaporate and erupt from inside the neutron star when a crack forms and then heals during a starquake. Under the influence of the existing oscillation modes of the star, the crack may have sufficiently large size and long lifetime. An appropriate amount of gas can erupt into the magnetosphere with relativistic and nearly uniform velocity, producing various transient and bursting phenomena.

Thermal evolution of neutron stars with decaying magnetic fields

Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field （10^8 G） could have a lower temper- ature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437-4715.

The Origin of Glitches in Pulsars—Phase Oscillation between Anisotropic Superfluid and Normal State of Neutrons in Neutron Stars

Considering neutron star heating by magnetic dipole radiation from ^3PF2 superfluid neutron vortices inside the star, we propose a neutron phase oscillation model between the normal neutron Fermi fluid and the ^3PF2 superfluid neutron vortices at the transition temperature of Ttrans = （2 - 3）× 10^8 K. With this model we can qualitatively explain most of the observations on pulsar glitches up to date.

The optical/ultraviolet excess of isolated neutron stars in the resonant cyclotron scattering model

X-ray dim isolated neutron stars are peculiar pulsar-like objects, characterized by their Planck-like spectrum. In studying their spectral energy distributions, optical/ultraviolet （UV） excess is a long standing problem. Recently Kaplan et al. measured the optical/UV excess for all seven sources, which is understandable in the resonant cyclotron scattering （RCS） model previously addressed. The RCS model calculations show that the RCS process can account for the observed optical/UV excess for most sources. The flat spectrum of RX J2143.0＋0654 may be due to contributions from the bremsstrahlung emission of the electron system in addition to the RCS process.