The Equation of State of Nuclear Matter and Neutron Stars Properties

The equation of state (EOS) of symmetric nuclear and pure neutron matter has been investigated extensively by adopting the non-relativistic Brueckner-Hartree-Fock (BHF). For more comparison, the extended BHF approaches using the self-consistent Green’s function approach or by including a three-body force will be done. The EOS will be studied for different approaches at zero temperature. We can calculate the total mass and radius of neutron stars using various equations of state. A comparison with relativistic BHF calculations will be done. Relativistic effects are known to be important at high densities, giving an increased repulsion. This leads to a stiffer EOS compared to the EOS derived with a non-relativistic approach.

Equation of state for aluminum in warm dense matter regime

A semi-empirical equation of state model for aluminum in a warm dense matter regime is constructed. The equation of state, which is subdivided into a cold term, thermal contributions of ions and electrons, covers a broad range of phase diagram from solid state to plasma state. The cold term and thermal contribution of ions are from the Bushman–Lomonosov model, in which several undetermined parameters are fitted based on equation of state theories and specific experimental data. The Thomas–Fermi–Kirzhnits model is employed to estimate the thermal contribution of electrons. Some practical modifications are introduced to the Thomas–Fermi–Kirzhnits model to improve the prediction of the equation of state model. Theoretical calculation of thermodynamic parameters, including phase diagram, curves of isothermal compression at ambient temperature, melting, and Hugoniot, are analyzed and compared with relevant experimental data and other theoretical evaluations.

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.

Computing Differentially Rotating Neutron Stars Obeying Realistic Equations of State by Using Hartle’s Perturbation Method

In this paper, we use the well-known Hartle’s perturbation method in order to compute models of differentially rotating neutron stars obeying realistic equations of state. In our numerical treatment, we keep terms up to third order in the angular velocity. We present indicative numerical results for models satisfying a particular differential rotation law. We emphasize on computing the change in mass owing to this differential rotation law.

Astrophysical constraints on a parametric equation of state for neutron-rich nucleonic matter

Extracting the equation of state(EOS) and symmetry energy of dense neutron-rich matter from astrophysical observations is a long-standing goal of nuclear astrophysics. To facilitate the realization of this goal, the feasibility of using an explicitly isospin-dependent parametric EOS for neutron star matter was investigated recently in [1–3]. In this contribution, in addition to outlining the model framework and summarizing the most important findings from [1–3], we report a few new results regarding constraining parameters characterizing the highdensity behavior of nuclear symmetry energy. In particular,the constraints on the pressure of neutron star matter extracted from combining the X-ray observations of the neutron star radius, the minimum–maximum mass M=2:01 M_⊙, and causality condition agree very well with those extracted from analyzing the tidal deformability data by the LIGO ? Virgo Collaborations. The limitations of using the radius and/or tidal deformability of neutron stars to constrain the high-density nuclear symmetry energy are discussed.

The Brueckner-Hartree-Fock Equation of State for Nuclear Matter and Neutron Skin

The equation of state for nuclear matter is presented within the Brueckner Hartree-Fock （BHF） scheme, by using the realistic Argonne VI8 or Bonn B two-nucleon potentials plus their corresponding microscopic three-nucleon forces. It is then applied to calculate the properties of finite nuclei within a simple liquid-drop model, and we compare the calculated volume, surface, and Coulomb parameters with the empirical ones from the liquid drop model. Nuclear density distributions and charge radii in good agreement with the experimental data are obtained~ and we predict the neutron skin thickness of various nuclei.

Equation of State for Neutralino Star as a Form of Cold Dark Matter

In order to study the structure of neutralino star and dark galaxy, we consider dynamical interactions due to boson-exchange in the neutralino matter. Taking into account interactions of neutralinos with bosons, we derive the equation of state （EOS） of neutralino stars in terms of the relativistic mean-field approach. Then we apply the resulting EOS to investigate properties of the neutralino star such as its density profile and mass limit. For example, if the neutralino mass is around 1 TeV, the Oppenheimer mass limit of the neutralino star is obtained as 6.06 ×10^-7 M⊙, and the corresponding radius is about 7.8 mm. Actually, due to an increasing annihilation rate as indicated by our calculation, this dense state can never be realized in practice. Our results also show that the low-density neutralino star may be a possible aggregation of the cold dark matter.

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.

Anisotropic stellar structure equations for magnetized strange stars

The fact that a fermion system in an external magnetic field breaks the spherical symmetry suggests that its intrinsic geometry is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presence of a magnetic field, in the structure equations of a magnetized quark star.We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that a strange star can sustain, closely related to the violation of the virial relations.

Strange Stars: Can Their Crust Reach the Neutron Drip Density?

The electrostatic potential of electrons near the surface of static strange stars at zero temperature is studied within the frame of the MIT bag model. We find that for QCD parameters within rather wide ranges, if the nuclear crust on the strange star is at a density leading to neutron drip, then the electrostatic potential will be insufficient to establish an outwardly directed electric field, which is crucial for the survival of such a crust. If a minimum gap width of 200 fm is brought in as a more stringent constraint, then our calculations will completely rule out the possibility of such crusts. Therefore, our results argue against the existence of neutron-drip crusts in nature.

Dependence of the tidal deformability of neutron stars on the nuclear equation of state

Within the Bayesian framework,using an explicitly isospin-dependent parametric equation of state(EOS)for the core of neutron stars(NSs),we studied how the NS EOS behaves when we confront it with the tidal deformabilitiesΛ1.4abilities of massive NSs.We found that it does not significantly improve the constraints on the NS EOS but has a weak effect on narrowing down the slope parameter of the symmetry energy by decreasing the measurement errors ofΛ1.4.Both the isospin-dependent and isospin-independent parts of the NS EOS were significantly constrained and raised as the tidal deformabilities of massive NSs were adopted in the calculations,especially in high-density regions.We also found thatΛ1.4symmetry energy,whereas the opposite occurs for the radius of canonical NSs R1.4.The tidal deformability of an NS with two times the solar massΛ2.0ergy,andΛ1.4and R1.4have no correlation with the former.

From masses and radii of neutron stars to EOS of nuclear matter through neural network

The equation of state(EOS)of dense nuclear matter is a key factor for determining the internal structure and properties of neutron stars.However,the EOS of high-density nuclear matter has great uncertainty,mainly because terrestrial nuclear experiments cannot reproduce matter as dense as that in the inner core of a neutron star.Fortunately,continuous improvements in astronomical observations of neutron stars provide the opportunity to inversely constrain the EOS of high-density nuclear matter.Several methods have been proposed to implement this inverse constraint,including the Bayesian analysis algorithm,the Lindblom’s approach,and so on.Neural network algorithm is an effective method developed in recent years.By employing a set of isospin-dependent parametric EOSs as the training sample of a neural network algorithm,we set up an effective way to reconstruct the EOS with relative accuracy using a few mass-radius data.Based on the obtained neural network algorithms and according to the NICER observations on masses and radii of neutron stars with assumed precision,we obtain the inversely constrained EOS and further calculate the corresponding macroscopic properties of the neutron star.The results are basically consistent with the constraint on EOS in Huth et al.[Nature 606,276(2022)]based on Bayesian analysis.Moreover,the results show that even though the neural network algorithm was obtained using the finite parameterized EOS as the training set,it is valid for any rational parameter combination of the parameterized EOS model.

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.

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.

Implications of neutron skin measurements on Skyrme equations of state

The recent measurements of neutron skins via parity violation in electron scattering have extracted an abnormally thick neutron skin for 208 Pb,which has significant consequences in nuclear equation of state(EoS)and neutron star observations.In this study,we perform optimizations of extended Skyrme forces in a consistent manner by including neutron skin thicknesses from PREX-Ⅱand CREX experiments and investigate nuclear EoSs and neutron stars in the GW170817 event By varying the fitting weights of neutron skins,several new Skyrme parameterizations are obtained.Our results show the competition in the fitting procedure to simultaneously describe neutron skins,other properties of finite nuclei,and neutron star observations.The prospects of resolving neutron skin issues are also discussed.

Singlet pairing gaps of neutrons and protons in hyperonic neutron stars

The ^1 S0 nucleonic superfluids are investigated within the relativistic meanfield model and Bardeen-Cooper-Schrieffer theory in hyperonic neutron stars. The ^1 S0 pairing gaps of neutrons and protons are calculated based on the Reid soft-core interaction as the nucleon-nucleon interaction. In particular, we have studied the influence of degrees of freedom for hyperons on the ^1 S0 nucleonic pairing gap in neutron star matter. It is found that the appearance of hyperons has little impact on the baryonic density range and the size of the ^1S0 neutronic pairing gap; the ^1S0 protonic pairing gap also decreases slightly in this region where ρB = 0.0-0.393 fm^-3. However, if baryonic density becomes greater than 0.393 fm^-3, the ^1S0 protonic pairing gap obviously increases. In addition, the possible range for a protonic superfluid is obviously enlarged due to the presence of hyperons. In our results, the hyperons change the 1 So protonic pairing gap, which must change the cooling properties of neutron stars.

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.

Microscopic Magnetic Dipole Radiation in Neutron Stars

There is a ^3P2 neutron superfluid region in NS （neutron star） interior. For a rotating NS the ^3P2 superfluid region is like a system of rotating magnetic dipoles. It will give out electromagnetic radiation, which may provide a new heating mechanism of NSs. This mechanism plus some cooling agent may give a sound explanation to NS glitches.

Effect of Mesons f0（975） and Ф（1020） and Variety of UΞ^（N） on Properties of Neutron Star Matter

We examine the effect of adding mesons fo(975)and φ(1020)as well as the variety of U(the potential well depth ofin nuclear matter)from -10 MeV to -28 MeV on the extent of the particles participation and the properties of the neutron star in the relativistic mean field model.We find that considering the contribution of fo and φ mesons,the equation of state of the neutron star turns soft,the maximum mass reduces while the corresponding radius increases.hyperons appear at lower density as Ubecomes deeper,and the variety of Uhas little effect on the equation of state and the properties of the neutron star.

Asymmetric neutron stars in the presence of vacuum fluctuations

The asymmetric neutron stars are investigated in a relativistic effective model with vacuum fluctuations(VF) taken into account. Due to the VF effects, various properties of the neutron matter become ‘softened' comparing to that obtained in the FSUGold model, and the maximum mass of the enpelT neutron stars is reduced from1.71 M to 1:35M.