Two New Hyperon Coupling Models in the Light of the Massive Neutron Star PSR J0348+0432*

In the context of the relativistic mean field theory, we propose two new hyperon coupling models, namely the limitation model and the potential well depth model, in the light of the observed data for the massive neutron PSR J0348+0432. The radius of PSR J0348+0432 given by the limitation model is found to be $12.52 \text{ km}\sim12.97\text{ km}$, while the radius given by the potential well depth model is found to be $12.19\text{ km}\sim12.89 \text{ km}$. We also calculate the gravitational redshift of PSR J0348+0432 within these two models, for which the limitation model gives $0.346\sim0.391$ and the potential well depth model gives $0.350\sim0.409$. Further exploration of these two models shows that, these two models are almost degenerate for neutron stars lighter than $1.85 M_{\odot}$, and start to give different results for massive neutron stars heavier than $1.85 M_{\odot}$. Therefore, the studies of massive neutron stars could be crucial for discriminating these two models and help deepen our understanding of hyper-nuclear interactions.     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

The moment of inertia of the proto neutron star PSR J0348+0432 under neutrino trapped

The moment of inertia of the proto neutron star PSR J0348+0432 is studied in the framework of relativistic mean field theory under neutrino trapped. We find that the temperature of the PNS PSR J0348+0432 increases with the increase of the baryon number density and at the center of the star it is in the range T_c = 41.662–45.685 MeV. Corresponding to the observation mass 1.97–2.05 M_⊙, the radius of the NS PSR J0348+0432 is in the range 12.948–12.16 km whereas that of the PNS PSR J0348+0432 is in the range 14.46–13.561 km. The radius of the PNS PSR J0348+0432 has increased by 11.7%–11.5% compared with that of the NS PSR J0348+0432. The central moment of inertia of the PNS PSR J0348+0432 is in the range 2.207?×?10⁴⁵–1.914?×?10⁴⁵ g cm² whereas that of the NS PSR J0348+0432 is only in the range 1.9?×?10⁴⁵–1.552?×?10⁴⁵ g cm². Compared with the moment of inertia of the NS PSR J0348+0432, the central moment of inertia of the PNS PSR J0348+0432 increases by 16%–23%.     

The hyperon coupling constants and the surface gravitational redshift of massive neutron stars

With relativistic mean field theory we examine effect of hyperon coupling constants of hyperon Ξ on the surface gravitational redshift of the massive neutron star (NS) PSR J1614-2230 and NS PSR J0348+0432 as the potential well depth of hyperon Ξ is fixed. We find that the mass and radius of a NS increase with the increase of the coupling constant of hyperon Ξ. With the increase of the coupling constant of the hyperon Ξ, the surface gravitational redshift will decrease for a same NS mass but will increase for a same NS radius. The surface gravitational redshift of the more massive NS PSR J0348+0432 decreases by more than that of the less massive NS PSR J1614-2230. We also find that the value range of the surface gravitational redshift of NS will become narrower with the increase of the coupling constant of hyperon Ξ. The greater the NS mass, the greater the influence of the coupling constant of hyperon Ξ on the value range of the surface gravitational redshift of the NS.     

The Stability of Some Viable Stars and Electromagnetic Field

We examine the impact of electromagnetic field on the stability of compact stars corresponding' to embedded class one metric using the concept of cracking.For this purpose,we develop the generalized hydrostatic equilibrium equation for charged perfect fluid distribution of compact stars and perturb it by means of local density perturbation scheme to check the stability of inner matter configuration.We investigate the cracking of Her X-1,PSR 1937+21,PSR J 1614-2230,PSR J 0348+0432 and RX J 1856-37.We conclude that PSR J 0348+0432 and RX J 1856-37 exhibit cracking when charge is introduced on these astrophysical objects.     

能通过大质量中子星转动惯量来限定超子参数吗?

在相对论平均场理论（RMFT）框架内,使用GL91参数组结合超核数据和大质量中子星的观测数据限定超子标量耦合参数X_σ=0.59~1.0,用慢转近似计算了大质量中子星和前中子星的转动惯量。当X_σ从0.59增加到1.0,中子星（前中子星）的最大转动惯量增幅达89%（60%）。在同样的变化范围内,用Crab的观测数据,计算得到中子星（前中子星）的最大能量损失（dE/dt）的增幅为44%（25%）,最大磁场增幅为48%（38%）。相比于前中子星,中子星的性质对超子参数更为敏感。当X_σ从0.59增加到1.0,PSR J0348+0432的转动惯量和dE/dt的增幅均为14%,而磁场减幅为10%。如果天文观测能够给出中子星转动惯量的上限,或者同时精确测量中子星的质量和转动惯量,能帮助人们进一步限定超子参数。In the framework of the relativistic mean field theory(RMFT) with GL91 cets, the momentum of inertia (I) of slowly rotating neutron stars is studied by perturbative approach. The scalar hyperon coupling should lie in the range of X_σ=0.59~1.0 to be compatible with massive neutron stars. As X_σ increases from 0.59 to 1.0, the maximum momentum of inertia(I_max) of neutron (protoneutron) stars increases by 89% (60%). According to the data of Crab, the maximum energy loss(dE/dt) of neutron (protoneutron) stars will increase by 44%(25%)and the maximum magnetic field (B) will increase by 48%(38%). I and dE/dt of PSR J0348+0432 both increase by 14%, while B decreases by 10% as X_σ increases from 0.59 to 1.0. So if the upper bound of I, or the accurate values of both the mass and I of neutron stars could be provided by the astronomical observations, the hyperon couplings should be further constrained in the future.     

Constraints on the properties of the massive neutron star PSR J0348+0432 from the f0(975) and φ(1020) mesons

The effect of the f ₀(975) and φ(1020) mesons on the properties of the massive neutron star PSR J0348+0432 is examined in the framework of the relativistic mean-field theory by choosing the suitable hyperon coupling constants. It is found that, compared with that without the f ₀(975) and φ(1020) mesons, the radius of the neutron star PSR J0348+0432 increases from R = 12.072 km to R = 12.08 km (i.e. by 0.07%), the central energy density ? _c decreases from 5.6695 fm^?4 to 5.6492 fm^?4 (i.e. by 0.36%), the central pressure decreases from 1.585 fm^?4 to 1.58 fm^?4 (i.e. by 0.32%), the moment of inertia increases from 1.4592 × 10⁴⁵ g · cm² to 1.4615 × 10⁴⁵ g · cm² (i.e. by 0.16%) and the surface gravitational redshift decreases from z = 0.4026 to z = 0.4022 (i.e. by 0.1%). Our results show that the effect of the f ₀(975) and φ(1020) mesons on the properties of the massive neutron star PSR J0348+0432 is very small (i.e. no more than 0.5%) and therefore they do not play a major role.     

Effects of a Weakly Interacting Light U Boson on Protoneutron Stars Including the Hyperon-Hyperon Interactions

In the framework of the relativistic mean field theory including the hyperon-hyperon(YY) interactions,protoneutron stars with a weakly interacting light U boson are studied. The U-boson leads to the increase of the star maximum mass. The modification to the maximum mass by the U-boson with the strong YY interaction is larger than that with the weak YY interaction. The maximum mass of the protoneutron star is less sensitive to the U-boson than that of the neutron star. The inclusion of the U-boson narrows down the mass window for the hyperonized protoneutron stars. As g~2/μ~2 increases, the species of hyperons, which can appear in a stable protoneutron star decrease. The rotation frequency, the red shift, the momentum of inertia and the total neutrino fraction of PSR J1903-0327 are sensitive to the U-boson and change with g~2/μ~2 in an approximate linear trend. The possible way to constrain the coupling constants of the U-boson is discussed.     

软物态方程支持大质量中子星机制概述

重离子碰撞实验分析及相关理论研究认为高密度非对称核物质可能具有较软的物态方程;在约2～3倍饱和核密度下超子等奇异物质的出现也可能会使物态方程变软。然而,软物态方程却无法支持大质量中子星。脉冲星PSR J1614-2230具有大质量(1.97±0.04)M⊙的观测发现使这一矛盾变得尤为突出。为了解决该矛盾,人们提出了各种可能的物理机制:包括考虑修正的引力理论、修改描述高密度物质物态的理论模型等。在概述和讨论这些能使软物态方程支持大质量中子星的可能物理机制的基础上,还计算和讨论了强电场、强磁场对中子星最大质量的影响,发现强电磁场可以有效地增大中子星的最大质量。     

超子耦合参数对热前中子星物质的影响

在相对论平均场理论框架内,利用Λ超子的结合能和中子星质量的观测数据得到超子标量介子耦合参数χσ的范围是0.33—0.77。在这个范围内, 研究了χσ取不同值时, 包含核子, Λ和Ξ超子的热前中子星（固定单个重子熵s=1）的性质。结果表明, 如果超子耦合参数变大, 前中子星核心温度变高, 中微子丰度变低, 前中子星的亚稳态质量范围变小。如果χσ超过了0.75, 前中子星不可能演变成黑洞。联系SN1987A讨论了这一结果的意义。In the framework of the relativistic mean field theory(RMFT), protoneutron stars with hyperons are studied. To be compatible with neutron star masses, the hyperon scalar coupling χσ should lie in the range of 0.33—0.77. As the hyperon scalar coupling increases, in protoneutron star matter, the core temperature increases whereas the abundance of neutrinos decreases. The metastable mass range of protoneutron stars narrows as the temperature increases. It is found that a protoneutron star cannot subside into a low mass black hole when χσ>0.75. Furthermore, the case of SN1987A is discussed.     

前中子星内的K-凝聚和超子的生成

用相对论平均场下的手征强子模型研究了前中子星内K^-凝聚和超子的生成。结果显示，前中子星内的中微子束缚使得出现K^-凝聚的临界密度推迟到更高的重子密度，而K^-0凝聚无法出现。同时中微子束缚使得前中子星的状态方程变硬，从而前中子星的最大质量变大。如果考虑超子，前中子星内无法出现K^-凝聚，同时系统的状态方程变软（与不含超子的情况相比），从而对应前中子星的最大质量变小。A chiral hadronic model is extended to investigate antikaon condensation and hyperons production of protoneutron stars. Our results show that neutrino trapping makes the critical density of K^- condensation delay to higher density and K^-0 condensation not occur. Meanwhile, the equation of state （EOS） of （proto）neutron star matter considering neutrino trapping is stiffer than the case without neutrino trapping. Therefore the maximum masses of rotoneutron stars with neutrino trapping are larger than those without neutrino trapping. If hyperons are considered, antikaon condensation does not appear in （proto） neutron stars. Meanwhile, the corresponding EOS becomes much softer, and the maximum masses of （proto）neutron stars are smaller than those without hyprons.     

Neutron star matter in a modified PNJL model

We discuss a three-flavor Nambu-Jona-Lasinio model for the quark matter equation of state with scalar diquark interaction, isoscalar vector interaction and Kobayashi-Maskawa-??t Hooft interaction. We adopt a phenomenological scheme to include possible effects of a change in the gluon pressure at finite baryon density by including a parametric dependence of the Polyakov-loop potential on the chemical potential. We discuss the results for the mass-radius relationships for hybrid neutron stars constructed on the basis of our model EoS in the context of the constraint from the recently measured mass of (1.97 ± 0.04) M _?? for the pulsar PSR J1614-2230.     

Antikaon Condensation and In-medium Kaon and Antikaon Production in Protoneutron Stars

Antikaon condensation and kaon and antikaon production in protoneutron stars are investigated in a chiral hadronic model （also referred to as the FST model in this paper）. The effects of neutrino trapping on protoneutron stars are analyzed systematically. It is shown that neutrino trapping makes the critical density of K^- condensation delay to higher density and fifo condensation not occur. The equation of state （EOS） of （proto）neutron star matter with neutrino trapping is stiffer than that without neutrino trapping. As a result, the maximum masses of （proto）neutron stars with neutrino trapping are larger than those without neutrino trapping. If hyperons are taken into account, antikaon does not form a condensate in （proto）neutron stars. Meanwhile, the corresponding EOS becomes much softer, and the maximum masses of （proto）neutron stars are smaller than those without hyprons. Finally, our results illustrate that the Q values for K^＋ and K^- production in （proto）neutron stars are not sensitive to neutrino trapping and inclusion of hyperons.     

Nonextensive statistical effects in protoneutron stars

We investigate the bulk properties of protoneutron stars in the framework of a relativistic mean-field theory based on nonextensive statistical mechanics, characterized by power-law quantum distributions. We study the relevance of nonextensive statistical effects on the b \beta -stable equation of state at fixed entropy per baryon, in the presence and in the absence of trapped neutrinos, for nucleonic and hyperonic matter. We show that nonextensive statistical effects could play a crucial role in the structure and in the evolution of the protoneutron stars also for small deviations from the standard Boltzmann-Gibbs statistics.     

Protoneutron star cooling with convection: the effect of the symmetry energy

We model neutrino emission from a newly born neutron star subsequent to a supernova explosion to study its sensitivity to the equation of state, neutrino opacities, and convective instabilities at high baryon density. We find the time period and spatial extent over which convection operates is sensitive to the behavior of the nuclear symmetry energy at and above nuclear density. When convection ends within the protoneutron star, there is a break in the predicted neutrino emission that may be clearly observable.     

Kaon properties in (proto-)neutron star matter

The modification of kaon and antikaon properties in the interior of (proto-)neutron stars is investigated using a chiral SU(3) model. The parameters of the model are fitted to nuclear-matter saturation properties, baryon octet vacuum masses, hyperon optical potentials and low-energy kaon-nucleon scattering lengths. We study the kaon/antikaon medium modification and explore the possibility of antikaon condensation in (proto-)neutron star matter at zero as well as finite temperature/entropy and neutrino content. The effect of hyperons on kaon and antikaon optical potentials is also investigated at different stages of the neutron star evolution.     

Effect of f0(975) and φ(1020) Mesons on Neutron Star Mater

In the RMF approach, considering the contributions of the σ^* and φ mesons and the hyperons in the baryon octet {N,P,Λ,∑^－,∑⁰,∑⁺,Ξ^－,Ξ⁰}, the properties of neutron star matter have been investigated. It is found that with the contributions of the σ^* and φ mesons, the critical baryon density of hyperon appearance decreases, the number of hyperons increases, the transition density ρ_0H of hyperon stars decreases, the equation of state turns soft, the maximum mass of neutron star decreases and the corresponding radius increases, the central density, the central energy density and the central pressure are all reduced.     

Quark deconfinement in neutron star cores

Whether or not the deconfined quark phase exists in neutron star cores is an open question. We use two realistic effective quark models, the three-flavor Nambu-Jona-Lasinio model and the modified quark-meson coupling model, to describe the neutron star matter. We show that the modified quark-meson coupling model, which is fixed by reproducing the saturation properties of nuclear matter, can be consistent with the experimental constraints from nuclear collisions. After constructing possible hybrid equations of state (EOSes) with an unpaired or color superconducting quark phase with the assumption of the sharp hadron-quark phase transition, we discuss the observational constraints from neutron stars on the EOSes. It is found that the neutron star with pure quark matter core is unstable and the hadronic phase with hyperons is denied, while hybrid EOSes with a two-flavor color superconducting phase or unpaired quark matter phase are both allowed by the tight and most reliable constraints from two stars Ter 5 I and EXO 0748-676. And the hybrid EOS with an unpaired quark matter phase is allowed even compared with the tightest constraint from the most massive pulsar star PSR J0751+1807.     

Pesponse of the Neutron Star Properties to the Equation of State at Low Density

Using the RMF theory to describe the neutron liquid region in the neutron star and the Fermi gas model or FMT, BPS,and BBP model to describe the crust of the neutron star (referred as Fermi gas+RMF and RMF* respectively),the properties of the neutron star are calculated and compared with those from the RMF theory. Although the EOS at low density has negligible influence on the maximum mass of the neutron star, and its corresponding central density, energy density, and pressure, it changes the mass-radius relationship of neutron stars considerably. The differences of the neutron star radius corresponding to maximum mass between the RMF theory and RMF* calculations are 0.23-0.33 km.