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%.     

Influence of Entropy on Composition and Structure of Massive Protoneutron Stars

Adjusting the suitable coupling constants in relativistic mean field (RMF) theory and focusing on thermal effect of an entropy per baryon (S) from 0 to 3, we investigate the composition and structure of massive protoneutron stars corresponding PSR J1614-2230 and PSR J0348+0432. It is found that massive protoneutron stars (PNSs) have more hyperons than cold neutron stars. The entropy per baryon will stiffen the equation of state, and the influence on the pressure is more obvious at low density than high density, while the influence on the energy density is more obvious at high density than low density. It is found that higher entropy will give higher maximum mass, higher central temperature and lower central density. The entropy per baryon changes from 0 to 3, the radius of a PNS corresponding PSR J0348+0432 will increase from 12.86 km to 19.31 km and PSR J1612-2230 will increase from 13.03 km to 19.93 km. The entropy per baryon will raise the central temperature of massive PNSs in higher entropy per baryon, but the central temperature of massive PNSs maybe keep unchanged in lower entropy per baryon. The entropy per baryon will increase the moment of inertia of a massive protoneutron star, while decrease gravitational redshift of a massive neutron star.     

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.     

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.     

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.     

Effects of Gravitational Correction on Neutron Stars with Antikaon Condensation

Effects of gravitational correction through the introduction of U bosons on neutron stars with antikaon condensation are studied in the relativistic mean field theory. How the global properties of neutron stars, redshift and the momentum of inertia are modified by gravitational correction and antikaon condensation are discussed here. Results show that antikaon condensation can occur at the core of pulsar PSR J1614-2230. Gravitational correction and antikaon condensation influence each other, and when coupling constant of U bosons and baryons becomes very high, effects of antikaon condensation almost vanish. Moreover, both the redshift and the momentum of inertia of neutron stars are sensitive to the constant of U bosons. Combining with observation data, we can provide a further constraint on coupling constant of U bosons.     

Meson Effect in the Proto Neutron Star PSR J0348+0432

The effect of mesons f ₀(975) (named as f), ?(1020) (named as ?) and δ on the moment of inertia of the PNS PSR J0348+0432 is examined in the framework of the relativistic mean field theory considering the baryon octet. It is found that the energy density ε and pressure p will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f,? and δ are considered, the energy density and pressure will all decrease. It is also found that the contribution of mesons f, ? and δ to the central energy density is only the central energy density’s 0.06 ～0.6% whereas the contribution of mesons f, ? and δ to the central pressure is the central pressure’s 4 ～7%. For the radius, it will decrease when the contributions of mesons f, ? and δ are considered. The moment of inertia I will increase considering the mesons δ whereas will decrease as the mesons f and ? being considered. When the mesons f, ? and δ are all considered, the moment of inertia will decrease. It is found that the contribution of mesons f and ? to moment of inertia is 4 ～9 times larger than that of mesons δ. Our results show that the mesons f, ? and δ contribute to the moment of inertia’s 2 ～5%.     

Calculations of mass and moment of inertia for neutron stars

Masses and moments of inertia for slowly-rotating neutron stars are calculated from the Tolman-Oppenheimer-Volkoff equations and various equations of state for neutron-star matter. We have also obtained pressure and density as a function of the distance from the centre of the star. Generally, two different equations of state are applied for particle densities n > 0.47 fm^?3 and n < 0.47 fm^?3.The maximum mass is, in our calculations for all equations of state except for the unrealistic non-relativistic ideal Fermi gas, given by 1.50 M_⊙ < M < 1.82 M_⊙, which agrees very well with “experimental results”. Corresponding results for the maximum moment of inertia are 9.5 × 10⁴⁴ g · cm² < I < 1.58 × 10⁴⁵ g · cm², which also seem to agree very well with “experimental results”. The radius of the star corresponding to maximum mass and maximum moment of inertia is given by 8.2 km < R < 10.0 km, but a smaller central density ρ_c will give a larger radius.     

Constraining the Surface Gravitational Redshift of Proto Neutron Stars with New Nucleon Coupling Constants

A new set of nucleon coupling constants (CZ11) is obtained for the relativistic mean field (RMF) theory based on the recent experimental information on the symmetry energy derived from the data from NSCL/MSU. The surface gravitational redshift of a proto neutron star (PNS) is examined within the RMF framework for the baryon octet system by using this set of parameters. It is found that the surface gravitational redshift for CZ11 is smaller than that for GL97. For the CZ11 parameter set, the surface gravitational redshift of a PNS at T=15 MeV is smaller than that at T=0 MeV. It is also found that the surface gravitational redshift corresponding to M _max/R for the CZ11 parameter set is smaller by about 10 percent than that for GL97, with M _max being the maximum mass and R being the corresponding radius.     

Search for strong gravitational lensing effect in the current GRB data of BATSE

Because gamma-ray bursts(GRBs)trace the high-z universe,there is an appreciable probability for a GRB to be gravitational lensed by galaxies in the universe.Herein we consider the gravitational lensing effect of GRBs contributed by the dark matter halos in galaxies.Assuming that all halos have the singular isothermal sphere(SIS)mass profile in the mass range 1010h?1M?M2×1013h?1M?and all GRB samples follow the intrinsic redshift distribution and luminosity function derived from the Swift LGRBs sample,we calculated the gravitational lensing probability in BATSE,Swift/BAT and Fermi/GBM GRBs,respectively.With an derived probability result in BATSE GRBs,we searched for lensed GRB pairs in the BATSE5B GRB Spectral catalog.The search did not find any convincing gravitationally lensed events.We discuss our result and future observations for GRB lensing observation.     

Effect of the neutrino magnetic moment on the properties of the muon

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2) _L × SU(2) _R × U(1) _B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ^? → e ^?γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2) _L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g ? 2)_µ anomaly are in excess of the theoretical predictions for this moment.     

A full potential all-electron calculation on electronic structure of NiO

We perform a first principle calculation on NiO system, a prototypical correlated electronic system due to partial filled 3d electronic shell, using various density functional theory (DFT) and hybrid functional methods inclusion of spin polarization (SP), on-site Coulomb repulsion U and spin–orbit coupling (SOC) effects. It is shown that localized spin density approximation (LSDA) plus U (LSDA?+?U) correctly reproduce experimental lattice parameter, while spin polarization generalized gradient approximation (SP?+?GGA?+?U) obviously overestimates lattice parameter. LSDA?+?U/SP?+?GGA?+?U band gaps and magnetic moments are in agreement with experimental data, and correctly predict NiO to be an insulator. NiO undergoes a Mott–Hubbard metal–insulator transition (MIT) by addition of Coulomb interaction U. Our LSDA?+?SOC calculation shows that SOC further splitting of Ni d e_g and t_2g orbitals into d_z2, d_xy, d_x2y2 and d_xz?+?d_yz orbitals, and SP nearly cancels out SOC effect, giving rise to symmetry of density of states (DOS) for spin-up and spin-down states, hence appearance of zero net magnetic moment. For LSDA?+?U?+?SOC calculation, combination effect of SP, U and SOC results in non-occupying of spin-up conduction band and a negligible density of states for spin-down states.     

Theg B*Bϱ andg D*Dϱ coupling constants in QCD

Theg _B*B? andg _D*D? coupling constants are calculated at the intermediate momentum transfer interval 0.5 GeV²≤Q ²≤1.5 GeV², in the context of QCD sum rules. Our predictions are in good agreement with those of the Vector Dominance Model     

The possibility of using cryofiber interferometer as detector of gravitational waves

The history of the question on the possibility of detecting gravitational waves, whose existence is predicted by the General Relativity Theory, is briefly presented. The schemes of cryofiber interferometer, which we propose to use as detector of gravitational waves with amplitude |δg _ij | = 10^?20, are described. We also consider other versions of the use of cryofiber interferometer in both applied and fundamental context, including laboratory experiments in which according to the estimates dark energy density variations can be detected. We describe briefly the optical scheme of a compact interferometric detector of vibrations of a mirror fixed at the end of a massive gravitational antenna; the compactness admits construction of a cryogenic version with cooling of all the elements of such a recording system.     

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.     

A common origin of neutralino stars and supermassive black holes

To account for the microlensing events observed in the Galactic halo, Gurevich, Zybin, and Sirota have proposed a model of gravitationally bound, noncompact objects with masses of ～(0.01–1)M _⊙. These objects are formed in the expanding Universe from adiabatic density perturbations and consist of weakly interacting particles of dark matter, for example, neutralinos. They assumed the perturbation spectrum on some small scale to have a distinct peak. We show that the existence of this peak would inevitably give rise to a large number of primordial black holes (PBHs) with masses of ～10⁵ M _⊙ at the radiation-dominated evolutionary stage of the Universe. Constraints on the coefficient of nonlinear contraction and on the compactness parameter of noncompact objects were derived from constraints on the PBH number density. We show that noncompact objects can serve as gravitational lenses only at a large PBH formation threshold, δ_c > 0.5, or if noncompact objects are formed from entropic density perturbations.     

Non-spherical magnetic moment in MnAlGe

The magnetic structure factors of MnAlGe (space groupP4/nmm) measured with polarised neutrons have been expressed in terms of the magnetic moment of the Mn atom (site symmetry tetrahedral with tetragonal distortion), the Bessel transforms 〈j _n〉 of the Mn radial functions and the fractional occupancies of the moment density in the various crystal field orbitals. The measured structure factors were least-squares fitted with the theoretical expression involving 〈j _n〉 appropriate to the Mn⁰, Mn⁺ and Mn²⁺ atoms. The best fit was got using Mn⁰ transforms, yielding 1·45µ _B as the Mn magnetic moment. The fractional occupancies of the moment density in the crystal field orbitalsA _1g,B _1g E _g andB _2g were obtained. This analysis shows the magnetic moment to be highly non-spherical with a large fractional occupancy (38%) in theA _1g orbital directed along the tetragonal axis while the fractional occupancies ofB _1g andB _2g are found to be 31% and 30% respectively. The fractional occupancy of the moment in theE _g orbital directed towards the Ge and Al atoms is very low (1%). The spatially averaged moment density of Mn in MnAlGe is more diffuse than that of Mn I and Mn II in isostructural Mn₂Sb.     

Electric dipole moment and chromoelectric dipole moment of the top quark inSU(3)C×SU(3)L×U(1)X model

We show that inSU(3) _C ×SU(3) _L ×U(1) _X model, the leading contribution to the electric and chromolelectric dipole moment of the top quark is due to the one-loop diagrams which come from exchanging the charged and neutral Higgs bosons. The dipole moments are typically of the order of 10^?19 e-cm and 10^?19 g-cm respectively, for the values of relative phases of the vev's such that CP violation is maximal. From an experimental point of view, theq ² dependence of dipole moment form factors is given.     

Neutron star magnetism

It is shown that

1. an appreciable change of magnetic moment of a neutron star cannot occur via ohmic dissipation
2. pulsars provide evidence for large internal magnetic fields in main sequence stars. If pulsars are born from stars with masses exceeding 3 ?_⊙ the internal field must be of the order of 10³-10⁴ Gauss while if they derived from less massive urstars 10² Gauss are sufficient to give rise to a magnetic moment ofM～10³⁰ Gauss cm³.