Constraint on nuclear symmetry energy imposed by f-mode oscillation of neutron stars

Due to improvements in the sensitivity of gravitational wave(GW)detectors,the detection of GWs originating from the fundamental quasi-normal mode(f-mode)of neutron stars has become possible.The future detection of GWs originating from the f-mode of neutron stars will provide a potential way to improve our understanding of the nature of nuclear matter inside neutron stars.In this work,we investigate the constraint imposed by the f-mode oscillation of neutron stars on the symmetry energy of nuclear matter using Bayesian analysis and parametric EOS.It is shown that if the frequency of the f-mode of a neutron star of known mass is observed precisely,the symmetry energy at twice the saturation density(E_(sym)(2_(ρ0)))of nuclear matter can be constrained within a relatively narrow range.For example,when all the following parameters are within the given intervals:220≤K0≤260 Me V,28≤E_(sym)(ρ0)≤36 Me V,30≤L≤90 Me V,-800≤J0≤400 Me V,-400≤K_(sym)≤100 Me V,-200≤Jsym≤800 Me V,E_(sym)(2ρ0)will be constrained to within-+48.85.56.6 Me V if the f-mode frequency of a canonical neutron star(1.4 M■)is observed to be 1.720 k Hz with a 1%relative error.Furthermore,if only f-mode frequency detection is available,i.e.there is no stellar mass measurement,a precisely detected f-mode frequency can also impose an accurate constraint on the symmetry energy.For example,given the same parameter space and the same assumed observed f-mode frequency mentioned above,and assuming that the stellar mass is in the range of 1.2–2.0 Me,E_(sym)(2ρ0)will be constrained to within 49.5■MeV.In addition,it is shown that a higher slope of 69≤L≤143 Me V will give a higher posterior distribution of E_(sym)(2ρ0),53.8■MeV.

Exploring nuclear symmetry energy with isospin dependence in neutron skin thickness of nuclei

We propose an alternative way to constrain the density dependence of the symmetry energy from the neutron skin thickness of nuclei which shows a linear relation to both the isospin asymmetry and the nuclear charge with a form of Z2/3. The relation of the neutron skin thickness to the nuclear charge and isospin asymmetry is systematically studied with the data from antiprotonic atom measurement, and with the extended Thomas-Fermi approach incorporating the Skyrme energy density functional. An obviously linear relationship between the slope parameter L of the nuclear symmetry energy and the isospin asymmetry dependent parameter of the neutron skin thickness can be found, by adopting 70 Skyrme interactions in the calculations. Combining the available experimental data, the constraint of -20 MeV 〈～ L 〈～ 82 MeV on the slope parameter of the symmetry energy is obtained. The Skyrme interactions satisfying the constraint are selected.

Experiment of constraining symmetry energy at supra-saturation density with π^-/π^+ at HIRFL-CSR

The possibility of the experiment for constraining the symmetry energy Esym（ρ） at supra-densities via π^-/π^＋ probe on the external target experiment of phase I （ ETE（I） ） with part coverage at forward angle at HIRFL-CSR is studied for the first time by using the isospin and momentum dependent hadronic transport model IBUU04. Based on the transport simulation with Au＋Au collisions at 400 MeV/u, it is found that the differential π^-/π^＋ ratios are more sensitive to Esym（ρ） at forward angles in laboratory reference, compared with the total yield ratio widely proposed. The insufficient coverage at lower transverse momentum maintains the sensitivity of the dependence of π^-/π^＋ ratio on the Esym（ρ） at high density, indicating that the ETF （I） under construction in Lanzhou provides the possibility of performing the experiment for probing the asymmetric nuclear equation of state.

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at Elab= 0.09 ~ 1.5 GeV/nucleon

By incorporating an iso spin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics(UrQMD)model,we systematically investigate effects of the neutron-proton effective mass splitting m*n-p=m*n-m*p/m and the density-dependent nuclear symmetry energy Esym(ρ)on the elliptic flow v2 in197Au+197 Au collisions at beam energies from 0.09 to 1.5 GeV/nucleon.It is found that at higher beam energies(≥0.25 GeV/nucleon)with the approximately 75 MeV difference in slopes of the two different Esym(ρ),and the variation of m*n-p ranging from-0.03 to 0.03 at saturation density with isospin asymmetryδ=(ρn-ρp)/ρ-0.2,the Esym(ρ)has a stronger influence on the difference in v2 between neutrons and protons,i.e.,v2n-v2p,than m*n-p has.Meanwhile,at lower beam energies(≤0.25 GeV/nucleon),v2n-v2p is sensitive to both the Esym(ρ)and the m*n-p.Moreover,the influence of m*n-p on v2n-v2p is more evident with the parameters of this study when using the soft,rather than stiff,symmetry energy.

Properties of nuclear pastas

In this review we study the nuclear pastas as they are expected to be formed in neutron star crusts.We start with a study of the pastas formed in nuclear matter(composed of protons and neutrons),we follow with the role of the electron gas on the formation of pastas,and we then investigate the pastas in neutron star matter(nuclear matter embedded in an electron gas).Nuclear matter(NM)at intermediate temperatures(1 MeV≤T≤15.MeV),at saturation and and sub-saturation densities,and with proton content ranging from 30%to 50%was found to have liquid,gaseous and liquid-gas mixed phases.The isospin-dependent phase diagram was obtained along with the critical points,and the symmetry energy was calculated and compared to experimental data and other theories.At low temperatures(T≤1 MeV)NM produces crystal-like structures around satura-tion densities,and pasta-like structures at sub-saturation densities.Properties of the pasta structures were studied with cluster-recognition algorithms,caloric curve,the radial distribution function,the Lindemann coefficient,Kolmogorov statistics,Minkowski functionals;the symmetry energy of the pasta showed a connection with its morphology.Neutron star matter(NSM)is nuclear matter embedded in an electron gas.The electron gas is included in the calculation by the inclusion of an screened Coulomb potential.To connect the NM pastas with those in neutron star matter(NSM),the role the strength and screening length of the Coulomb interaction have on the formation of the pastas in NM was investigated.Pasta was found to exist even without the presence of the electron gas,but the effect of the Coulomb interaction is to form more defined pasta structures,among other effects.Likewise,it was determined that there is a minimal screening length for the developed structures to be independent of the cell size.Neutron star matter was found to have similar phases as NM,phase transitions,symmetry energy,structure function and thermal conductivity.Like in NM,pasta forms at around T≈1.5 MeV,and liquid-to-solid phase changes were detected at T≈0.5 MeV.The structure function and the symmetry energy were also found to depend on the pasta structures.