Slope Of Symmetry Energy Research Articles

Role of the symmetry energy slope in neutron stars: Exploring the model dependency

Role of the symmetry energy slope in neutron stars: Exploring the model dependency

Hybrid Star Models in the Light of New Multimessenger Data

Recent astrophysical mass inferences of compact stars HESS J1731-347 and PSR J0952-0607, with extremely small and large masses respectively, as well as the measurement of the neutron skin of Ca in the CREX experiment challenge and constrain the models of dense matter. We examine the concept of hybrid stars—objects containing quark cores surrounded by nucleonic envelopes—as models that account for these new data along with other inferences. We employ a family of 81 nucleonic equations of state (EOSs) with variable skewness and slope of symmetry energy at saturation density and a constant speed-of-sound EOS for quark matter. For each nucleonic EOS, a family of hybrid EOSs is generated by varying the transition density, the energy jump, and the speed of sound. These models are tested against the data from GW170817 and J1731-347, which favor low-density soft EOS and J0592-0607 and J0740+6620, which require high-density stiff EOS. The addition of J0592-0607's mass measurement to the constraints has no significant impact on the parameter space of the admissible EOS, but allows us to explore the potential effect of pulsars more massive than J0740+6620, if such exists. We then examine the occurrence of twin configurations and quantify the ranges of masses and radii that they can possess. It is shown that including J1731-347 data favors EOSs that predict low-mass twins with M ≲ 1.3 M ⊙ that can be realized if the deconfinement transition density is low. If combined with large speed of sound in quark matter such models allow for maximum masses of hybrid stars in 2.0–2.6 M ⊙.

Correlation between the charge radii difference in mirror partner nuclei and thesymmetry energy slope* *Supported by the National Natural Science Foundation of China (12275025, 11975096) and the Fundamental Research Funds for the Central Universities (2020NTST06)

A correlation between the charge radii difference of mirror partner nuclei and the slope parameter L of symmetry energy has been built to ascertain the equation of state of isospin asymmetric nuclear matter. In this work, the influences of pairing correlations and isoscalar compression modulus on the are systematically investigated based on the Skyrme energy density functional theory. The calculated results suggest that the linear correlation between and L is decreased by the surface pairing correlations. The slope parameter deduced from the difference of charge radii of mirror-pair nuclei 32Ar-32Si, 36Ca-36S, 38Ca-38Ar, and 54Ni-54Fe falls into the range of − MeV, that is, the rather soft equation of state of asymmetric nuclear matter. Besides, the range of the slope parameter can also be influenced by the effective forces classified by various isoscalar incompressibility coefficients.

Decoding Rotating Neutron Stars: Role of the Symmetry Energy Slope

In 2023 December, the Fermi Large Area Telescope Catalog announced the discovery of 33 new millisecond pulsars. Motivated by that, in this work, I study how different values of the symmetry energy slope (L) affect the properties of static and slowly rotating neutron stars. For fixed values of angular velocity, I study how the slope influences the increase of the maximum mass, the radii of the canonical 1.4 M ⊙, its eccentricity, as well the same quantities for the 2.01 M ⊙ stars. I show that different slope values cause different variations not only in the absolute quantities but also in relative ones. Indeed, different slope values predict different values for the eccentricity, which does not depend on the absolute value of the neutron stars’ radii. Therefore, this quantity can be a powerful tool to constrain the symmetry energy slope.

Cost of Inferred Nuclear Parameters toward the f-mode Dynamical Tide in Binary Neutron Stars

Gravitational-wave (GW) observations from neutron stars (NSs) in a binary system provide an excellent scenario to constrain the nuclear parameters. The investigation of Pratten et al. has shown that the ignorance of f-mode dynamical tidal correction in the GW waveform model of the binary NS system can lead to substantial bias in the measurement of NS properties and NS equations of state. In this work, we investigate the bias in the nuclear parameters resulting from the ignorance of dynamical tidal correction. In addition, this work demonstrates the sensitivity of the nuclear parameters and the estimated constraints on nuclear parameters and NS properties from future GW observations. We infer the nuclear parameters from GW observations by describing the NS matter within the relativistic mean field model. For a population of GW events, we notice that the ignorance of dynamical tide predicts a lower median for nucleon effective mass (m*) by ∼6% compared to the scenario when dynamical tidal correction is considered. Whereas, at a 90% credible interval, m* gets constrained up to ∼5% and ∼3% in A+ (the LIGO-Virgo detectors with a sensitivity of the fifth observing run) and Cosmic Explorer, respectively. We also discuss the resulting constraints on all other nuclear parameters, including compressibility, symmetry energy, and slope of symmetry energy, considering an ensemble of GW events. We do not notice any significant impact in analyzing nuclear parameters other than m* due to the ignorance of f-mode dynamical tides.

Correlation between the symmetry energy slope and the deconfinement phase transition

We study how the nuclear symmetry energy slope (L) can affect the hadron-quark phase transition and neutron star properties. We show that the main physical quantities as the critical chemical potential and pressure are strongly influenced by the symmetry energy slope. In extreme cases, the total amount of deconfined quarks can reach up to 99% of the hybrid star mass. Published by the American Physical Society 2024

Neutron star core-crust transition and the crustal moment of inertia in the nonlinear relativistic Hartree approximation* *Supported in part by the National Natural Science Foundation of China (11775049, 12375112)

We investigate the effects of the σ meson mass ( ), symmetry energy, and slope of the symmetry energy on the neutron star core-crust transition density and the crustal moment of inertia ( ) in the nonlinear relativistic Hartree approach (RHA), which includes vacuum polarization. Although the core-crust transition density ( ), pressure ( ), and neutron star radius (R), which are all dependent on the symmetry energy, contribute to determining , we find that changing only the slope of symmetry energy within a reasonable range is not sufficient to reach % to achieve the large glitches of the Vela pulsar. However, since all three factors ( , , and R) increase with the increase in through scalar vacuum polarization, adjusting can easily achieve %.

Study of the Symmetry Energy and the Nuclear Equation of State for 13O -13B and 13N-13C Mirror Nuclei

In parallel with the shell model using the harmonic oscillator's single-particle wave functions, the Hartree-Fock approximation was also used to calculate the neutron skin thickness, the mirror charge radii, and the differences in proton radii for 13O-13B and 13N-13C mirror nuclei. The calculations were done for both mirror nuclei in the psdpn model space. Depending on the type of potential used, the calculated values of skin thickness are affected. The symmetry energy and the symmetry energy's slope at nuclear saturation density were also determined, and the ratio of the density to the saturation density of nuclear matter and the symmetry energy has a nearly linear correlation. The mirror energy displacement was calculated, and the findings corresponded well with the available experimental data for the binding energies of the studied mirror nuclei. The measured values of the symmetry energy coefficient for the pair of mirror nuclei agreed with the computed ones, and this coefficient's value rises exponentially as the difference in charge radius increases.

Imprints of the nuclear symmetry energy slope in gravitational wave signals emanating from neutron stars

Imprints of the nuclear symmetry energy slope in gravitational wave signals emanating from neutron stars

New Covariant Density Functionals of Nuclear Matter for Compact Star Simulations

We generate three families of extended covariant density functionals of nuclear matter that have varying slope of symmetry energy and skewness at nuclear saturation density, but otherwise share the same basic parameters (symmetry energy, compressibility, saturation parameters, etc.) with the standard DDME2, DD2, and MPE functionals. Tables of the parameters of these new density functionals are given, which can be straightforwardly used in DDME2, DD2, and MPE parameterization-based codes. Furthermore, we provide tables of a large number of equations of state (81 for each family) that can be used in astrophysical simulations to assess the impact of variations of the not-well-known slope of symmetry energy and skewness of nuclear systems on the astrophysics of compact objects. We also provide tables of computed integral parameters (mass, radius, and tidal deformability) that can be used, e.g., for modeling gravitational waveforms. Finally, for the extended DDME2-based parameterization, we implement a first-order phase transition to quark matter to obtain a family of equations of state that accommodates a phase transition to quark matter. Analogous tables of the equations of state and integral parameters are provided for this case as well.

Bayesian analysis of a relativistic hadronic model constrained by recent astrophysical observations

ABSTRACTWe use Bayesian analysis in order to constrain the equation of state for nuclear matter from astrophysical data related to the recent measurements from the NICER mission, LIGO/Virgo collaboration, and probability distributions of mass and radius from other 12 sources, including thermonuclear busters, and quiescent low-mass X-ray binaries. For this purpose, we base our study on a relativistic hadronic mean field model including an ω − ρ interaction. Our results indicate optimal ranges for some bulk parameters at the saturation density, namely, effective mass, incompressibility, and symmetry energy slope (L0). For instance, we find $L_0 = 50.79^{+15.16}_{-9.24}$ MeV (Case 1) and $L_0 = 75.06^{+8.43}_{-4.43}$ MeV (Case 2) in a 68 per cent confidence interval for the two cases analysed (different input ranges for L0 related to the PREX-II data). The respective parametrizations are in agreement with important nuclear matter constraints, as well as observational neutron star data, such as the dimensionless tidal deformability of the GW170817 event. From the mass–radius curves obtained from these best parametrizations, we also find the ranges of 11.97 km ≤ R1.4 ≤ 12.73 km (Case 1) and 12.34 km ≤ R1.4 ≤ 13.06 km (Case 2) for the radius of the $1.4\, \mathrm{M}_\odot$ neutron star.

Stripping Model for Short GRBs: The Impact of Nuclear Data

We investigate the impact of forthcoming nuclear data on the predictions of the neutron star (NS) stripping model for short gamma-ray bursts. The main area to which we pay attention is the NS crust. We show that the uncertain properties of the NS equation of state can significantly influence the stripping time tstr, the main dynamical parameter of the model. Based on the known time delay (tstr≈1.7 s) between the peak of the gravitational wave signal GW170817 and the detection of gamma photons from GRB170817A, we obtain new restrictions on the nuclear matter parameters, in particular, the symmetry energy slope parameter: L<114.5MeV. In addition, we study the process of nucleosynthesis in the outer and inner crusts of a low-mass NS. We show that the nucleosynthesis is strongly influenced by both the forthcoming nuclear data and the equation of state of the NS matter.

Recent astrophysical observations reproduced by a short-range correlated van der Waals-type model?

ABSTRACT We perform an improvement in a van der Waals-type model by including its effects of short-range correlations (SRCs). Attractive and repulsive parts of the nucleon–nucleon interaction are assumed to be density-dependent functions, more specifically, we adopt the Carnahan–Starling (CS) method for the latter, and a suitable expression for the former in order to reproduce the structure of the Clausius (C) real gas model. The parametrizations of the resulting model, named as Clausius-–Carnahan–Starling (CCS)-SRC model, are shown to be capable of reproducing the flow constraint at the high-density regime of symmetric nuclear matter for incompressibility values inside the range of K0 = (240 ± 20) MeV. In the context of stellar matter, our findings point out a good agreement of the CCS-SRC model with recent astrophysical observational data, namely, mass–radius contours and dimensionless tidal deformability regions and values, coming from gravitational waves data related to the GW170817 and GW190425 events, and from the NASA’s Neutron star Interior Composition Explorer mission. Furthermore, the values for the symmetry energy slope of the model (L0) are in agreement with a recent range found for this quantity, claimed to be consistent with results reported by the updated lead radius experiment (PREX-2) collaboration. In this case, higher values of L0 are favoured, while the opposite scenario does not allow simultaneous compatibility between the model and the astrophysical data.

Nuclear masses and the equation of state of nuclear matter

Abstract The incompressible liquid-drop (ILD) model reproduces masses of stable nuclei rather well. Here we show how the ILD volume, surface, symmetry, and Coulomb energies are related to the equation of state of nuclear matter using the Oyamatsu–Iida (OI) macroscopic nuclear model, which has reasonable many-body energy and isoscalar inhomogeneity gradient energy. We use 304 update interactions, covering wide ranges of the incompressibility K0 of symmetric matter and the density slope of symmetry energy L, which fit almost equally empirical mass and radius data of stable nuclei. Thus, the K0 and L dependences are nearly frozen in stable nuclei as in the ILD model, leading to clear correlations among interaction and saturation parameters. Furthermore, we assume that the surface energy of the OI model is twice as large as the gradient energy using the size equilibrium conditions of the ILD and OI models. Then, the four energies of the ILD and OI models agree well for stable nuclei with A ≳ 40. Meanwhile, the OI model with L ≲ 100 MeV predicts the latest mass data better than those of stable nuclei, and we suggest 20 ≲ L ≲ 90 MeV, although the lower boundary is not constrained well.

Impacts of symmetry energy slope on the oscillation frequencies of neutron stars with short-range correlation and admixed dark matter

Oscillation modes of compact stars, in general, can serve as a fingerprint in determining the equation of state (EOS) of dense matter. In this study, we examine the impact of symmetry energy slope (L) on the oscillation frequencies of neutron stars (NSs) with nucleon–nucleon short range correlation (SRC) and admixed dark matter (DM) for the first time within the relativistic mean-field theory. By adjusting the L, we revise the EOS and coupling parameters in light of the SRC and DM effects, and construct the new sets. The results reveal that NSs containing SRC and DM inside are more likely to satisfy the observational constraints, and we find that smaller L exhibits larger fundamental non-radial and radial frequencies, and that the effect on large separation is also mainly concentrated in the low-mass region. Moreover, we update the linear relationship between the non-radial frequency and mean density, and we further give empirical relations between non-radial and radial frequencies and tidal deformability at different L for 1.4 and 2. These findings will enable us to more effectively confine the NS EOSs, in turn, also provide a strategy to place constraints on the L.

A Deep Learning Approach to Extracting Nuclear Matter Properties from Neutron Star Observations

Understanding the equation of state of dense neutron-rich matter remains a major challenge in modern physics and astrophysics. Neutron star observations from electromagnetic and gravitational wave spectra provide critical insights into the behavior of dense neutron-rich matter. The next generation of telescopes and gravitational wave detectors will offer even more detailed neutron-star observations. Employing deep learning techniques to map neutron star mass and radius observations to the equation of state allows for its accurate and reliable determination. This work demonstrates the feasibility of using deep learning to extract the equation of state directly from observations of neutron stars, and to also obtain related nuclear matter properties such as the slope, curvature, and skewness of nuclear symmetry energy at saturation density. Most importantly, it shows that this deep learning approach is able to reconstruct realistic equations of state and deduce realistic nuclear matter properties. This highlights the potential of artificial neural networks in providing a reliable and efficient means to extract crucial information about the equation of state and related properties of dense neutron-rich matter in the era of multi-messenger astrophysics.

Systematic analysis of the impacts of symmetry energy parameters on neutron star properties

The impacts of various symmetry energy parameters on the properties of neutron stars (NSs) have been recently investigated, and the outcomes are at variance, as summarized in Table III of Phys. Rev. D 106, 063005 (2022). We have systematically analyzed the correlations of slope and curvature parameters of symmetry energy at the saturation density ($\rho_0=0.16 \text{fm}^{-3}$) with the tidal deformability and stellar radius of non-spinning neutron stars in the mass range of $1.2 - 1.6 M_\odot$ using a large set of minimally constrained equations of state (EoSs). The EoSs at low densities correspond to the nucleonic matter and are constrained by empirical ranges of a few low-order nuclear matter parameters from the finite nuclei data and the pure neutron matter EoS from chiral effective field theory. The EoSs at high densities ($\rho > 1.5 - 2\rho_0$) are obtained by a parametric form for the speed of sound that satisfies the causality condition. Several factors affecting the correlations between the NS properties and the individual symmetry energy parameters usually encountered in the literature are considered. These correlations are quite sensitive to the choice of the distributions of symmetry energy parameters and their interdependence. But, variations of NS properties with the pressure of $\beta -$ equilibrated matter at twice the saturation density remain quite robust which maybe due to the fact that the pressure depends on the combination of multiple nuclear matter parameters that describe the symmetric nuclear matter as well as the density dependence of the symmetry energy. Our results are practically insensitive to the behavior of EoS at high densities.

Systematic correlation analysis between the nuclear matter parameters and neutron star properties within relativistic mean-field theory

Motivated by constraining the neutron star properties and eliminating their uncertainties based on the constraints on nuclear matter parameters extracted from the terrestrial experiments, the correlations between a mount of nuclear matter parameters and neutron star properties have been analyzed by the selected equation of states within the relativistic mean-field theory and used to constrain the neutron star properties. It is found that the radius $R$, tidal deformability $\mathrm{\ensuremath{\Lambda}}$, and other neutron star properties have a notable correlation with the slope of symmetry energy $L$ for the typical neutron stars, and the ${R}_{1.4}$ and ${\mathrm{\ensuremath{\Lambda}}}_{1.4}$ restricted by the constraint on $L=54\ifmmode\pm\else\textpm\fi{}8\text{ }\text{ }\mathrm{MeV}$ can be consistent with the GW170817 and NICER observation constraints. Furthermore, it is shown that $L$ also has a good correlation with the properties of low-mass neutron stars, such as the gravitational binding energy $|{E}_{g}|$. The $|{E}_{g}|$ of low-mass neutron stars can be theoretically well constrained with the constraint range of $L$.

Elastic properties of nuclear pasta in a fully three-dimensional geometry

Realistic estimations on the elastic properties of neutron star matter are carried out with a large strain (ε≲0.5) in the framework of relativistic-mean-field model with Thomas-Fermi approximation, where various crystalline configurations are considered in a fully three-dimensional geometry with reflection symmetry. Our calculation confirms the validity of assuming Coulomb crystals for the droplet phase above neutron drip density, which nonetheless does not work at large densities since the elastic constants are found to be decreasing after reaching their peaks. Similarly, the analytic formulae derived in the incompressible liquid-drop model give excellent description for the rod phase at small densities, which overestimates the elastic constants at larger densities. For slabs, due to the negligence on the variations of their thicknesses, the analytic formulae from liquid-drop model agree qualitatively but not quantitatively with our numerical estimations. By fitting to the numerical results, these analytic formulae are improved by introducing dampening factors. The impacts of nuclear symmetry energy are examined adopting two parameter sets, corresponding to the slope of symmetry energy L=41.34 and 89.39 MeV. Even with the uncertainties caused by the anisotropy in polycrystallines, the elastic properties of neutron star matter obtained with L=41.34 and 89.39 MeV are distinctively different, results in detectable differences in various neutron star activities.

Constraints on Neutron Skin Thickness and Nuclear Deformations Using Relativistic Heavy-ion Collisions from STAR

In these proceedings, we present the measurements of neutron skin thickness and nuclear deformation using isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV by the STAR detector. The significant deviations from unity of the isobar ratios of elliptic flow $v_{2}$, triangular flow $v_{3}$, mean $p_{\rm T}$ fluctuations $\langle\delta p_{\rm T}^{2}\rangle/\langle p_{\rm T}\rangle^{2}$, and asymmetric cumulant ${\rm ac}_{2}\{3\}$ indicate large differences in their quadrupole and octuple deformations. The significant deviations of the isobar ratios of produced hadron multiplicity $N_{\rm ch}$, mean transverse momentum $\langle p_{\rm T}\rangle$, and net charge number $\Delta Q$ indicate a halo-type neutron skin for the Zr nucleus, much thicker than for the Ru nucleus, consistent with nuclear structure calculations. We discuss how we extract the neutron skin thickness, the symmetry energy slope parameter, and deformation parameters from data.