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Register a new userCurvature-slope correlation of nuclear symmetry energy and its imprints on the crust-core transition, radius and tidal deformability of canonical neutron stars
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Background: The nuclear symmetry energy $E_{sym}(rho)$ encodes information about the energy necessary to make nuclear systems more neutron-rich. While its slope parameter L at the saturation density $rho_0$ of nuclear matter has been relatively well constrained by recent astrophysical observations and terrestrial nuclear experiments, its curvature $K_{rm{sym}}$ characterizing the $E_{sym}(rho)$ around $2rho_0$ remains largely unconstrained. Over 520 calculations for $E_{sym}(rho)$ using various nuclear theories and interactions in the literature have predicted several significantly different $K_{rm{sym}}-L$ correlations. Purpose: If a unique $K_{rm{sym}}-L$ correlation of $E_{sym}(rho)$ can be firmly established, it will enable us to progressively better constrain the high-density behavior of $E_{sym}(rho)$ using the available constraints on its slope parameter L. We investigate if and by how much the different $K_{rm{sym}}-L$ correlations may affect neutron star observables. Method: A meta-model of nuclear Equation of States (EOSs) with three representative $K_{rm{sym}}-L$ correlation functions is used to generate multiple EOSs for neutron stars. We then examine effects of the $K_{rm{sym}}-L$ correlation on the crust-core transition density and pressure as well as the radius and tidal deformation of canonical neutron stars. Results:The $K_{rm{sym}}-L$ correlation affects significantly both the crust-core transition density and pressure. It also has strong imprints on the radius and tidal deformability of canonical neutron stars especially at small L values. The available data from LIGO/VIRGO and NICER set some useful limits for the slope L but can not distinguish the three representative $K_{rm{sym}}-L$ correlations considered.
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The slope of the nuclear symmetry energy at saturation density $L$ is pointed out as a crucial quantity to determine the mass and width of neutron-star crusts. This letter clarifies the relation between $L$ and the core-crust transition. We confirm that the transition density is soundly correlated with $L$ despite differences between models, and we propose a clear understanding of this correlation based on a generalised liquid drop model. Using a large number of nuclear models, we evaluate the dispersion affecting the correlation between the transition pressure $P_t$ and $L$. From a detailed analysis it is shown that this correlation is weak due to a cancellation between different terms. The correlation between the isovector coefficients $K_{rm sym}$ and $L$ plays a crucial role in this discussion.
The radii and tidal deformabilities of neutron stars are investigated in the framework of relativistic mean-field (RMF) model with different density-dependent behaviors of symmetry energy. To study the effects of symmetry energy on the properties of neutron stars, an $omega$ meson and $rho$ meson coupling term is included in a popular RMF Lagrangian, i.e. the TM1 parameter set, which is used for the widely used supernova equation of state (EoS) table. The coupling constants relevant to the vector-isovector meson, $rho$, are refitted by a fixed symmetry energy at subsaturation density and its slope at saturation density, while other coupling constants remain the same as the original ones in TM1 so as to update the supernova EoS table. The radius and mass of maximum neutron stars are not so sensitive to the symmetry energy in these family TM1 parameterizations. However, the radii at intermediate mass region are strongly correlated with the slope of symmetry energy. Furthermore, the dimensionless tidal deformabilities of neutron stars are also calculated within the associated Love number. We find that its value at $1.4 M_odot$ has a linear correlation to the slope of symmetry energy being different from the previous studied. With the latest constraints of tidal deformabilities from GW170817 event, the slope of symmetry energy at nuclear saturation density should be smaller than $60$ MeV in the family TM1 parameterizations. This fact supports the usage of lower symmetry energy slope for the update supernova EoS, which is applicable to simulations of neutron star merger. Furthermore, the analogous analysis are also done within the family IUFSU parameter sets. It is found that the correlations between the symmetry energy slope with the radius and tidal deformability at $1.4 M_odot$ have very similar linear relations in these RMF models.
A number of observed phenomena associated with individual neutron star systems or neutron star populations find explanations in models in which the neutron star crust plays an important role. We review recent work examining the sensitivity to the slope of the symmetry energy $L$ of such models, and constraints extracted on $L$ from confronting them with observations. We focus on six sets of observations and proposed explanations: (i) The cooling rate of the neutron star in Cassiopeia A, confronting cooling models which include enhanced cooling in the nuclear pasta regions of the inner crust, (ii) the upper limit of the observed periods of young X-ray pulsars, confronting models of magnetic field decay in the crust caused by the high resistivity of the nuclear pasta layer, (iii) glitches from the Vela pulsar, confronting the paradigm that they arise due to a sudden re-coupling of the crustal neutron superfluid to the crustal lattice after a period during which they were decoupled due to vortex pinning, (iv) The frequencies of quasi-periodic oscillations in the X-ray tail of light curves from giant flares from soft gamma-ray repeaters, confronting models of torsional crust oscillations, (v) the upper limit on the frequency to which millisecond pulsars can be spun-up due to accretion from a binary companion, confronting models of the r-mode instability arising above a threshold frequency determined in part by the viscous dissipation timescale at the crust-core boundary, and (vi) the observations of precursor electromagnetic flares a few seconds before short gamma-ray bursts, confronting a model of crust shattering caused by resonant excitation of a crustal oscillation mode by the tidal gravitational field of a companion neutron star just before merger.
The possibility to draw links between the isospin properties of nuclei and the structure of compact stars is a stimulating perspective. In order to pursue this objective on a sound basis, the correlations from which such links can be deduced have to be carefully checked against model dependence. Using a variety of nuclear effective models and a microscopic approach, we study the relation between the predictions of a given model and those of a Taylor density development of the corresponding equation of state: this establishes to what extent a limited set of phenomenological constraints can determine the core-crust transition properties. From a correlation analysis we show that a) the transition density $rho_t$ is mainly correlated with the symmetry energy slope $L$, b) the proton fraction $Y_{p,t}$ with the symmetry energy and symmetry energy slope $(J,L)$ defined at saturation density, or, even better, with the same quantities defined at $rho=0.1$ fm$^{-3}$, and c) the transition pressure $P_t$ with the symmetry energy slope and curvature $(J,K_{rm sym})$ defined at $rho=0.1$ fm$^{-3}$.
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