Nuclear Laboratory Experiments Research Articles

Constraints on the Muon Fraction and Density Profile in Neutron Stars

Abstract Muons in neutron stars (NSs) play especially important roles in addressing several interesting new physics questions associated with detecting as well as understanding interactions and astrophysical effects of muonphilic dark matter particles. The key model inputs for studying the latter are the total muon mass M μ , the muon mass fraction M μ /M NS over the NS mass M NS, and the muon radial density profile ρ μ (r) in NSs of varying masses. We investigate these quantities within a minimum model for the core of NSs consisting of neutrons, protons, electrons, and muons using an explicitly isospin-dependent parametric equation of state (EOS) constrained by available nuclear laboratory experiments and the latest astrophysical observations of NS masses, radii, and tidal deformabilities. We found that the absolutely maximum muon mass M μ and its mass fraction M μ /M NS in the most massive NSs allowed by causality are about 0.025 M ⊙ and 1.1%, respectively. For the most massive NS of mass 2.14 M ⊙ observed so far, they reduce to about 0.020 M ⊙ and 0.9%, respectively. We also study respective effects of individual parameters describing the EOS of high-density neutron-rich nucleonic matter on the muon contents in NSs with varying masses. We found that the most important but uncertain nuclear physics ingredient for determining the muon contents in NSs is the high-density nuclear symmetry energy.

Implications of the Mass M⊙ of PSR J0740+6620 on the Equation of State of Super-dense Neutron-rich Nuclear Matter

Abstract We study the implications of the very recently reported mass M ⊙ of PSR J0740+6620 on the equation of state (EOS) of super-dense neutron-rich nuclear matter with respect to existing constraints on the EOS based on the mass M = 2.01 ± 0.04 M ⊙ of PSR J0348+0432, the maximum tidal deformability of GW170817, and earlier results of various terrestrial nuclear laboratory experiments. The lower limit of the skewness J 0 measuring the stiffness of super-dense isospin-symmetric nuclear matter is raised from about −220 MeV to −150 MeV, significantly reducing its current uncertainty range. The lower bound of the high-density symmetry energy also increases appreciably leading to a rise of the minimum proton fraction in neutron stars at β-equilibrium from about 0% to 5% around three times the saturation density of nuclear matter. The difficulties for some of the most widely used and previously well tested model EOSs to simultaneously predict both a maximum mass higher than 2.17 M ⊙ and a pressure consistent with that extracted from GW170817 present some interesting new challenges for nuclear theories.

Imprints of the nuclear symmetry energy on the tidal deformability of neutron stars

Applying an equation of state (EOS) with its symmetric nuclear matter contribution and low-density symmetry energy Esym(ρ) constrained by heavy-ion reaction data, we calculate the dimensionless tidal deformability Λ of neutron stars in coalescing binary systems. Corresponding to the partially constrained EOS that previously predicted a radius of 11.5 km ≤ ≤ 13.6 km for canonical neutron-star configurations, Λ is found to be in the range of 292 ≤ ≤ 680, consistent with the very recent observation of the GW170817 event. We investigate the effect of the high-density behavior of Esym(ρ) on the tidal properties of neutron stars and find that while Λ depends strongly on the details of the symmetry energy, different trends of Esym(ρ) lead to very similar values of Λ. In particular, the transition from stiff/soft-to-soft/stiff Esym(ρ) could yield the same Λ. Thus, measuring Λ alone may not determine completely the density dependence of the symmetry energy. Coherent analyses of the dense neutron-rich nuclear matter EOS underlying both nuclear laboratory experiments and astrophysical observations are therefore necessary to break this degeneracy and determine precisely the details of the Esym(ρ).

Impact of the equation-of-state–gravity degeneracy on constraining the nuclear symmetry energy from astrophysical observables

There is a degeneracy between the equation of state (EOS) of superdense neutron-rich nuclear matter and the strong-field gravity in understanding properties of neutron stars. While the EOS is still poorly known, there are also longstanding ambiguities in choosing General Relativity or alternative gravity theories in the not-so-well tested strong-field regime. Besides possible appearance of hyperons and new phases, the most uncertain part of the nucleonic EOS is currently the density dependence of nuclear symmetry energy. To provide information that may help break the EOS-gravity degeneracy, we investigate effects of symmetry energy within its uncertain range determined by terrestrial nuclear laboratory experiments on the gravitational binding energy and spacetime curvature of neutron stars within GR and the scalar-tensor (ST) theory of gravity. In particular, we focus on effects of the following parameters characterizing the EOS of neutron-rich nucleonic matter: (1) the incompressibility $K_0$ of symmetric nuclear matter, (2) the slope $L$ of symmetry energy at saturation density and (3) the high-density behavior of symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of symmetry energy leads to large changes in both the binding energy and curvature of neutron stars while effects of varying the more constrained $K_0$ are negligibly small. The difference in predictions using the GR and the ST theory appears only for massive neutron stars, and is significantly smaller than the differences resulting from variations in the symmetry energy. We conclude that within the ST theory of gravity, the EOS-gravity degeneracy has been broken by the recent relativistic pulsar measurements, and that measurements of neutron star properties sensitive to the compactness constrain mainly the density dependence of the symmetry energy.

Constraining the neutron–proton effective mass splitting using empirical constraints on the density dependence of nuclear symmetry energy around normal density

According to the Hugenholtz–Van Hove theorem, nuclear symmetry energy Esym(ρ) and its slope L(ρ) at an arbitrary density ρ are determined by the nucleon isovector (symmetry) potential Usym(ρ,k) and its momentum dependence ∂Usym∂k. The latter determines uniquely the neutron–proton effective k-mass splitting mn−p⁎(ρ,δ)≡(mn⁎−mp⁎)/m in neutron-rich nucleonic matter of isospin asymmetry δ. Using currently available constraints on the Esym(ρ0) and L(ρ0) at normal density ρ0 of nuclear matter from 28 recent analyses of various terrestrial nuclear laboratory experiments and astrophysical observations, we try to infer the corresponding neutron–proton effective k-mass splitting mn−p⁎(ρ0,δ). While the mean values of the mn−p⁎(ρ0,δ) obtained from most of the studies are remarkably consistent with each other and scatter very closely around an empirical value of mn−p⁎(ρ0,δ)=0.27⋅δ, it is currently not possible to scientifically state surely that the mn−p⁎(ρ0,δ) is positive within the present knowledge of the uncertainties. Quantifying, better understanding and then further reducing the uncertainties using modern statistical and computational techniques in extracting the Esym(ρ0) and L(ρ0) from analyzing the experimental data are much needed.