Extracting nuclear symmetry energies at high densities from observations of neutron stars and gravitational waves

Abstract

By numerically inverting the Tolman-Oppenheimer-Volkov (TOV) equation using an explicitly isospin-dependent parametric Equation of State (EOS) of dense neutron-rich nucleonic matter, a restricted EOS parameter space is established using observational constraints on the radius, maximum mass, tidal deformability and causality condition of neutron stars (NSs). The constraining band obtained for the pressure as a function of energy (baryon) density is in good agreement with that extracted recently by the LIGO+Virgo Collaborations from their improved analyses of the NS tidal deformability in GW170817. Rather robust upper and lower boundaries on nuclear symmetry energies are extracted from the observational constraints up to about twice the saturation density ρ0 of nuclear matter. More quantitatively, the symmetry energy at 2ρ0 is constrained to Esym(2ρ0) = 46.9 ± 10.1 MeV excluding many existing theoretical predictions scattered between Esym(2ρ0) = 15 and 100 MeV. Moreover, by studying variations of the causality surface where the speed of sound equals that of light at central densities of the most massive neutron stars within the restricted EOS parameter space, the absolutely maximum mass of neutron stars is found to be 2.40 M⊙ approximately independent of the EOSs used. This limiting mass is consistent with findings of several recent analyses and numerical general relativity simulations about the maximum mass of the possible super-massive remanent produced in the immediate aftermath of GW170817. deformability PACS. 2 6.60.Kp 1.0 1.2 1.4 1.6 1.8 2.0 2.2 0 200 400 600 800 1.0 1.2 1.4 1.6 1.8 2.0 2.2 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 J sym =600 MeV J 0 =-200 MeV K sym =-400 MeV K sym =-200 MeV K sym =0 K sym =-200 MeV J 0 =-200 MeV J sym =400 MeV J sym =600 MeV J sym =800 MeV M/M sun K sym =-200 MeV J sym =600 MeV J 0

Pseudoconformal structure in dense baryonic matter

“…It is noteworthy that as the density exceeds n 1/2 with the appearance of the pseudoconformal structure, the energy of the system E/A gets greater the higher n 1/2 is. In contrast, the property of the ground state of nuclear matter is unaffected by the location of n 1/2 : At the saturation density n 0 ≃ 0.16 fm −3 , the binding energy BE and the compression modulus K are given, for all n 1/2 considered, by BE = 15.65 MeV; K = 228.9 MeV, (55) respectively, in consistency with the values widely quoted in the literature. The symmetry energy E sym predicted by the theory is given in Fig.…”

“…Assuming that the validity holds up to n 1/2 , we can take the result of [2] as a support for the PCM EOS for the case of n 1/2 = 2n 0 . Since the V lowk RG approach successfully explains all properties of symmetric nuclear matter at n = n 0 and even up to near 2n 0 as measured in heavy-ion experiments (e.g., the symmetry energy at n = 2n 0 [55]; see below), that the PCM -that treats RI in V lowk and RII with (50) -reproduces the full V lowk RG results supports the intricate scaling behavior in RII being captured by the pseudoconformal structure.…”

Role of the symmetry energy and the neutron-matter stiffness on the tidal deformability of a neutron star with unified equations of state

“…Using the measured value M tot = 2.74 +0.04 −0.01 M from gravitational-wave observations [1] together with an empirical relation for M thres and the causality condition, Bauswein et al [84] obtained the following lower limit on the radius of a 1.6 M NS: R 1.6 ≥ 10.30 +0. 15 −0.03 km. Assuming further that the remnant lived for more than 10 ms, they obtained the more stringent constraint R 1.6 ≥ 10.68 +0.…”

“…Assuming further that the remnant lived for more than 10 ms, they obtained the more stringent constraint R 1.6 ≥ 10.68 +0. 15 −0.04 km. Note that the estimated uncertainties in these constraints do not take into account the systematic errors in the empirical relations.…”

Topology change and nuclear symmetry energy in compact-star matter

“…1 (from [5]) which summarizes the total wilderness in the NSE landscape beyond n 0 predicted by hundreds of models in SNPA. More recent analyses [6] that take into account up-to-date information including the LIGO-Virgo gravitational waves from coalescing neutron stars [7] do clear up the situation somewhat, but the wilderness largely remains. What this FIG.…”