Symmetry Parameter Constraints from a Lower Bound on Neutron-matter Energy

Abstract

We propose the existence of a lower bound on the energy of pure neutron matter (PNM) on the basis of unitary-gas considerations. We discuss its justification from experimental studies of cold atoms as well as from theoretical studies of neutron matter. We demonstrate that this bound results in limits to the density-dependent symmetry energy, which is the difference between the energies of symmetric nuclear matter and PNM. In particular, this bound leads to a lower limit to the volume symmetry energy parameter S 0 . In addition, for assumed values of S 0 above this minimum, this bound implies both upper and lower limits to the symmetry energy slope parameter L, which describes the lowest-order density dependence of the symmetry energy. A lower bound on neutron-matter incompressibility is also obtained. These bounds are found to be consistent with both recent calculations of the energies of PNM and constraints from nuclear experiments. Our results are significant because several equations of state that are currently used in astrophysical simulations of supernovae and neutron star mergers, as well as in nuclear physics simulations of heavy-ion collisions, have symmetry energy parameters that violate these bounds. Furthermore, below the nuclear saturation density, the bound on neutron-matter energies leads to a lower limit to the density-dependent symmetry energy, which leads to upper limits to the nuclear surface symmetry parameter and the neutron-star crust-core boundary. We also obtain a lower limit to the neutron-skin thicknesses of neutronrich nuclei. Above the nuclear saturation density, the bound on neutron-matter energies also leads to an upper limit to the symmetry energy, with implications for neutron-star cooling via the direct Urca process.

Open-source nuclear equation of state framework based on the liquid-drop model with Skyrme interaction

“…We note that the symmetry energy parameters J and L for all of the Skyrme parametrizations, except for LS220, are consistent with recently conjectured unitary gas constraints [17].…”

“…Hence, any EOS built for astrophysical applications depends on extrapolations based on theoretical models of microscopic interactions as well as astrophysical and experimental inputs. Ideally, these models should be supported by available nuclear experimental data [9,10] and make predictions that fulfill known astrophysical [11][12][13][14][15][16] and theoretical constraints [17][18][19].…”

Constraints on the symmetry energy and its associated parameters from nuclei to neutron stars

“…The symmetry energy obtained in this work is also consistent with them [30,31,84,93,94] within 2σ uncertainties. The curved line in the right panel is the boundary of S0 and L obtained based on the unitary gas, and the pink region is allowed [95].…”

Effects of Symmetry Energy on the Equation of State for Simulations of Core-collapse Supernovae and Neutron-star Mergers

“…Furthermore, the TM1e model predicts much smaller neutron-star radii than the original TM1 model due to the difference in the slope parameter L. It is found that the TM1e model yields a radius of 13.1 km for a canonical 1.4M ⊙ neutron star, while the corresponding value of the original TM1 model is as large as 14.2 km (Ji et al 2019). According to the constraints based on astrophysical observations and terrestrial nuclear experiments (Oertel et al 2017;Tews et al 2017;Birkhan et al 2017), the slope parameter L = 40 MeV of the TM1e model is more favored than L = 110.8 MeV of the original TM1 model. Moreover, the neutron-star radius in the TM1e model is well within the new observational data by NICER.…”