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Register a new userTowards Understanding Astrophysical Effects of Nuclear Symmetry Energy
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Determining the Equation of State (EOS) of dense neutron-rich nuclear matter is a shared goal of both nuclear physics and astrophysics. Except possible phase transitions, the density dependence of nuclear symmetry esym is the most uncertain part of the EOS of neutron-rich nucleonic matter especially at supra-saturation densities. Much progresses have been made in recent years in predicting the symmetry energy and understanding why it is still very uncertain using various microscopic nuclear many-body theories and phenomenological models. Simultaneously, significant progresses have also been made in probing the symmetry energy in both terrestrial nuclear laboratories and astrophysical observatories. In light of the GW170817 event as well as ongoing or planned nuclear experiments and astrophysical observations probing the EOS of dense neutron-rich matter, we review recent progresses and identify new challenges to the best knowledge we have on several selected topics critical for understanding astrophysical effects of the nuclear symmetry energy.
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In the framework of the relativistic mean field model with Thomas-Fermi approximation, we study the structures of low density nuclear matter in a three-dimensional geometry with reflection symmetry. The numerical accuracy and efficiency are improved by expanding the mean fields according to fast cosine transformation and considering only one octant of the unit cell. The effect of finite cell size is treated carefully by searching for the optimum cell size. Typical pasta structures (droplet, rod, slab, tube, and bubble) arranged in various crystalline configurations are obtained for both fixed proton fractions and $beta$-equilibration. It is found that the properties of droplets/bubbles are similar in body-centered cubic (BCC) and face-centered cubic (FCC) lattices, where the FCC lattice generally becomes more stable than BCC lattice as density increases. For the rod/tube phases, the honeycomb lattice is always more stable than the simple one. By introducing an $omega$-$rho$ cross coupling term, we further examine the pasta structures with a smaller slope of symmetry energy $L = 41.34$ MeV, which predicts larger onset densities for core-crust transition and non-spherical nuclei. Such a variation due to the reduction of $L$ is expected to have impacts on various properties in neutron stars, supernova dynamics, and binary neutron star mergers.
We exploit the many-body self-consistent Greens function method to analyze finite-temperature properties of infinite nuclear matter and to explore the behavior of the thermal index used to simulate thermal effects in equations of state for astrophysical applications. We show how the thermal index is both density and temperature dependent, unlike often considered, and we provide an error estimate based on our ${it ab~initio}$ calculations. The inclusion of many-body forces is found to be critical for the density dependence of the thermal index. We also compare our results to a parametrization in terms of the density dependence of the nucleon effective mass. Our study questions the validity of predictions made for the gravitational-wave signal from neutron-star merger simulations with a constant thermal index.
A thorough understanding of properties of neutron stars requires both a reliable knowledge of the equation of state (EOS) of super-dense nuclear matter and the strong-field gravity theories simultaneously. To provide information that may help break this EOS-gravity degeneracy, we investigate effects of nuclear symmetry energy on the gravitational binding energy of neutron stars within GR and the scalar-tensor subset of alternative gravity models. We focus on effects of the slope $L$ of nuclear symmetry energy at saturation density and the high-density behavior of nuclear symmetry energy. We find that the variation of either the density slope $L$ or the high-density behavior of nuclear symmetry energy leads to large changes in the binding energy of neutron stars. The difference in predictions using the GR and the scalar-tensor theory appears only for massive neutron stars, and even then is significantly smaller than the difference resulting from variations in the symmetry energy.
The density dependence of the nuclear symmetry energy is inspected using the Statistical Multifragmentation Model with Skyrme effective interactions. The model consistently considers the expansion of the fragments volumes at finite temperature at the freeze-out stage. By selecting parameterizations of the Skyrme force that lead to very different equations of state for the symmetry energy, we investigate the sensitivity of different observables to the properties of the effective forces. Our results suggest that, in spite of being sensitive to the thermal dilation of the fragments volumes, it is difficult to distinguish among the Skyrme forces from the isoscaling analysis. On the other hand, the isotopic distribution of the emitted fragments turns out to be very sensitive to the force employed in the calculation.
New observational data of neutron stars since GW170817 have helped improve our knowledge about nuclear symmetry energy especially at high densities. We have learned particularly: (1) The slope parameter $L$ of nuclear symmetry energy at saturation density $rho_0$ of nuclear matter from 24 new analyses is about $Lapprox 57.7pm 19$ MeV at 68% confidence level consistent with its fiducial value, (2) The curvature $K_{rm{sym}}$ from 16 new analyses is about $K_{rm{sym}}approx -107pm 88$ MeV, (3) The magnitude of nuclear symmetry energy at $2rho_0$, i.e. $E_{rm{sym}}(2rho_0)approx 51pm 13$ MeV at 68% confidence level, has been extracted from 9 new analyses of neutron star observables consistent with results from earlier analyses of heavy-ion reactions and the latest predictions of the state-of-the-art nuclear many-body theories, (4) while the available data from canonical neutron stars do not provide tight constraints on nuclear symmetry energy at densities above about $2rho_0$, the lower radius boundary $R_{2.01}=12.2$ km from NICERs very recent observation of PSR J0740+6620 of mass $2.08pm 0.07$ $M_{odot}$ and radius $R=12.2-16.3$ km at 68% confidence level sets a tight lower limit for nuclear symmetry energy at densities above $2rho_0$, (5) Bayesian inferences of nuclear symmetry energy using models encapsulating a first-order hadron-quark phase transition from observables of canonical neutron stars indicate that the phase transition shift appreciably both the $L$ and $K_{rm{sym}}$ to higher values but with larger uncertaintie , (6) The high-density behavior of nuclear symmetry energy affects significantly the minimum frequency necessary to rotationally support GW190814s secondary component of mass (2.50-2.67) $M_{odot}$ as the fastest and most massive pulsar discovered so far.
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