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Register a new userSymmetry energy at supra-saturation densities via the Gravitational Waves from GW170817
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Motivated by the historical detection of gravitational waves from GW170817, the neutron star and the neutron drop, i.e., a certain number of neutrons confined in an external field, are systematically investigated by ab initio calculations as well as the nonrelativistic and relativistic state-of-art density functional theories. Strong correlations are found among the neutron star tidal deformability, the neutron star radius, the root-mean-square radii of neutron drops, and the symmetry energies of nuclear matter at supra-saturation densities. From these correlations and the upper limit on the tidal deformability extracted from GW170817, the neutron star radii, the neutron drop radii, and the symmetry energy at twice saturation density are respectively constrained as $R_{1.4M_{odot}}leqslant 12.94$ km, $R_{rm nd} leqslant 2.36$ fm, and $E_{mathrm{sym}}(2rho_0) leqslant 53.2$ MeV.
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Nuclear symmetry energy $E_{rm{sym}}(rho)$ at density $rho$ is normally expanded or simply parameterized as a function of $chi=(rho-rho_0)/3rho_0$ in the form of $E_{rm{sym}}(rho)approx S+Lchi+2^{-1}K_{rm{sym}}chi^2+6^{-1}J_{rm{sym}}chi^3+cdots$ using its magnitude $S$, slope $L $, curvature $K_{rm{sym}}$ and skewness $J_{rm{sym}}$ at the saturation density $rho_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not converge at supra-saturation densities where $chi$ is not small enough, hindering an accurate determination of high-density $E_{rm{sym}}(rho)$ even if its characteristic parameters at $rho_0$ are all well determined by experiments/observations. By expanding the $E_{rm{sym}}(rho)$ in terms of a properly chosen auxiliary function $Pi_{rm{sym}}(chi,Theta_{rm{sym}})$ with a parameter $Theta_{rm{sym}}$ fixed accurately by an experimental $E_{rm{sym}}(rho_{rm{r}})$ value at a reference density $rho_{rm{r}}$, we show that the shortcomings of the $chi$-expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{rm{sym}}(rho)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $chi$-order contributions and converges to the same $E_{rm{sym}}(rho)$ much faster than the conventional $chi$-expansion at densities $lesssim3rho_0$. Several quantitative demonstrations using Monte Carlo simulations are given.
Within an isospin- and momentum-dependent hadronic transport model it is shown that the recent FOPI data on the $pi^-/pi^+$ ratio in central heavy-ion collisions at SIS/GSI energies (Willy Reisdorf {it et al.}, NPA {bf 781}, 459 (2007)) provide circumstantial evidence suggesting a rather soft nuclear symmetry energy esym at $rhogeq 2rho_0$ compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.
The elliptic-flow ratio of neutrons with respect to protons in reactions of neutron rich heavy-ions systems at intermediate energies has been proposed as an observable sensitive to the strength of the symmetry term in the nuclear Equation Of State (EOS) at supra-saturation densities. The recent results obtained from the existing FOPI/LAND data for $^{197}$Au+$^{197}$Au collisions at 400 MeV/nucleon in comparison with the UrQMD model allowed a first estimate of the symmetry term of the EOS but suffer from a considerable statistical uncertainty. In order to obtain an improved data set for Au+Au collisions and to extend the study to other systems, a new experiment was carried out at the GSI laboratory by the ASY-EOS collaboration in May 2011.
The LIGO-Virgo collaboration detection of the binary neutron-star merger event, GW170817, has expanded efforts to understand the Equation of State (EoS) of nuclear matter. These measurements provide new constraints on the overall pressure, but do not elucidate its origins, by not distinguishing the contribution to the pressure from symmetry energy which governs much of the internal structure of a neutron star. By combining the neutron star EoS extracted from the GW170817 event and the EoS of symmetric matter from nucleus-nucleus collision experiments, we extract the symmetry pressure, which is the difference in pressure between neutron and nuclear matter over the density region from 1.2$rho_{0}$ to $4.5rho_{0}$. While the uncertainties in the symmetry pressure are large, they can be reduced with new experimental and astrophysical results.
Determination of the high density behavior of the symmetry energy through the simultaneous measurement of elliptic flow excitation functions of neutrons, protons and light clusters is proposed. The elliptic flow developed in relativistic heavy ion collisions has been proven theoretically and experimentally to have a unique sensitivity and robustness in probing the symmetry energy up to around $2 rho_{o}$. The knowledge of the density dependence of the symmetry energy in a broad range of densities will provide a missing link for astrophysical predictions of the neutron star mass--radius relation. In particular, the data colud provide tighter constraints on the slope parameter L and entirely new limits on $K_{sym}$, the currently poorly constrained symmetry energy curvature parameter.
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