Constraining the relativistic mean-field model equations of state with gravitational wave observations

The first detection of gravitational waves from the binary neutron star merger event GW170817 has started to provide important new constraints on the nuclear equation of state at high density. The tidal deformability bound of GW170817 combined with the observed two solar mass neutron star poses a serious challenge to theoretical formulations of realistic equations of state. We analyze a fully comprehensive set of relativistic nuclear mean-field theories by confronting them with the observational bounds and the measured neutron-skin thickness. We find that only a few models can withstand these bounds which predict a stiff overall equation of state but with a soft neutron-proton symmetry energy. Two possible indications are proposed: Circumstantial evidence of hadron-quark phase transition inside the star and new parametrizations that are consistent with ground-state properties of finite nuclei and observational bounds. Based on extensive analysis of these sets, an upper limit on the radius of a $1.4M_{\odot }$ neutron star of $R_{1.4}\lesssim 12.9$ km is deduced.

Figure 1

Tidal deformability ${\mathrm{\Lambda }}_{1.4}$ of neutron star of mass $1.4M_{\odot }$ vs maximum mass $M_{\max }$ for all the RMF EOSs. The horizontal and vertical lines respectively refer to the recent upper bound ${\mathrm{\Lambda }}_{1.4}=580$ of GW170817 data [23] and lower bound $M_{\max }=1.97M_{\odot }$ from the observed pulsar PSR J0348+0432 [10].

Figure 2

Mass-radius relation of neutron stars predicted for all the RMF EOSs that fulfill various ${\mathrm{\Lambda }}_{1.4}$ bounds.

Figure 3

(a) Correlation between tidal deformability ${\mathrm{\Lambda }}_{1.4}$ and radius $R_{1.4}$ of neutron stars of mass $M=1.4M_{\odot }$. The solid line represents the fit ${\mathrm{\Lambda }}_{1.4}=1.53\times {10}^{-5}{(R_{1.4}/\mathrm{km})}^{6.83}$. (b) Correlation between neutron-skin thickness of ${}^{208}\mathrm{Pb}$ nuclei $R_{\mathrm{skin}}^{208}$ and $R_{1.4}$. The results are for EOSs that support stars with $M_{\max }\ge 1.97M_{\odot }$.

Figure 4

Binding energy and charge radius of nuclei calculated for viable RMF sets and compared with data; see text for details.

Figure 5

Correlations between $R_{1.4}$ and ${\mathrm{\Lambda }}_{1.4}$ (left scale) and $M_{\max }$ and ${\mathrm{\Lambda }}_{1.4}$ (right scale) for EOSs with hadron-quark phase transition constructed from the RMF model for the hadronic phase and bag model for the quark phase. In each individual RMF set shown, the bag parameter is varied [21] to generate different EOSs with first-order phase transition using Gibbs conditions.