Constraints on the phase transition and nuclear symmetry parameters from PSR $\mathrm{J}0740+6620$ and multimessenger data of other neutron stars

Recently, the radius of neutron star (NS) PSR $\mathrm{J}0740+6620$ was measured by Neutron Star Interior Composition Explorer (NICER), and an updated measurement of neutron skin thickness of ${}^{208}\mathrm{Pb}$ ($R_{\mathrm{skin}}^{208}$) was reported by the PREX-II experiment. These new measurements can help us better understand the unknown equation of state (EOS) of dense matter. In this work, we adopt a hybrid parameterization method, which incorporates the nuclear empirical parameterization and some widely used phenomenological parameterizations, to analyze the results of nuclear experiments and astrophysical observations. With the joint Bayesian analysis of GW170817, PSR $\mathrm{J}0030+0451$, and PSR $\mathrm{J}0740+6620$, the parameters that characterize the ultradense matter EOS are constrained. We find that the slope parameter $L$ is approximately constrained to ${70}_{-18}^{+21}\mathrm{MeV}$, which predicts $R_{\mathrm{skin}}^{208}=0.204_{-0.026}^{+0.030}\mathrm{fm}$ by using the universal relation between $R_{\mathrm{skin}}^{208}$ and $L$. The bulk properties of canonical $1.4M_{\odot }$ NS (e.g., $R_{1.4}$ and ${\mathrm{\Lambda }}_{1.4}$) as well as the pressure ($P_{2{\rho }_{\mathrm{sat}}}$) at two times the nuclear saturation density are well constrained by the data; i.e., $R_{1.4}$, ${\mathrm{\Lambda }}_{1.4}$, and $P_{2{\rho }_{\mathrm{sat}}}$ are approximately constrained to $12.3\pm 0.7\mathrm{km}$, ${330}_{-100}^{+140}$, and ${4.1}_{-1.2}^{+1.5}\times {10}^{34}\mathrm{dyn}{\mathrm{cm}}^{-2}$, respectively. Besides, we find that the Bayes evidences of the hybrid star and normal NS assumptions are comparable, which indicates that current observation data are compatible with quarkyonic matter existing in the core of massive star. Finally, in the case of normal NS assumption, we obtain a constraint for the maximum mass of nonrotating NS $M_{\mathrm{TOV}}=2.30_{-0.18}^{+0.30}{M}_{\odot }$. Based on this result and the current observational and theoretical knowledge about the NS population and its EOS, we find that a binary black hole merger scenario for GW190814 is more plausible. All of the uncertainties reported above are for 68.3% credible levels.

Figure 1

Corner plots of symmetry energy parameters ($L$, $K_{\mathrm{sym}}$), bulk properties of canonical $1.4M_{\odot }$ NS ($R_{1.4}$, ${\mathrm{\Lambda }}_{1.4}$), pressure at $2{\rho }_{\mathrm{sat}}$, and radius corresponding to $M_{\mathrm{TOV}}$. Priors (considering the enforced conditions) are represented by gray color, and the top and bottom panels respectively show the results of PT and NPT models. Meanwhile, values in the diagonal plots are 68.3% credible intervals (Figs. 2 and 7 are the same).

Figure 2

Corner plots of mass-radius properties at maximum mass configuration and EOS parameters $\{{\rho }_2,\mathrm{\Delta }\rho ,{\mathrm{\Gamma }}_{\mathrm{m}},c_{\mathrm{q}}^2\}$.

Figure 3

Top panel: a comparison of symmetry energy parameters among the constraints from astrophysical observations (red hatched, $1\sigma$ confidence level), “intersection” parameter space (green area, $2\sigma$ confidence level) from nuclear experiments [10], and that inferred from PREX-II (blue errorbar, $1\sigma$ confidence level) [15]. Bottom panel: the 90% uncertainty regions of constrained EOS in the form of rest-mass density versus the total pressure for PT (blue hatched) and NPT (red hatched) models.

Figure 4

Posterior $M\text{−}\text{versus}\text{−}R$ distributions for PT (top panel) and NPT (bottom panel) models. The black dashed line and orange solid line denote, respectively, the 68.3% uncertainty region of $M\text{−}\text{versus}\text{−}R$ relations of the prior and the posterior obtained with data set $\mathcal{D}$. The $M\text{−}\text{versus}\text{−}R$ measurements of PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$ are represented by the blue and cyan dot-dashed contours, respectively. The red and green dot-dashed contours represent the $M\text{−}\text{versus}\text{−}R$ posteriors in the right panel of Fig. 3 of Ref. [20]. The associated reconstructed $M\text{−}\text{versus}\text{−}R$ of these sources are represented by the colored solid contours.

Figure 5

Joint plots of radius of $1.4M_{\odot }$ NS and neutron-skin thickness $R_{\mathrm{skin}}^{208}$ transformed from slope parameter $L$ using universal relation in Ref. [13]. The blue color represents the measurement from PREX-II.

Figure 6

Joint plots of the reconstructed radius of PSR $\mathrm{J}0740+6620$ from posterior samples and maximum mass of nonrotating NS $M_{\mathrm{TOV}}$ for both PT (blue) and NPT (red) models. The purple and green lines represent the probability density distributions of $M_{\mathrm{TOV}}$ in Ref. [28] and Ref. [64], respectively. The dashed vertical line marks the 90% lower limit of the secondary mass of GW190814.

Figure 7

Corner plots of posteriors for EOS parameters $\{K_0,S_v,v_0,v_1,v_2,v_3\}$.