Constraining neutron star properties with a new equation of state insensitive approach

Instead of parametrizing the pressure-density relation of a neutron star (NS), one can parametrize its macroscopic properties such as mass ($M$), radius ($R$), and dimensionless tidal deformability ($\mathrm{\Lambda }$) to infer the equation of state (EOS) combining electromagnetic and gravitational wave (GW) observations. We present a new method to parametrize $R(M)$ and $\mathrm{\Lambda }(M)$ relations, which approximates the candidate EOSs with accuracy better than 5% for all masses and spans a broad region of the $M-R-\mathrm{\Lambda }$ plane. Using this method we combine the $M-\mathrm{\Lambda }$ measurement from GW170817 and GW190425, and simultaneous $M-R$ measurement of pulsars PSR $\mathrm{J}0030+0451$ and PSR $\mathrm{J}0740+6620$ to place joint constraints on NS properties. At 90% confidence, we infer $R_{1.4}=12.05_{-0.87}^{+0.98}\mathrm{km}$ and ${\mathrm{\Lambda }}_{1.4}=372_{-150}^{+220}$ for a $1.4M_{\odot }$ NS, and $R_{2.08}=12.65_{-1.46}^{+1.36}\mathrm{km}$ for a $2.08M_{\odot }$ NS. Furthermore, we use the inferred values of the maximum mass of a nonrotating NS $M_{\max }=2.52_{-0.29}^{+0.33}{M}_{\odot }$ to investigate the nature of the secondary objects in three potential neutron star–black hole merger (NSBH) systems.

Figure 1

In the upper panel, mass ($M$) and its fitted curve are plotted for three candidate EOSs SLy (soft) [41], MPA1 (intermediate) [51], and MS1 (stiff) [53] as a function of dimensionless tidal deformability ($\mathrm{\Lambda }$). In the lower panel, the percentage of error of the fit is also shown.

Figure 2

Posterior distribution of EOS-sensitive parameters and their correlations with $R_{1.4}$, ${\mathrm{\Lambda }}_{1.4}$, $R_{2.08}$, and $M_{\max }$ are shown here after adding each type of observational data successively.

Figure 3

90% credible interval (CI) of mass radius are shown. At first, in the upper left panel prior is shown in black shade. Then the upper right panel shows the effect of adding the mass measurement of PSR $0740+6620$ from [19] and compared against the prior. In a similar manner, two BNS merger signals and mass-radius measurements of two pulsars by NICER collaboration are added successively in the lower panel.

Figure 4

Posterior distributions of $R_{1.4}$, ${\mathrm{\Lambda }}_{1.4}$, $R_{2.08}$, and $M_{\max }$ are compared between Riley et al. and Miller et al. dataset and also their marginalized distributions are overlaid. Distribution of the measured secondary masses from three potential NSBH mergers are shown in the lower panel along with $M_{\max }$ distributions.