Effect of nuclear saturation parameters on a possible maximum mass of neutron stars

To systematically examine the possible maximum mass of neutron stars, which is one of the important properties characterizing the physics in high-density regions, I construct neutron star models by adopting phenomenological equations of state with various values of nuclear saturation parameters for low-density regions, which are connected to the equation of state for high-density regions characterized by the possible maximum sound velocity in medium. I derive an empirical formula for the possible maximum mass of neutron stars. If massive neutron stars are observed, it could be possible to get a constraint on the possible maximum sound velocity for high-density regions.

Figure 1

Mass and radius relation for various EOSs for lower-density regions with $\eta =50.6$ (dashed line), 74.7 (dotted line), and 107.4 (solid line). The left, middle, and right panels correspond to different sound velocities for higher-density regions, i.e., $\alpha =1/3$, 0.6, and 1, respectively. The open marks correspond to the stellar models with maximum mass for various EOS models, while the solid marks correspond to the stellar models with local maximum radii. For reference, the stellar models constructed with the central density ${\rho }_c=2{\rho }_0$ are denoted by the double circles.

Figure 2

The expected maximum masses for various EOS models are shown with different marks, while the solid, dashed, and dotted lines, respectively, denote the fitting formulas given by Eq. (4) for $\alpha =1/3$, 0.6, and 1. In the legend, I show the values of the saturation parameters for the adopted EOS, such as $(-y,K_0)$. The region between the horizontal dot-dashed lines denotes the mass observation of PSR J1614–2230 [3], while the horizontal shaded region denotes the mass observation of PSR J0348+0432 [4]. The stippled region denotes a plausible range for $\eta$ determined from the current terrestrial nuclear experiments.

Figure 3

The expected radii for the stellar models with maximum mass constructed with various EOS models are shown with different marks, while the solid, dashed, and dotted lines, respectively, denote the fitting formula given by Eq. (5) for $\alpha =1/3$, 0.6, and 1. In the legend, I show the values of the saturation parameters for the adopted EOS, such as $(-y,K_0)$. The stippled region denotes a plausible range for $\eta$ determined from the current terrestrial nuclear experiments.

Figure 4

The coefficients $a_1$ and $a_2$ in Eq. (4) as a function of $\alpha$. The dashed lines are fittings given by Eqs. (6) and (7).

Figure 5

The coefficients $b_1$ and $b_2$ in Eq. (5) as a function of $\alpha$. The dashed lines are fittings given by Eqs. (8) and (9).

Figure 6

The maximum mass of neutron stars predicted with the plausible value of $\eta$, i.e., $55.5\lesssim \eta \lesssim 120$ MeV, is shown as a function of $\alpha$ in the region between the solid lines. The shaded regions correspond to the observations of neutron star mass for $\mathrm{J}1748-2021\mathrm{B}$ [17] and for PSR J0348+0432 [4].