Constraining the density dependence of the nuclear symmetry energy from an x-ray bursting neutron star

Neutrons stars lighter than the Sun are basically composed of nuclear matter of density up to around twice normal nuclear density. In our recent analyses, we showed that possible simultaneous observations of masses and radii of such neutron stars could constrain $\eta \equiv {\left(K_0{L}^2\right)}^{1/3}$, a combination of the incompressibility of symmetric nuclear matter $K_0$ and the density derivative of the nuclear symmetry energy $L$ that characterizes the theoretical mass-radius relation. In this paper, we focus on the mass-radius constraint of the x-ray burster 4U 1724-307 given by Suleimanov et al. [V. Suleimanov, J. Poutanen, M. Revnivtsev, and K. Werner, Astrophys. J. 742, 122 (2011)]. We therefrom obtain the constraint that $\eta$ should be larger than around 130 MeV, which in turn leads to $L$ larger than around 110, 98, 89, and 78 MeV for $K_0=180$, 230, 280, and 360 MeV. Such a constraint on $L$ is more or less consistent with that obtained from the frequencies of quasi-periodic oscillations in giant flares observed in soft gamma repeaters.

Figure 1

$\eta$ as a function of $L$. The dots are taken from the 247 OI-EOSs, while the solid line denotes the fitting in a functional form of $L^{2/3}$.

Figure 2

Parameter $S_0$ plotted as a function of $L$ for the 247 OI-EOSs.

Figure 3

Allowed regions in the mass-radius relation obtained from the observation of the x-ray burster 4U 1724-307 by Suleimanov et al. [28], where they adopted three different atmosphere models, i.e., pure hydrogen (checkered region), pure helium (filled region), and the solar ratio of H/He with subsolar metal abundance $Z=0.3Z_{\odot }$ (shaded region). On the other hand, the lines with marks denote the stellar models constructed from nine EOSs with different values of $\eta$ (attached numbers) for ${\rho }_c\le 2.0{\rho }_0$, where each mark corresponds to the mass and radius of a star with ${\rho }_c=1.5{\rho }_0$. Additionally, the upper left region is ruled out by the causality [38].

Figure 4

Nuclear matter EOS parameters constrained from $\eta \ge 130$ MeV, which correspond to the region above the solid line. For reference, $\eta =120$ and 140 MeV are plotted with the dashed and dotted lines. We also display the parameter space constrained from the observations of quasi-periodic oscillations in giant flares with the filled and checkered regions [21] (see text for details).