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 $\eta\equiv(K_0L^2)^{1/3}$, 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. (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.