Connecting Neutron Star Observations to Three-Body Forces in Neutron Matter and to the Nuclear Symmetry Energy

Using a phenomenological form of the equation of state of neutron matter near the saturation density which has been previously demonstrated to be a good characterization of quantum Monte Carlo simulations, we show that currently available neutron star mass and radius measurements provide a significant constraint on the equation of state of neutron matter. At higher densities we model the equation of state by using polytropes and a quark matter model. We show that observations offer an important constraint on the strength of the three-body force in neutron matter, and thus some theoretical models of the three-body force may be ruled out by currently available astrophysical data. In addition, we obtain an estimate of the symmetry energy of nuclear matter and its slope that can be directly compared to the experiment and other theoretical calculations.

Figure 1

The probability distributions and 68% (dark red areas) and 95% (green areas) confidence ranges for the parameters $b$ and $\beta$ and the density derivative of the symmetry energy, $L$. All distributions have been rescaled so that their peak is unity and then vertically shifted by an arbitrary amount. We compare our predicted value of $L$ with constraints from nuclear masses (“Masses”) [38], heavy-ion collisions (“HIC”) [1], pygmy dipole resonances (“PDR”) [2], isobaric analog states in nuclei (“IAS”) [39], and antiprotonic atoms [“Pb(p,p)”] [40]. The parametrization of the high-density part of the EOS is presented as Supplemental Material [31].

Figure 2

The 68% (dashed and dot-dashed lines) and 95% (shadowed areas) confidence ranges for the energy per baryon as a function of the baryon density as constrained by the astrophysical observations. The APR [14] and SLy4 [33] EOSs are also plotted, as well as the limits obtained in Ref. 23 (GCR).

Figure 3

The mass-radius curves for the models considered in this work. The range of radii for 1.4 solar mass neutron stars, between 11 and 12 km, is similar to that obtained in Ref. 20. The mass-radius curves for APR [14] and SLy4 [33] are also given. The labeling is the same as in Fig. 2.

Figure 4

The pressure as a function of the energy density. The labeling is the same as in Fig. 2.