The Equation of State From Observed Masses and Radii of Neutron Stars

Abstract

We determine an empirical dense matter equation of state from a heterogeneous dataset of six neutron stars: three type I X-ray bursters with photospheric radius expansion, studied bÿ Ozel et al., and three transient low-mass X-ray binaries. We critically assess the mass and radius determinations from the X-ray burst sources and show explicitly how systematic uncertainties, such as the photospheric radius at touchdown, affect the most probable masses and radii. We introduce a parameterized equation of state and use a Markov Chain Monte Carlo algorithm within a Bayesian framework to determine nuclear parameters such as the incompressibility and the density dependence of the bulk symmetry energy. Using this framework we show, for the first time, that these parameters, predicted solely on the basis of astrophysical observations, all lie in ranges expected from nuclear systematics and laboratory experiments. We find significant constraints on the mass-radius relation for neutron stars, and hence on the pressure-density relation of dense matter. The predicted symmetry energy and the equation of state near the saturation density are soft, resulting in relatively small neutron star radii around 11-12 km for M = 1.4 M ⊙ . The predicted equation of state stiffens at higher densities, however, and our preferred model for X-ray bursts suggests that the neutron star maximum mass is relatively large, 1.9-2.2 M ⊙ . Our results imply that several commonly used equations of state are inconsistent with observations.

Mass and Radius of Neutron Stars Constrained by Photospheric Radius Expansion X-ray Bursts

“…Previous studies adopted flat (i.e., uniform) distributions for two parameters, f c between 1.3 and 1.4 and X between 0.0 and 0.7 [3]. The estimates of mass and radius from the previous studies, which we reproduce, are shown in the left panel of Figure 1.…”

“…For EXO 1745-248, three observed quantities with measurement errors are available; D = 6.3 ± 0.6 kpc, A = 1.17 ± 0.13 cm 2 kpc −2 , and F TD,∞ = (6.25 ± 0.2) × 10 −8 ergs cm −2 s −1 (taken from [3]). Previous studies adopted flat (i.e., uniform) distributions for two parameters, f c between 1.3 and 1.4 and X between 0.0 and 0.7 [3].…”

“…In this work, we follow the methods suggested by [3] who assumed that touchdown occurs at the radius far from the surface of the neutron star. In this case, equation (1) becomes simple by dropping the general relativistic term,…”

“…Because we focus on the effect of X in this work, it is better to use the methods that produce statistically meaningful results. For this reason, we adopt the assumption of [3] and use equation (3) instead of (1). 3, and 0.7), respectively.…”

The EOS of Neutron Matter and the Effect of Λ Hyperons to Neutron Star Structure

“…However, the recent measurements of the large neutron star mass values of 1.97(4)M ⊙ [29] and 2.01(4)M ⊙ [34] require a stiff equation of state. Other NS observations of masses and radii seem to disfavor a very soft EOS of neutron star matter [31,32,35]. This seems to contradict the appearance of strange baryons in high-density matter, given what is known at present about the hyperon-nucleon interaction.…”