GW170817: Measurements of Neutron Star Radii and Equation of State

TLDR

The first direct detection of gravitational waves from a neutron‑star merger (GW170817) provides a unique probe of dense matter, allowing tidal‑effect constraints to be translated into limits on neutron‑star radii. The study extends prior work by assuming both bodies are neutron stars sharing a common equation of state and having spins typical of Galactic binaries. The analysis uses two approaches: equation‑of‑state‑insensitive relations among macroscopic properties and an efficient parametrization of the pressure–density function p(ρ). From LIGO/Virgo data alone, the radii are R₁=10.8⁺².⁰₋₁.⁷ km and R₂=10.7⁺².¹₋₁.⁵ km; imposing a 1.97 M⊙ mass limit and the p(ρ) parametrization yields R₁=R₂=11.9⁺¹.⁴₋₁.⁴ km, and the pressure at twice nuclear saturation density is 3.5⁺².⁷₋₁.⁷×10³⁴ dyn cm⁻².

Abstract

On 17 August 2017, the LIGO and Virgo observatories made the first direct detection of gravitational waves from the coalescence of a neutron star binary system. The detection of this gravitational-wave signal, GW170817, offers a novel opportunity to directly probe the properties of matter at the extreme conditions found in the interior of these stars. The initial, minimal-assumption analysis of the LIGO and Virgo data placed constraints on the tidal effects of the coalescing bodies, which were then translated to constraints on neutron star radii. Here, we expand upon previous analyses by working under the hypothesis that both bodies were neutron stars that are described by the same equation of state and have spins within the range observed in Galactic binary neutron stars. Our analysis employs two methods: the use of equation-of-state-insensitive relations between various macroscopic properties of the neutron stars and the use of an efficient parametrization of the defining function p(ρ) of the equation of state itself. From the LIGO and Virgo data alone and the first method, we measure the two neutron star radii as R_{1}=10.8_{-1.7}^{+2.0} km for the heavier star and R_{2}=10.7_{-1.5}^{+2.1} km for the lighter star at the 90% credible level. If we additionally require that the equation of state supports neutron stars with masses larger than 1.97 M_{⊙} as required from electromagnetic observations and employ the equation-of-state parametrization, we further constrain R_{1}=11.9_{-1.4}^{+1.4} km and R_{2}=11.9_{-1.4}^{+1.4} km at the 90% credible level. Finally, we obtain constraints on p(ρ) at supranuclear densities, with pressure at twice nuclear saturation density measured at 3.5_{-1.7}^{+2.7}×10^{34} dyn cm^{-2} at the 90% level.