GW170817: Measurements of Neutron Star Radii and Equation of State

TL;DR

This study analyzes GW170817 under the premise that both neutron stars share a single equation of state and possess small spins. By combining EOS-insensitive tidal relations with a direct EOS-parameterization approach, the authors tighten measurements of tidal deformabilities and NS radii, obtaining R1 and R2 around 11 km when imposing a ≥1.97 M⊙ maximum-mass constraint. They also extract the pressure at supranuclear densities, p(2ρnuc), from the GW data, indicating a soft-to-moderately stiff EOS within the probed density range. The work demonstrates that GW observations, when combined with physically motivated EOS constraints, can meaningfully limit the dense-matter EOS and NS structure. These results are compatible with other observational constraints and highlight the value of improved waveform models and multi-messenger follow-up for future BNS mergers.

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 $R_1=10.8^{+2.0}_{-1.7}$ km for the heavier star and $R_2= 10.7^{+2.1}_{-1.5}$ 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 $1.97 \,M_\odot$ 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 $3.5^{+2.7}_{-1.7}\times 10^{34} \,\mathrm{dyn}/\mathrm{cm}^{2}$ at the 90% level.

Figures (3)

• Figure 1: Marginalized posterior for the tidal deformabilities of the two binary components of GW170817. The green shading shows the posterior obtained using the $\Lambda_a(\Lambda_s,q)$ EOS-insensitive relation to impose a common EOS for the two bodies, while the green, blue, and orange lines denote 50% (dashed) and 90% (solid) credible levels for the posteriors obtained using EOS-insensitive relations, a parametrized EOS without a maximum mass requirement, and independent EOSs (taken from Abbott:2018wiz), respectively. The gray shading corresponds to the unphysical region $\Lambda_2<\Lambda_1$ while the seven black scatter regions give the tidal parameters predicted by characteristic EOS models for this event PhysRevC.38.10101998PhRvC..58.1804ADouchin:2001sv1987PhLB..199..469M2006PhRvD..73b4021LMueller:1996pmRead:2008iy.
• Figure 2: Marginalized posterior (green bands) and prior (purple dashed) for the pressure $p$ as a function of the rest-mass density $\rho$ of the NS interior using the spectral EOS parametrization and imposing a lower limit on the maximum NS mass supported by the EOS of $1.97 \, \mathrm{M}_\odot$. The dark (light) shaded region corresponds to the 50% (90%) posterior credible level and the purple dashed lines show the 90% prior credible interval. Vertical lines correspond to once, twice, and six times the nuclear saturation density. Overplotted in gray are representative EOS models PhysRevC.38.10101998PhRvC..58.1804A2006PhRvD..73b4021L, using data taken from Ozel:2016oaf; from top to bottom at $2 \rho_{\mathrm{nuc}}$ we show H4, APR4, and WFF1. The corner plots show cumulative posteriors of central densities $\rho_c$ (top) and central pressures $p_c$ (right) for the two NSs (blue and orange), as well as for the heaviest NS that the EOS supports (black). The 90% credible intervals for $\rho_c$ and $p_c$ are denoted by vertical and horizontal lines respectively for the heavier (blue dashed) and lighter (orange dot-dashed) NS.
• Figure 3: Marginalized posterior for the mass $m$ and areal radius $R$ of each binary component using EOS-insensitive relations (left panel) and a parametrized EOS where we impose a lower limit on the maximum mass of $1.97 \, \mathrm{M}_\odot$ (right panel). The top blue (bottom orange) posterior corresponds to the heavier (lighter) NS. Example mass-radius curves for selected EOSs are overplotted in gray. The lines in the top left denote the Schwarzschild BH ($R=2m$) and Buchdahl ($R=9m/4$) limits. In the one-dimensional plots, solid lines are used for the posteriors, while dashed lines are used for the corresponding parameter priors. Dotted vertical lines are used for the bounds of the 90% credible intervals.