Tidal Deformabilities and Radii of Neutron Stars from the Observation of GW170817

We use gravitational-wave observations of the binary neutron star merger GW170817 to explore the tidal deformabilities and radii of neutron stars. We perform a Bayesian parameter estimation with the source location and distance informed by electromagnetic observations. We also assume that the two stars have the same equation of state; we demonstrate that, for stars with masses comparable to the component masses of GW170817, this is effectively implemented by assuming that the stars’ dimensionless tidal deformabilities are determined by the binary’s mass ratio $q$ by ${\mathrm{\Lambda }}_1/{\mathrm{\Lambda }}_2=q^6$. We investigate different choices of prior on the component masses of the neutron stars. We find that the tidal deformability and 90% credible interval is $\tilde{\mathrm{\Lambda }}={222}_{-138}^{+420}$ for a uniform component mass prior, $\tilde{\mathrm{\Lambda }}={245}_{-151}^{+453}$ for a component mass prior informed by radio observations of Galactic double neutron stars, and $\tilde{\mathrm{\Lambda }}={233}_{-144}^{+448}$ for a component mass prior informed by radio pulsars. We find a robust measurement of the common areal radius of the neutron stars across all mass priors of $8.9\le \widehat{R}\le 13.2\mathrm{km}$, with a mean value of $⟨\widehat{R}⟩=10.8\mathrm{km}$. Our results are the first measurement of tidal deformability with a physical constraint on the star’s equation of state and place the first lower bounds on the deformability and areal radii of neutron stars using gravitational waves.

Figure 1

The tidal deformability $\mathrm{\Lambda }$ as a function of mass for physically realistic polytropes. A TOV integration with each EOS parameter set results in a series of values of $\mathrm{\Lambda }(m)$ that are shown as points colored by their radii $R$. Dashed curves are lower bounds to $\mathrm{\Lambda }$ for a given mass $m$ which vary depending on the assumed lower limit to the neutron star maximum mass, $m_{\max }$. All values of $m_{\max }$ produce the same upper bound.

Figure 2

Posterior probability densities for ${\mathrm{\Lambda }}_{1,2}$ with the common EOS constraint using uniform (left), double neutron stars (middle), and Galactic neutron stars (right) component mass priors. The 50% and 90% credible region contours are shown as solid curves. Overlaid are contours of $\tilde{\mathrm{\Lambda }}$ (in magenta) and $q$ (in gray). The values of ${\mathrm{\Lambda }}_1$ and ${\mathrm{\Lambda }}_2$ forbidden by causality have been excluded from the posteriors.

Figure 3

The 90% credible region of the posterior probability for the common radius $\widehat{R}$ and binary tidal deformability $\tilde{\mathrm{\Lambda }}$ with the common EOS constraint for the three mass priors. The posteriors for the individual parameters are shown with dotted lines at the 5%, 50%, and 95% percentiles. The values of $\tilde{\mathrm{\Lambda }}$, and hence, $\widehat{R}$ forbidden by causality have been excluded from the posteriors.