Tidal deformability from GW170817 as a direct probe of the neutron star radius (1803.07687v1)

Abstract: Gravitational waves from the coalescence of two neutron stars were recently detected for the first time by the LIGO-Virgo collaboration, in event GW170817. This detection placed an upper limit on the effective tidal deformability of the two neutron stars and tightly constrained the chirp mass of the system. We report here on a new simplification that arises in the effective tidal deformability of the binary, when the chirp mass is specified. We find that, in this case, the effective tidal deformability of the binary is surprisingly independent of the component masses of the individual neutron stars, and instead depends primarily on the ratio of the chirp mass to the neutron star radius. Thus, a measurement of the effective tidal deformability can be used to directly measure the neutron star radius. We find that the upper limit on the effective tidal deformability from GW170817 implies that the radius cannot be larger than ~13km, at the 90% level, independent of the assumed masses for the component stars. The result can be applied generally, to probe the stellar radii in any neutron star-neutron star merger with a measured chirp mass. The approximate mass-independence disappears for neutron star-black hole mergers. Finally, we discuss a Bayesian inference of the equation of state that uses the measured chirp mass and tidal deformability from GW170817 combined with nuclear and astrophysical priors and discuss possible statistical biases in this inference.

• The paper demonstrates that tidal deformability from GW170817 provides a robust measurement for the neutron star radius, establishing an upper limit of around 13 km.
• It introduces a simplification where effective tidal deformability is nearly independent of individual masses and primarily linked to the chirp mass-to-radius ratio.
• The study employs Bayesian inference with quasi-universal relations to refine dense-matter EOS constraints, paving the way for improved gravitational-wave data interpretation.

Tidal Deformability from GW170817 as a Probe of Neutron Star Radius

The detection of gravitational waves from the binary neutron star coalescence event GW170817 by the LIGO-Virgo collaboration has provided substantial information on the neutron star properties and the dense-matter equation of state (EOS). This paper by Raithel, Özel, and Psaltis presents a pivotal advancement in the interpretation of gravitational-wave data, specifically addressing how such data can constrain neutron star radii through tidal deformability measurements.

The authors propose a novel simplification regarding the effective tidal deformability ($\tilde{\Lambda}$) of binary systems, deduced from such gravitational wave events. Notably, they find that the dependence of $\tilde{\Lambda}$ on component neutron star masses becomes negligible when the chirp mass is specified. Instead, $\tilde{\Lambda}$ primarily correlates with the ratio of the chirp mass to the star's radius. This finding implies that by measuring the effective tidal deformability, it is feasible to directly constrain the neutron star radius without necessitating precise knowledge of individual star masses—a significant deduction in astrophysical modeling.

For GW170817, they determine that the effective tidal deformability places the neutron star radius at an upper limit of approximately 13 km at the 90% confidence level, irrespective of presumed component masses. The paper relies on a quasi-universal relation between the tidal deformability and the compactness of the star. Within this framework, it is observed that effective tidal deformability scales roughly with $R^5$ (where $R$ is the radius), thus becoming a robust proxy for the radius, reducing complexities in direct EOS determinations.

An intriguing aspect of their results is the negligible impact of component masses on $\tilde{\Lambda}$, driven by inherent symmetries in the expressions for a neutron star-neutron star merger. This symmetry is lost in neutron star-black hole mergers, where the tidal deformability of the black hole is zero, and therefore, $\tilde{\Lambda}$ is more sensitive to the stellar compactness instead of the radius.

The paper also explores possible implications for EOS constraints via Bayesian inference techniques. Integrating priors based on nuclear physics and astrophysical observations—including maximum neutron star masses—they illustrate how upcoming observations similar to GW170817 can refine constraints on EOS. The analysis highlights potential biases inherent in methodologically older approaches that emphasize radius marginalization, thereby advocating for more rigorous statistical treatments.

From a theoretical standpoint, this paper underscores the emergence of tidal deformability as a central data point in constraining neutron star properties, offering a simplified path to indirectly measure neutron star radii via gravitational wave observations. Practically, these insights open avenues for using future similar events to strengthen our understanding of the neutron star radius and associated EOS parameters, bringing gravitational wave astronomy and the physics of dense matter into closer confluence.

The advancement herein motivates further investigation into the nuances of gravitational wave data interpretation, with a particular focus on considering conditions where the derived simplifications hold and exploring broader applications where neutron star-black hole mergers might behave differently. As gravitational wave astronomy matures, the methodologies elucidated here could substantially refine EOS parameter spaces, leading to pivotal strides in nuclear astrophysics.