Inferring neutron-star Love-Q relations from gravitational waves in the hierarchical Bayesian framework

TL;DR

This paper demonstrates how hierarchical Bayesian analysis of simulated gravitational wave data can measure the neutron-star Love-Q relation and test modified gravity theories.

Contribution

It introduces a method to infer the Love-Q relation from multiple GW events and assesses its precision with next-generation detectors.

Findings

Linear lnΛ-lnQ relation suffices for next-gen GW detectors.

Strong correlations found between Love-Q model parameters.

Future GW observations can constrain modified gravity length scales to 10 km.

Abstract

Despite the large uncertainties in the equation of state for neutron stars (NSs), a tight universal ``Love-Q'' relation exists between their dimensionless tidal deformability, $\Lambda$, and the dimensionless quadrupole moment, $Q$. However, this relation has not yet been directly measured through observations. Gravitational waves (GWs) emitted from binary NS (BNS) coalescences provide an avenue for such a measurement. In this study, we adopt a hierarchical Bayesian framework and combine multiple simulated GW events to measure the Love-Q relation. We simulate 1000 GW sources and select 20 events with the highest signal-to-noise ratios and NS spins for the analysis. By inspecting four parameterization models of the Love-Q relation, we observe strong correlations between the model parameters. We verify that a linear relation between $\ln\Lambda$ and $\ln Q$ is practically sufficient to describe the Love-Q relation with the precision expected from next-generation GW detectors. Furthermore, we utilize the inferred Love-Q relation to test modified gravity. Taking the dynamical Chern-Simons gravity as an example, our results suggest that the characteristic length can be constrained to $10\, \mathrm{km}$ or less with future GW observations.