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

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, $Λ$, 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 $\lnΛ$ 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.

Figures (6)

• Figure 1: Illustration of the Love-Q relation. In the upper panel, the orange solid line indicates the original Yagi-Yunes relation \ref{['5-d_Love_Q_eq']}, while the green dashed line represents our fitting with the linear model \ref{['2-d_Love_Q_eq']}. We also show the Love-Q relation for the APR4 EOS as reference with blue circles. In the lower panel, we show the absolute relative differences between the two models (denoted as $Q_5$ and $Q_2$) and the APR4 EOS (denoted as $Q_{\rm APR4}$).
• Figure 2: Posterior distributions of the hyperparameters ${\bm H} = \{a_2,b_2\}$ in the linear fitting model. The contours refer to 50% and 90% credible regions, while the numbers above the histograms on the diagonal stand for the median and the central 90% credible interval of the marginalized distribution. We use blue and red colors to represent the results based on the loudest 20 and 10 events from the 1000 simulated events, respectively. The black lines represent the reference values in table \ref{['prior_table']}. The grey lines on the diagonal represent the priors for comparison.
• Figure 3: Recovered Love-Q relation from the posterior of the hyperparameters in the linear model. In the left panel, the Love-Q relation is inferred with the 20 loudest events from the 1000 simulated GW events. The gray points mark the median values of inferred $\Lambda$ and $Q$ for each event with $68\%$ errorbars. The blue solid line marks the median of the distribution of $Q$ as a function of $\Lambda$, accompanied by the $50\%$ and $90\%$ credible intervals in shaded regions. The red dashed line represents the maximum-posterior Love-Q relation. For comparison, we plot the original Yagi-Yunes Love-Q relation Yagi_2017 in orange. The right panel shows how the $90\%$ credible region of the recovered Love-Q relation depends on the number of events, marked with different colors.
• Figure 4: The posterior of the hyperparameters and the recovered Love-Q relation in the quartic polynomial model, where all 20 loudest events are included in the inference. Figure settings of two panels are respectively similar to those in figure \ref{['corner2-d']} and the left panel of figure \ref{['2-d_Love_Q']}.
• Figure 5: Similar to figure \ref{['5-d_Love_Q']}, while for the quadratic and cubic polynomial models.