A meta inspiral-merger-ringdown consistency test of general relativity with gravitational wave signals from compact binaries

TL;DR

The paper introduces the meta IMR consistency test (meta IMRCT), a generalized approach to test general relativity by comparing remnant final mass $M_f$ and spin $\chi_f$ inferred from two independent GR analyses or from a GR analysis paired with another GR test. It extends the original IMRCT by allowing any pair of GR analyses to be compared, including inspiral vs merger-ringdown portions or different parameterized tests, and shows it is computationally efficient since it uses already-produced posterior results. Through extensive simulations with GR and non-GR signals (including eccentric NR waveforms) and several real LVK events, the meta IMRCT generally agrees with GR for GR signals, while showing enhanced sensitivity to certain deviations—sometimes outperforming individual tests in detecting departures from GR. The results validate the method’s utility for cross-checking GR analyses across a broad range of binary configurations and motivate future work exploring additional parameter choices and tidal effects, as well as potential applications to neutron-star–black-hole systems.

Abstract

The observation of gravitational waves from compact binary coalescences is a promising tool to test the validity of general relativity (GR) in a highly dynamical strong-field regime. There are now a variety of tests of GR performed on the observed compact binary signals. In this paper, we propose a new test of GR that compares the results of these individual tests. This meta inspiral-merger-ringdown consistency test (IMRCT) involves inferring the final mass and spin of the remnant black hole obtained from the analyses of two different tests of GR and checking for consistency. If there is a deviation from GR, we expect that different tests of GR will recover different values for the final mass and spin, in general. We check the performance of the meta IMRCT using a standard set of null tests used in various gravitational-wave analyses: the original IMRCT, parameterized phasing tests (TIGER and FTI) and the modified dispersion test. However, the meta IMRCT is applicable to any tests of GR that infer the initial masses and spins or the final mass and spin, including ones that are applied to binary neutron star or neutron star--black hole signals. We apply the meta IMRCT to simulated quasi-circular GR and non-GR binary black hole (BBH) signals as well as to eccentric BBH signals in GR (analyzed with quasicircular waveforms). We find that the meta IMRCT gives consistency with GR for the quasi-circular GR signals and picks up a deviation from GR in the other cases, as do other tests. In some cases, the meta IMRCT finds a significant GR deviation for a given pair of tests (and specific testing parameters) while the individual tests do not, showing that it is more sensitive than the individual tests to certain types of deviations. In addition, we also apply this test to a few selected real compact binary signals and find them consistent with GR.

Figures (8)

• Figure 1: P-p plots for the standard IMRCT analysis of simulated observations in Gaussian noise (left) and the meta IMRCT applied to mock data with different prior ranges for the two analyses (right). The red straight line in both the plots represents theoretical expectation. In both cases, we show the $95\%$ bound on the expected statistical variation due to the finite number of simulated observations considered. The red dashed line represents the theoretical expectation.
• Figure 2: The results of meta IMRCT on the GW150914-like GR simulated observations and those with the larger GR deviation presented as 2d contour plots of the posteriors on the deviation parameters. The side panels shows the 1d histograms of the marginalized posteriors of $\Delta M_\text{f}/{\bar{M}_\text{f}}$ and $\Delta \chi_\text{f}/{\bar{\chi}_\text{f}}$. The gray contour delineates pairs of individual tests with color gradient varying based on the value of GR quantile (where darker gray denotes larger GR quantile and lighter gray denotes smaller GR quantile). We highlight in color the three cases with the largest meta IMRCT GR quantile where this is larger than the GR quantile from either of the tests of GR in the pair (or the single test of GR for pairs with GR PE) and also $> 90\%$. Specifically, we assign magenta color to the largest GR quantile, purple to the second-largest, and blue to the third-largest.
• Figure 3: Similar to figure \ref{['fig:GW150914-like_larger']}, but for the GW150914-like smaller GR deviation simulated observations.
• Figure 4: Similar to figure \ref{['fig:GW150914-like_larger']} for the GW170608-like smaller GR deviation simulated observations.
• Figure 5: The results of meta IMRCT on the numerical relativity quasicircular and eccentric simulated observations with $q = 1$ presented as 2d contour plots of the posteriors on the deviation parameters. These are plotted the same way as in figure \ref{['fig:GW150914-like_larger']}.