Improved parametrized test of general relativity using the IMRPhenomX waveform family: Including higher harmonics and precession

TL;DR

The paper advances theory-agnostic tests of GR with gravitational waves by integrating a TIGER parametrization into the state-of-the-art IMRPhenomX waveform family, including higher-order modes and spin precession. It propagates non-GR deviations through the inspiral HM phases via a scaling with mode indices and applies twist-up to precessing frames, all within a Bayesian analysis framework, to GWTC-3 events (plus earlier runs) with both common-parameter and hierarchical population approaches. Systematic injections show that neglecting HM or precession can bias GR tests, motivating the full HM+precession model. Application to GWTC-3 demonstrates no evidence for GR violations, and the hierarchical analysis provides robust, population-level constraints on a set of PN- and post-inspiral-deviation coefficients, enhancing robustness for highly asymmetric and precessing binaries.

Abstract

When testing general relativity (GR) with gravitational wave observations, parametrized tests of deviations from the expected strong-field source dynamics are one of the most widely used techniques. We present an updated version of the parametrized framework with the state-of-art IMRPhenomX waveform family. Our new framework incorporates deviations in the dominant mode as well as in the higher-order modes of the waveform. We demonstrate that the missing physics of either higher-order modes or precession in the parametrized model can lead to a biased conclusion of false deviation from GR. Our new implementation mitigates this issue and enables us to perform the tests for highly asymmetric and precessing binaries without being subject to systematic biases due to missing physics. Finally, we apply the improved test to analyze events observed during the second half of the third observing run of LIGO and Virgo (O3b). We provide constraints on GR deviations by combining O3b results with those from previous observation runs. Our findings show no evidence for violations of GR.

Figures (8)

• Figure 1: Systematic errors and false deviation in the parametrized test of GR with TIGER due to missing physics, shown for GW200129-like injections; corresponding parameter values are listed in Table \ref{['tab:GW200129maxL']}. The GR injection (shown in red) was generated using a precessing spin with higher-order modes model IMRPhenomXPHM, and recovered with precessing spin without higher-order modes model IMRPhenomXP (blue), non-precessing spin with higher-order modes model IMRPhenomXHM (green), and IMRPhenomXPHM (orange) model, which includes both. The small horizontal lines represent the 90% credible interval of the posteriors. In the middle and bottom rows, for some deviation parameters, the posteriors obtained using IMRPhenomXP are significantly broader than those from the other two models. These cases are shown in two consecutive subplots to highlight the difference and to clearly display the narrower posteriors. The full results are shown in Fig. \ref{['fig:gw200129-like_inj_full']}.
• Figure 2: Illustrating the combined results for the inspiral deviation parameters, obtained from the GWTC-1/2/3 events listed in Table \ref{['tab:event_selection']}. The filled color probability distributions represent the results from the hierarchical approach, while the unfilled black solid lines show the combined results assuming a common value for each deviation parameter across all events. In contrast, the hierarchical approach allows for an independent value for each event. The horizontal blue ticks indicate the 90% credible intervals derived from the hierarchical analyses.
• Figure 3: Same as Fig. \ref{['fig:violin_gwtc3_insp']} but showing the combined results for the post-inspiral deviation parameters, obtained from the GW190412, GW190814, and GWTC-3 events listed in Table \ref{['tab:event_selection']}.
• Figure 4: Illustrating the joint distribution for the hyperparameters $\mu_i$ and $\sigma_i$ of the beyond-GR parameters $\delta\hat{p}_i$ for the parametrized tests. The left panel shows the results for inspiral parameters obtained using the selected events in GWTC-1/2/3 as reported in Table \ref{['tab:event_selection']}. The right panel shows the results for post-inspiral parameters obtained using the selected events in GWTC-3, GW190412, and GW190814. The contours denote the 90% credible regions of the joint distribution. The contours for $\delta\hat{\varphi}_{-2}$ and intermediate parameters ($\delta\hat{b}_i$) are rescaled by a factor of 1000 and 20, respectively, to improve visibility. All contours include $\mu_i = \sigma_i = 0$, consistent with the GR prediction.
• Figure 5: Illustrating the posterior distributions of parametrized deviation parameters obtained from GW190412 (shown in blue) and GW190814 (shown in orange) events, inferred using IMRPhenomXPHM model. The black unfilled violin plots show the results inferred using IMRPhenomXP model, highlighting the systematic biases when higher-order modes are missing in the TIGER baseline waveform model. The horizontal solid lines indicate the 90% credible intervals, and the gray dashed line at $\delta\hat{p}_i = 0$ denotes the GR values. The full results are shown in Fig. \ref{['fig:violin_gw190412_gw190814_full']}.