Reconsidering the consistent use of precessing, higher order multipole models for gravitational wave analyses

TL;DR

This work addresses the computational challenge of population inferences with gravitational-wave data by proposing a selection criterion that uses $\rho_{\mathrm{p}}$ and $\rho_{\mathrm{HM}}$ to decide when to apply the expensive precessing, higher-multipole waveform models. The authors implement a threshold-based approach that idle-switches among XAS, XP, XHM, and XPHM and validate it on worst-case high-spin, asymmetric-mass populations as well as GWTC-like astrophysical populations, showing that a threshold of $\rho_{\mathrm{thres}}=1.5$ preserves mass and spin inferences while reducing the total Bayesian cost by about $\sim 20\%$, with larger potential gains in more favorable populations. They also analyze the risks of misclassification and discuss trade-offs, including biases that can arise at higher thresholds and the potential for integrating the method into sampling. The results suggest a practical, scalable path for accurate population studies with current detectors and provide a basis for extending the approach to future detectors and additional physics such as eccentricity.

Abstract

The growing number of gravitational-wave (GW) observations allows for constraints to be placed on the underlying population of black holes; current estimates show that black hole spins are small, with binaries more likely to have comparable component masses. Since general relativistic effects, such as spin-induced orbital precession and higher order multipole moments, are more likely to be observed for asymmetric binary systems, a direct measurement remains unlikely. Nevertheless, we continue to consistently probe these effects by performing Bayesian inference with our most accurate and computationally expensive models. As the number of GW detections increases, it may soon become infeasible to consistently use these models for analyses. In this paper, we provide a selection criterion that determines when less accurate and computationally cheaper models can be used without giving biased estimates for the population properties of black holes in the Universe. We show that when using our selection criterion, comparable estimates can be obtained for the underlying mass and spin distribution of black holes for a simulated "worst-case" scenario population, while reducing the overall cost of performing Bayesian inference on our population by $\sim 20\%$. We anticipate a reduction of up to $78\%$ in the overall cost for an astrophysically motivated population, since there are fewer events with observable spin-precession and higher order multipole power.

Figures (9)

• Figure 1: Plot showing the amplitude of the plus polarization, $h_{+}$, for two GW signals when assuming different physics; XAS assumes no spin-precession and higher order multipoles, XP assumes no higher order multipoles, XHM assumes no spin-precession, and XPHM includes both spin-precession and higher order multipoles. The Top panel compares the GW signals for an equal mass ratio binary with small spin magnitudes, $\chi_{1} = \chi_{2} = 0.2$, observed at an inclination angle of $\pi / 6\, \mathrm{rad}$. This represents a binary that is consistent with the observed population, and therefore likely to be detected by the LVK LIGOScientific:2025pvj. The Bottom panel compares the GW signals for a mass ratio $q = 0.1$ binary with large spin magnitudes, $\chi_{1} = \chi_{2} = 0.8$, observed at an inclination angle of $\pi / 2\, \mathrm{rad}$.
• Figure 1: Plot showing the inferred Left: primary mass and mass ratio and Right: effective parallel spin $\chi_{\mathrm{eff}}$ and effective perpendicular spin $\chi_{\mathrm{p}}$ when performing Bayesian inference on a misidentified GW signal; a signal that we identify as having no evidence for spin-precession despite there being strong observable features. This injection corresponds to a false negative in Fig. \ref{['fig:snr_accuracy']}. The GW signal was produced with XPHM into idealised Gaussian noise. The black cross hairs show the true values and the contours show the inferred 90% credible interval. The reweighting and conditioning technique applied to XAS is described in Sec. \ref{['sec:verification']} and Fig. \ref{['fig:rweighting']}.
• Figure 2: Plot showing the inferred primary mass and mass ratio when performing Bayesian inference on the GW signals shown in Fig. \ref{['fig:motivation_models']}. We inject each GW signal into LIGO-Hanford and LIGO-Livingston, operating at their design densitivities LIGOScientific:2014pky. The Left panel corresponds to a GW signal with no observable precession and higher order multipoles, the Top panel in Fig. \ref{['fig:motivation_models']}. The Right panel corresponds to a GW signal with observable precession and higher order multipoles, the Bottom panel in Fig. \ref{['fig:motivation_models']}. In both cases we inject a simulated GW signal produced with XPHM into idealised Gaussian noise, and perform inference with XAS, XP, XHM and XPHM. The black cross hairs show the true values. The contours show the inferred 90% credible interval.
• Figure 2: Corner plot showing a subset of the inferred hyper parameters controlling the mass distribution of black holes. We consider a GWTC-like population with a uniform distribution of spins, see App. \ref{['sec:gwtclike_population']} for details. The black cross hairs show the true values.
• Figure 3: Plot comparing the matched filtered SNR in precession $\rho_{\mathrm{p}}$ and higher order multipoles $\rho_{\mathrm{HM}}$ to the true SNR for our worst-case scenario population. The shaded red region shows false negatives: a region where we identify the binary as having no evidence for precession and/or higher order multipoles from the filtered SNR despite there being observable features in the signal. The green region shows false positives, true positives and true negatives. We define $\rho_{\mathrm{p}} = \rho_{\mathrm{HM}} = 2.0$ for a binary with significant evidence of precession and/or higher order multipoles.