A theory-agnostic hierarchical Bayesian framework for black-hole spectroscopy: a case study on GW250114 in Einstein-dilaton-Gauss-Bonnet gravity

TL;DR

This work introduces a theory-agnostic hierarchical Bayesian framework for black-hole spectroscopy that operates directly on the spectral content of the ringdown, modeled as damped sinusoids, to compare observed quasinormal-mode frequencies with theory-predicted spectra. By coupling a stable-ringdown window diagnostic with a soft-truncation scheme, the method rigorously accounts for the finite validity of beyond-GR theories while remaining agnostic about waveform deviations. Applied to GW250114 in Einstein–dilaton–Gauss–Bonnet gravity, the framework yields remnant-property posteriors consistent with GR IMR analyses and places a broad, weakly informative bound on the EdGB coupling $\zeta$, with injection tests confirming the ability to recover nonzero couplings in idealized settings. The study highlights the sensitivity of beyond-GR inferences to remnant priors and motivates a theory-agnostic, modular approach for upcoming high-SNR observations with next-generation detectors.

Abstract

Black-hole spectroscopy has emerged as a powerful probe of strong-field gravity in the era of gravitational-wave astronomy. In this context, many current tests of modified or extended gravity are implemented by searching for predicted signatures modeled as perturbative corrections to general-relativistic waveforms; however, this approach may introduce model-dependent systematics and limit applicability to broader classes of theories. To complement such methods, we develop a theory-agnostic hierarchical Bayesian framework that connects ringdown observations -- modeled as damped sinusoids -- directly with theoretical quasinormal mode spectra, performing the comparison at the spectral level rather than through theory-specific waveform matching. The framework incorporates a soft-truncation module to account for the finite domain of validity in the theory's parameter space and is equipped with quantitative diagnostics that identify stable analysis time windows. As an illustrative application, we implement the framework within Einstein-dilaton-Gauss-Bonnet gravity and apply it to the gravitational-wave event GW250114, finding that the resulting posterior for the dimensionless coupling $ζ$ is robust against prior assumptions yet remains only weakly informative over the range considered in this work. We further perform controlled ringdown injection studies across different values of $ζ$, confirming that nonzero couplings can be recovered while also indicating a potential systematic effect: Kerr-based priors in the $ζ$ inference may partially absorb spectral deviations arising in alternative theories of gravity. This work establishes a transparent and extensible foundation for future strong-field gravity tests, naturally compatible with the growing precision and modal resolution of next-generation gravitational-wave detectors.

Figures (11)

• Figure 1: Posterior distributions of the dimensionless coupling parameter $\zeta$ for GW250114 under three different priors on the remnant parameters $(M,\chi)$: a broad ringdown-only uniform prior (light blue), a uniform prior within an IMR-informed extended range (violet), and the IMR posterior itself used directly as a prior (rose pink). Vertical dashed lines of matching color denote the corresponding $90\%$ upper credible limits, while colored triangles and rectangles mark the maximum a posteriori (MAP) estimates and the boundaries of the $90\%$ credible intervals, respectively.
• Figure 2: Posterior comparisons of the EdGB coupling $\zeta$, the remnant mass $M$, and spin $\chi$ from our ringdown-only analysis of GW250114 using a RD-uniform prior on $(M,\chi)$. Results are shown under the GR assumption $(\zeta=0)$ in orange (solid lines) and when allowing $\zeta$ to vary in the weak-coupling regime in light blue (dashed lines). Shaded regions in the two-dimensional panels indicate $90\%$ credible regions, with the corresponding one-dimensional marginal posteriors displayed along the diagonal.
• Figure 3: Posterior distributions of the EdGB coupling $\zeta$ from ringdown-only injection tests. The three curves correspond to injections with $\zeta_{\mathrm{true}}=0$ (blue), $0.15$ (violet), and $0.25$ (rose), respectively. Colored triangles mark the MAP estimates, and rectangular bars indicate the boundaries of the $90\%$ credible intervals.
• Figure 4: Posterior distributions of the EdGB coupling $\zeta$ from ringdown injections with $\zeta_{\mathrm{true}}=0.25$, analyzed with two different fixed remnant configurations: the injected $(M,\chi)$ (rose) and the Kerr-based $(M,\chi)$ obtained from a GR ringdown fit to the same data (blue). Triangles mark the MAP estimates and rectangle bars indicate the boundaries of the $90\%$ credible intervals.
• Figure 5: Quantitative diagnostics for selecting stable post-merger start times $t_0$. The upper panel shows the combined score $W$ (black solid) together with its components $S_{\mathrm{bal}}$ (blue dashed) and $S_{\mathrm{stab}}$ (pink dotted). The lower panel displays the one-dimensional consistency metrics for the recovered QNM parameters: $S_f$ for the frequency (cyan dashed) and $S_\tau$ for the damping time (orange dotted). The shaded band marks the stable window identified by the joint criterion of maximal $W$ and smooth $S_{\mathrm{stab}}$.