Theory-agnostic searches for non-gravitational modes in black hole ringdown

TL;DR

This work introduces a theory-agnostic test for non-gravitational ringdown modes in black hole mergers by modeling the ringdown as standard Kerr QNMs plus additional scalar or vector modes with known Kerr-background frequencies and free amplitudes/phases. It implements a Bayesian analysis on real events (GW150914, GW190521, GW200129) and finds no strong evidence for extra modes, though allowing them affects the inferred remnant spin and mode amplitudes. The authors provide forecasts showing future detectors (including CE/ET and LISA) could constrain or detect such modes with amplitude ratios as small as $\sim$0.003–0.02, depending on the observed SNR, underscoring the method's potential to test gravity in the strong-field regime without committing to a specific beyond-GR theory.

Abstract

In any extension of General Relativity (GR), extra fundamental degrees of freedom couple to gravity. Besides deforming GR forecasts in a theory-dependent way, this coupling generically introduces extra modes in the gravitational-wave signal. We propose a novel theory-agnostic test of gravity to search for these nongravitational modes in black hole merger ringdown signals. To leading order in the GR deviations, their frequencies and damping times match those of a test scalar or vector field in a Kerr background, with only amplitudes and phases as free parameters. By applying this test to GW150914, GW190521, and GW200129, we find no strong evidence for an extra mode; however, its inclusion modifies the inferred distribution of the remnant spin. This test will be applicable for future detectors, which will achieve signal-to-noise ratios higher than 100 (and as high as 1000 for space-based detectors such as LISA). Such sensitivity will allow measurement of these modes with amplitude ratios as low as 0.02 for ground-based detectors (and as low as 0.003 for LISA), relative to the fundamental mode, enabling stringent agnostic constraints or detection of scalar/vector modes.

Figures (6)

• Figure 1: $\log_{10}$ Bayes factors for various ringdown models with extra scalar or vector modes (labelled with 'A') with respect to the GR1 model as a function of the offset time $t_{\rm offset}$. Different colors and line styles denote different events, while different markers show the chosen model. Note that each event has a different mass thus, a different time scale $t_{\text{offset}}$. Therefore, the $\log_{10}$ Bayes factor trends, specially at negative times, are expected to differ.
• Figure 2: Left panel: Minimum SNR necessary for detecting a scalar mode at $1-\sigma$ confidence level, according to the detectability criterion outlined in Berti:2005ysJimenezForteza:2020cve using a Fisher matrix approximation, which makes our estimates approximately independent of the sensitivity-curve profile. The blue and red dashed curves denote a different remnant spin $\chi_f$ with the phase difference between the GR and scalar modes fixed to $\delta \phi = 0$. The dependence on $\delta\phi\in [0,2\pi]$ is bracketed by the corresponding colored bands. The horizontal shaded bands represent the expected ringdown SNR for a GW150914-like event with a remnant mass of $M_f = 62 \,M_\odot$ as observed by ground-based detectors, including the LIGO-Virgo-KAGRA network (light blue), A+ (light green), and CE/ET (yellow). The orange band corresponds to the expected ringdown SNR for a similar event with a remnant mass of $M_f = 10^7 \,M_\odot$ observed by LISA (orange). We consider the range of amplitude ratios $A_{R,220}\in [0.001,1]$. Right: The same quantity shown in a contour plot on the $(A_{R,220},\delta\phi)$ plane for fixed $\chi_f=0.67$.
• Figure 3: Posterior distributions for the event GW200129 with $t_{\text{offset}}=0 \text{ms}$ for the models GR1 (left) and GR0+S (right). In both cases, the case without (resp., with) precession is indicated in yellow (resp., purple).
• Figure 4: Frequencies (left) and damping times (right) for a few gravitational modes and for $(220)$ scalar and vector modes of Kerr as a function of the spin. Results are normalized for a remnant mass compatible with GW150914, $M_f=62\,M_\odot$.
• Figure 5: Posterior distributions of some ringdown parameters for GW150914 in our analysis: $M_f$ and $\chi_f$ are the remnant's mass and spin, $A_{220}$ is the amplitude of the fundamental gravitational mode, and $A_{220}^R$ is the amplitude ratio of the ($220$) scalar mode relative to the fundamental gravitational one. We consider $t_{\rm offset}= 2\,{\rm ms}$ and the GR1 (magenta), GR0+S (yellow), and GR1+S (cyan) models. The contours state the 90$\%$ credible levels.