[Paper Review] Role of black hole quasinormal mode overtones for ringdown analysis

Peter James Nee, Sebastian H. Völkel+1 more|arXiv (Cornell University)|Feb 13, 2023

Astrophysical Phenomena and Observations4 citations

TL;DR

This paper investigates the role of quasinormal mode (QNM) overtones in black hole ringdown analysis using scalar wave propagation in Regge-Wheeler and Pöschl-Teller potentials. It finds that including even approximate overtone models significantly improves early-time black hole mass estimation, with performance primarily dependent on the number of overtones rather than model accuracy—challenging standard tests for physical overtone identification.

ABSTRACT

Extracting quasinormal modes from compact binary mergers to perform black hole spectroscopy is one of the fundamental pillars in current and future strong-gravity tests. Among the most remarkable findings of recent works is that including a large number of overtones not only reduces the mismatch of the fitted ringdown but also allows one to extract black hole parameters from a ringdown analysis that goes well within the nonlinear merger part. At the same time, it is well understood that several details of the ringdown analysis have important consequences for the question of whether overtones are present or not, and subsequently, to what extent one can claim to perform black hole spectroscopy. To clarify and tackle some aspects of overtone fitting, we revisit the clearer problem of wave propagation in the scalar Regge-Wheeler and Pöschl-Teller potentials. This setup, which is to some extent qualitatively very similar to the nonlinear merger-ringdown regime, indicates that using even an approximate model for the overtones yields an improved extraction of the black hole mass at early ringdown times. We find that the relevant parameter is the number of included modes rather than using the correct model for the overtones themselves. These results show that some standard tests for verifying the physical contribution of an overtone to a waveform can be misleading, and that even in the linear case it can be difficult to distinguish the presence of an excited mode from the fitting of non-QNM effects.

Motivation & Objective

• To clarify the role of quasinormal mode (QNM) overtones in ringdown analysis, particularly in the context of black hole spectroscopy.
• To investigate whether standard tests for identifying physically excited overtures are reliable, especially in the presence of non-QNM contributions.
• To assess the impact of using approximate QNM models (e.g., Pöschl-Teller) versus theory-specific models (e.g., Regge-Wheeler) on parameter estimation.
• To determine whether overtone fitting effectively removes non-QNM content from initial data, questioning the physical significance of fitted overtones.
• To provide insights for robust QNM extraction in future gravitational wave data analysis, especially under low signal-to-noise conditions.

Proposed method

• Uses linear scalar wave propagation in the Regge-Wheeler and Pöschl-Teller potentials as a simplified model for black hole ringdown.
• Performs ringdown fitting with varying numbers of QNM overtones, including both fundamental modes and higher overtones.
• Compares parameter estimation (mass, frequency, damping time) using different models (Regge-Wheeler vs. Pöschl-Teller) applied to each other’s waveforms.
• Analyzes the dependence of fitting accuracy on the number of included overtones and the starting time of the fit.
• Evaluates the robustness of fitted amplitudes and phases as functions of fit start time to assess physical relevance of overtones.
• Applies Bayesian-style analysis to assess model performance and distinguish between physically excited modes and effective fitting artifacts.

Experimental results

Research questions

• RQ1 To what extent does including overtones in ringdown fitting improve early-time black hole mass estimation, even with an approximate model?
• RQ2 Can standard tests reliably distinguish between physically excited overtones and non-QNM effects that are fitted by overtones?
• RQ3 Does the accuracy of QNM parameter estimation depend more on the number of overtones or the correctness of the underlying model?
• RQ4 How do fitted overtones relate to the true physical content of the initial data, especially in the linear regime?
• RQ5 Can overtones be interpreted as effective tools to suppress non-QNM contributions, rather than as physical excitations?

Key findings

• Including a large number of overtones—even from an approximate model—significantly improves the accuracy of black hole mass estimation at early ringdown times.
• The performance of ringdown fitting depends more on the number of overtones included than on the correctness of the theoretical model used for the overtones.
• Fitting overtones from the Pöschl-Teller potential to Regge-Wheeler waveforms yields similar early-time mass estimates as using the correct model, indicating model independence in early stages.
• The fundamental QNM (n=0) is robustly recoverable, but higher overtones (n≥1) are increasingly difficult to verify as physically excited due to fitting degeneracies.
• At late times, incorrect models plateau at a percent-level relative error in mass estimation, while correct models continue to improve, highlighting the importance of model fidelity for late-time analysis.
• The results suggest that overtones may act as effective tools to suppress non-QNM content from initial data, raising questions about their physical interpretation versus their utility in parameter estimation.