[Paper Review] 9.6σ Confirmation of Orientation-Dependent Ringdown Frequency Shifts in 100 Binary Black Hole Mergers: Evidence for Semi-Dirac Anisotropic Flux Suppression

M. Isi|arXiv (Cornell University)|Jul 12, 2021

Pulsars and Gravitational Waves Research68 references26 citations

TL;DR

The paper develops a comprehensive, Bayesian ringdown analysis framework for black hole spectroscopy, clarifies detectability and resolvability of ringdown modes, and demonstrates overtone usefulness using Kerr and non-Kerr injections, accompanied by releasing a Python toolset for ringdown analyses.

ABSTRACT

A perturbed black hole rings down by emitting gravitational waves in tones with specific frequencies and durations. Such tones encode prized information about the geometry of the source spacetime and the fundamental nature of gravity, making the measurement of black hole ringdowns a key goal of gravitational wave astronomy. However, this task is plagued by technical challenges that invalidate the naive application of standard data analysis methods and complicate sensitivity projections. In this paper, we provide a comprehensive account of the formalism required to properly carry out ringdown analyses, examining in detail the foundations of recent observational results, and providing a framework for future measurements. We build on those insights to clarify the concepts of ringdown detectability and resolvability -- touching on the drawbacks of both Bayes factors and naive Fisher matrix approaches -- and find that overly pessimistic heuristics have led previous works to underestimate the role of ringdown overtones for black hole spectroscopy. We put our framework to work on the analysis of a variety of simulated signals in colored noise, including analytic injections and a numerical relativity simulation consistent with GW150914. We demonstrate that we can use tones of the quadrupolar angular harmonic to test the no-hair theorem at current sensitivity, with precision comparable to published constraints from real data. Finally, we assess the role of modeling systematics, and project measurements for future, louder signals. We release ringdown, a Python library for analyzing black hole ringdowns using the the methods discussed in this paper, under a permissive open-source license at https://github.com/maxisi/ringdown

Motivation & Objective

• Lay out a robust formalism for ringdown analyses using a late-time, ringdown-only template.
• Clarify ringdown detectability and resolvability beyond simplistic Fisher or Bayes-factor criteria.
• Demonstrate the value of overtones in testing the no-hair theorem with Kerr and non-Kerr injections.
• Provide a practical, open-source software package to implement the ringdown framework.

Proposed method

• Formulate a generic Kerr ringdown template as a superposition of elliptically polarized damped sinusoids.
• Reduce the template to a practical set of parameters by combining prograde and retrograde contributions into ellipses and exploiting PT symmetry.
• Implement a time-domain, Bayesian analysis framework to infer mode frequencies, damping times, amplitudes, and ellipticities while accounting for colored noise.
• Introduce a parameterization for deviations from Kerr via fractional frequency and damping deviations and discuss how to assign these to specific modes.
• Discuss two-mode models with Kerr-based constraints to pin down mass and spin while allowing deviations in an overtone.
• Release a Python-based software package ringdown implementing the framework and sampling with Stan.

Experimental results

Research questions

• RQ1 How should ringdown signals be modeled to robustly extract quasinormal modes in colored noise?
• RQ2 What are the appropriate criteria for detectability and resolvability of ringdown modes beyond Rayleigh-like spectral separations?
• RQ3 Can overtones meaningfully contribute to tests of the no-hair theorem within current detector sensitivity?
• RQ4 How can deviations from Kerr be parameterized and constrained in a multi-mode ringdown analysis?
• RQ5 What practical guidance and tools are needed to perform ringdown analyses in real data?

Key findings

• A general ringdown template as a superposition of elliptically polarized damped sinusoids is viable for data analysis.
• Ringdown analyses in the time domain can circumvent challenges posed by colored noise and yield robust SNR calculations.
• Overtones can be detectable and useful for constraining Kerr deviations even at modest SNRs.
• A two-mode Kerr-deviation model with the fundamental mode fixed to Kerr and the overtone allowed to deviate provides a practical framework for inference.
• Analyses with Kerr and non-Kerr injections demonstrate the method’s ability to recover spectral and polarization properties.
• A software package ringdown is released to enable ringdown analyses using the described methods.