[Paper Review] Modeling ringdown II: non-precessing binary black holes

L. T. London|arXiv (Cornell University)|Jan 24, 2018

Pulsars and Gravitational Waves Research53 references6 citations

TL;DR

This paper presents the first complete, parametrized model (RDNP) for gravitational wave ringdown signals from nonprecessing binary black holes, expressing quasinormal mode amplitudes and phases as functions of initial binary parameters. It reveals that the dominant mode excitation is a remarkably simple linear function of system parameters—specifically, -4 times the symmetric mass ratio for nonspinning binaries—strongly suggesting the potential for an analytic, post-Newtonian-like theory of ringdown excitation.

ABSTRACT

The aftermath of binary black hole coalescence is a perturbed remnant whose gravitational radiation rings down, encoding information about the new black hole's recent history and current state.It is expected that this ringdown radiation will be composed primarily of Kerr quasinormal modes, and thereby enable tests of general relativity.Here, the first complete ringdown signal model for nonprecessing binary black hole systems is presented: multipole amplitudes and phases are modeled as functions of initial binary parameters. It is found that using the peak time of the dominant merger multipole as a reference results in the dominant mode's excitation being a remarkably simple linear function of system parameters, strongly suggesting that an analytic treatment may be within reach.In particular, for initially nonspinning black holes, the dominant quadrupole is excited as -4 times the system's symmetric mass ratio.Application of the model to parameter estimation allows general relativity predictions for mode amplitudes independently of signal strength.Treatment of GW150914 indicates some mode amplitudes and relative phases are intrinsically difficult to constrain.

Motivation & Objective

• To develop a physically parametrized, complete signal model for the ringdown phase of nonprecessing binary black hole mergers, enabling direct comparison with gravitational wave data.
• To map initial binary parameters (mass ratio, spins) to quasinormal mode amplitudes and phases, overcoming the lack of an analytic theory for ringdown excitation.
• To enable general relativity tests by providing independent predictions for mode amplitudes and phases, decoupled from signal strength.
• To identify robust features in the parameter space—such as abrupt phase transitions—that must be reproduced by any future analytic theory of ringdown.
• To validate the model against numerical relativity simulations and assess its performance in parameter estimation for real events like GW150914.

Proposed method

• Constructing the RDNP model by fitting multipole amplitudes and phases from numerical relativity (NR) waveforms of nonprecessing binary black hole systems.
• Using the peak time of the dominant merger multipole as a reference time to stabilize amplitude and phase measurements across diverse binary configurations.
• Modeling amplitudes and phases as polynomial functions of the symmetric mass ratio (η), spin parameters (χs, χa), and δ = (χs - χa)/2, with complex coefficients derived from NR data.
• Validating the model using independent NR waveforms (e.g., BAM simulations), with match metrics showing high fidelity across multipoles (ℓ ≤ 5).
• Applying the model to parameter estimation for GW150914 to assess the intrinsic difficulty of constraining mode amplitudes and relative phases.
• Demonstrating that the dominant mode amplitude scales linearly with η, with a coefficient of -4.0071 for nonspinning binaries, indicating potential for analytic treatment.

Experimental results

Research questions

• RQ1 Can quasinormal mode amplitudes and phases in the ringdown of nonprecessing binary black holes be accurately modeled as functions of initial binary parameters?
• RQ2 Is the excitation of the dominant (220) mode linearly dependent on the symmetric mass ratio, and does this suggest a path toward an analytic, post-Newtonian-like theory of ringdown?
• RQ3 What are the intrinsic limitations in constraining mode amplitudes and relative phases for real gravitational wave events like GW150914?
• RQ4 Do abrupt transitions in relative phase across the parameter space represent robust features that must be captured by any future theoretical model?
• RQ5 Can the ringdown signal model be used to make general relativity predictions for mode amplitudes independently of signal strength?

Key findings

• The dominant (220) mode amplitude is a linear function of the symmetric mass ratio, with a coefficient of -4.0071 for nonspinning binaries, strongly indicating a potential for an analytic theory.
• The model shows that non-monotonic excitations and abrupt phase transitions are robust features of the nonprecessing binary black hole parameter space, not numerical artifacts.
• Using the peak strain time as a reference time results in stable and observationally convenient amplitude measurements, despite the peak lying in a nonperturbative regime.
• For GW150914, the model indicates that some mode amplitudes and relative phases are intrinsically difficult to constrain, even with high signal-to-noise ratio data.
• The model achieves high match (>0.99) with validation NR waveforms across multipoles with ℓ ≤ 5, confirming its accuracy and robustness.
• The complex coefficients in the amplitude models (e.g., A2220 = η(−0.6537χs − 4.0071)) are derived from NR data and show consistent scaling across the parameter space, supporting the model’s predictive power.