[Paper Review] Time domain phenomenological model of gravitational wave subdominant harmonics for quasi-circular non-precessing binary black hole coalescences

H. Estellés, S. Husa+6 more|arXiv (Cornell University)|Dec 22, 2020

Pulsars and Gravitational Waves Research5 citations

TL;DR

This paper presents a time-domain phenomenological gravitational wave model, IMRPhenomT+, that extends the IMRPhenomT framework to include subdominant $l=2,m=\pm1$, $l=3,m=\pm3$, $l=4,m=\pm4$, and $l=5,m=\pm5$ spherical harmonic modes for quasi-circular, non-precessing binary black hole mergers. The model is calibrated to numerical relativity and Teukolsky equation solutions up to mass ratio 18, achieving high accuracy and computational efficiency for Bayesian parameter estimation, particularly for signals with significant higher-mode content.

ABSTRACT

In this work we present an extension of the time domain phenomenological model IMRPhenomT for gravitational wave signals from binary black hole coalescences to include subdominant harmonics, specifically the $(l=2, m=\pm 1)$, $(l=3, m=\pm 3)$, $(l=4, m=\pm 4)$ and $(l=5, m=\pm 5)$ spherical harmonics. We also improve our model for the dominant $(l=2, m=\pm 2)$ mode and discuss mode mixing for the $(l=3, m=\pm 2)$ mode. The model is calibrated to numerical relativity solutions of the full Einstein equations up to mass ratio 18, and to numerical solutions of the Teukolsky equations for higher mass ratios. This work complements the latest generation of traditional frequency domain phenomenological models (IMRPhenomX), and provides new avenues to develop computationally efficient models for gravitational wave signals from generic compact binaries.

Motivation & Objective

• To develop a computationally efficient, time-domain phenomenological model that includes subdominant gravitational wave modes for non-precessing binary black hole coalescences.
• To improve the modeling of the dominant $l=2,m=\pm2$ mode and extend it to include $l=2,m=\pm1$, $l=3,m=\pm3$, $l=4,m=\pm4$, and $l=5,m=\pm5$ modes.
• To calibrate the model across the full mass ratio range using numerical relativity and Teukolsky equation solutions, ensuring accuracy for both low and high mass ratios.
• To enable more accurate Bayesian parameter estimation for gravitational wave events with significant higher-mode content, such as GW190412 and GW190814.
• To lay the foundation for future time-domain models that can incorporate precession and mode mixing effects with improved physical fidelity.

Proposed method

• The model uses a phenomenological ansatz in the time domain, with amplitude and phase functions constructed from post-Newtonian (PN) expressions for the inspiral regime and calibrated to numerical waveforms for the merger and ringdown.
• Post-Newtonian amplitudes for each mode are derived up to 3.5PN order, incorporating spin corrections and higher-order contributions, with mode-specific prefactors and phase evolution.
• The model employs a hybrid approach: PN expressions for the inspiral, and a phenomenological merger-ringdown transition using calibrated parameters from numerical relativity and Teukolsky solutions.
• The $l=2,m=\pm1$ and $l=3,m=\pm3$ modes are modeled with specific amplitude and phase functions, including spin and mass-ratio dependence, while $l=4,m=\pm4$ and $l=5,m=\pm5$ are included with similar structure.
• The model is calibrated using a large set of numerical relativity waveforms up to mass ratio 18 and Teukolsky-based waveforms for higher mass ratios, ensuring robustness across the parameter space.
• The model is tested for accuracy in both time-domain waveform matching and Bayesian parameter estimation, with performance validated against known events like GW170729 and GW190412.

Experimental results

Research questions

• RQ1 How accurately can a time-domain phenomenological model represent subdominant gravitational wave modes in binary black hole coalescences?
• RQ2 Can a time-domain model achieve comparable accuracy and computational efficiency to existing frequency-domain models like IMRPhenomXHM while including higher harmonics?
• RQ3 What is the impact of including $l=2,m=\pm1$, $l=3,m=\pm3$, $l=4,m=\pm4$, and $l=5,m=\pm5$ modes on parameter estimation for massive binary systems?
• RQ4 How does the inclusion of higher-order modes affect the consistency of parameter estimation in events like GW190412 and GW190814?
• RQ5 Can the time-domain framework naturally accommodate mode mixing and precession effects in future extensions?

Key findings

• The model IMRPhenomT+ achieves high accuracy across the full mass ratio range, with mismatches below $10^{-3}$ for most configurations, even at high mass ratios.
• The inclusion of subdominant modes significantly improves parameter estimation accuracy for massive binary systems, as demonstrated in tests on GW190412 and GW190814.
• The model outperforms single-mode time-domain models in capturing the full signal structure, particularly in the merger and ringdown phases where higher modes dominate.
• Calibration to both numerical relativity and Teukolsky solutions ensures robustness for mass ratios up to 18 and beyond, with the latter used for extrapolation to higher ratios.
• The time-domain formulation enables a more natural separation of inspiral, merger, and ringdown regimes, facilitating tests of general relativity and parameterized deviations.
• The model provides a computationally efficient alternative to frequency-domain models, with performance comparable to IMRPhenomXHM while being fully formulated in the time domain.