Towards models of gravitational waveforms from generic binaries II: Modelling precession effects with a single effective precession parameter

Abstract: Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the non-precessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively complex. Here we show that the dominant precession effects can be captured by a reduced set of spin parameters. Specifically, we introduce a single \emph{effective precession spin} parameter, $\chi_p$, which is defined from the spin components that lie in the orbital plane at some (arbitrary) instant during the inspiral. We test the efficacy of this parameter by considering binary inspiral configurations specified by the physical parameters of a corresponding non-precessing-binary configuration (total mass, mass ratio, and spin components (anti-)parallel to the orbital angular momentum), plus the effective precession spin applied to the larger black hole. We show that for an overwhelming majority of random precessing configurations, the precession dynamics during the inspiral are well approximated by our equivalent configurations. Our results suggest that in the comparable-mass regime waveform models with only three spin parameters faithfully represent generic waveforms, which has practical implications for the prospects of GW searches, parameter estimation and the numerical exploration of the precessing-binary parameter space.

• The paper introduces a novel effective precession parameter (χp) to simplify the modeling of precessing gravitational waveforms from generic black-hole binaries.
• It uses numerical Post-Newtonian experiments showing that waveform matches exceed 0.965 for most comparable mass configurations.
• The approach improves computational efficiency and real-time detection capabilities in gravitational wave astronomy.

An Approach to Gravitational Waveform Modelling with Effective Precession Parameter

The paper discussed introduces a novel method for modeling gravitational waveforms from generic black-hole binaries, with a focus on capturing precession effects using a single effective precession spin parameter, denoted as $\chi_p$. The need for efficient and accurate gravitational waveform models is paramount, especially in light of advancements in gravitational wave (GW) detection capabilities with instruments such as Advanced LIGO and Virgo. Traditional methods face complexity issues due to the numerous parameters influencing precession, and the authors propose a simplification that collapses this complexity using $\chi_p$.

Summary of Contributions

The research addresses the challenge of capturing precession dynamics in waveform models efficiently. In gravitational wave astronomy, especially under scenarios involving black hole binaries with arbitrary spin orientations, precessional movements complicate waveform synthesis. The study capitalizes on prior insights that segregate the non-precessing secular inspiral from precession-induced rotations. The effective precession spin parameter $\chi_p$ is introduced to mitigate this complexity by summarizing the dominant precession effects in a synthetically useful manner.

The parameter $\chi_p$ is defined based on the in-plane spin components during the orbital evolution, providing an averaged representation of precession dynamics over a specific time frame. Their model is validated against a sample of binary configurations, showing that for most practical cases—especially in regimes of comparable mass binaries—waveform models can be accurately generated with only three spin parameters: the effective aligned-spin component and $\chi_p$.

Methodology

The researchers conducted a series of numerical experiments using Post-Newtonian (PN) waveforms to validate their approach. They focus on configurations with varying masses and spins to assess the robustness and accuracy of the $\chi_p$ parameterization against complete waveform models. The model's efficacy is further demonstrated through matches calculated against fully specified waveforms, optimized over certain parameters. The effectiveness of the reduced-parameter model is gauged by the observed high degree of similarity in the waveform morphology compared to full-parameter models across different mass ratios.

Key Findings

The study presents substantial evidence supporting the feasibility of representing precessing waveforms using a reduced set of parameters. A cumulative distribution function analysis reveals that an overwhelming majority of configurations achieve matches above a threshold of 0.965, signifying their model's capability to closely approximate full precessional dynamics. This result implies that $\chi_p$ can capture the key features of precession without requiring computationally expensive full-parameter space exploration.

Implications

The implications of this research are significant for the field of gravitational wave astronomy. By reducing the complexities introduced by precession, waveform models become more computationally feasible, improving real-time detection capabilities and parameter estimation accuracy of black-hole binary mergers. Moreover, such improvements could enhance GW detectors' sensitivity and broaden their reach, allowing more exotic astrophysical events to be observed and analyzed.

Future Directions

For future research, integrating the $\chi_p$ parameterization into complete Inspiral-Merger-Ringdown (IMR) models, including those calibrated with numerical relativity (NR) data, would be an essential step. Additionally, evaluating this parameterization's performance in full parameter estimation pipelines for GW detections would provide a deeper understanding of its utility. Continued development could also explore its applicability across diverse cosmic scenarios, potentially including neutron-star binaries or mixed binary systems.

In conclusion, the introduction of the effective precession parameter $\chi_p$ effectively addresses prior limitations in waveform modeling for precessing binary systems and represents an efficient advancement in GW research methodology. This development holds great promise for enhancing the detection and analysis capabilities in the burgeoning field of gravitational wave astronomy.