[Paper Review] Identification of Gravitational-waves from Extreme Mass Ratio Inspirals

Changqing Ye, Huimin Fan+3 more|arXiv (Cornell University)|Oct 5, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy3 citations

TL;DR

This paper presents a hierarchical search method for identifying gravitational waves from extreme mass ratio inspirals (EMRIs) using a combination of phenomenological waveforms and physical parameter priors, achieving high-precision measurements with relative errors below 4% for the massive black hole mass and as low as 0.5% for other parameters, even without prior physical information.

ABSTRACT

Space-based gravitational wave detectors like TianQin or LISA could observe extreme-mass-ratio-inspirals (EMRIs) at millihertz frequencies. The accurate identification of these EMRI signals from the data plays a crucial role in enabling in-depth study of astronomy and physics. We aim at the identification stage of the data analysis, with the aim to extract key features of the signal from the data, such as the evolution of the orbital frequency, as well as to pinpoint the parameter range that can fit the data well for the subsequent parameter inference stage. In this manuscript, we demonstrated the identification of EMRI signals without any additional prior information on physical parameters. High-precision measurements of EMRI signals have been achieved, using a hierarchical search. It combines the search for physical parameters that guide the subsequent parameter inference, and a semi-coherent search with phenomenological waveforms that reaches precision levels down to $10^{-4}$ for the phenomenological waveform parameters $ω_{0}$, $\dotω_{0}$, and $\ddotω_{0}$. As a result, we obtain measurement relative errors of less than 4% for the mass of the massive black hole, while keeping the relative errors of the other parameters within as small as 0.5%.

Motivation & Objective

• To enable high-precision identification of EMRI signals in space-based gravitational wave data without relying on prior physical parameter information.
• To overcome the challenge of multi-peak posterior distributions in EMRI parameter space that hinder efficient stochastic sampling.
• To develop a search strategy that combines phenomenological waveform templates for broad parameter coverage with physical waveforms to guide accurate inference.
• To achieve precision measurements of key EMRI parameters, such as orbital frequency evolution, at levels down to 10−4 for phenomenological parameters.
• To establish a foundation for future end-to-end EMRI data analysis pipelines using fully relativistic waveforms and advanced signal processing.

Proposed method

• Employ a two-stage hierarchical search: first using phenomenological waveforms to identify broad parameter ranges with high precision in $ω_0$, $Øω_0$, and $ØØω_0$ at $10^{-4}$ levels.
• Use the phenomenological search results to generate informed priors for subsequent physical parameter searches, reducing the search space.
• Apply FastEMRIWaveforms (FEW) in the Schwarzschild eccentric condition to generate accurate, fully relativistic EMRI waveforms for physical modeling.
• Implement a semi-coherent search strategy to enhance sensitivity and precision in detecting long-duration EMRI signals.
• Leverage cubic spline interpolation of sparse phase data in FEW to reconstruct complete phase evolution, especially in early inspiral stages.
• Use Taylor-series expansion of phase up to third order to model signal evolution, ensuring compatibility with phenomenological fitting.

Experimental results

Research questions

• RQ1 Can EMRI signals be identified with high precision without prior knowledge of physical parameters?
• RQ2 How effective is a hybrid search strategy combining phenomenological and physical waveforms in overcoming posterior multi-peak challenges?
• RQ3 To what extent can phenomenological waveforms accurately capture the phase evolution of EMRI signals in the early inspiral phase?
• RQ4 What level of precision can be achieved in measuring key parameters like $ω_0$, $Øω_0$, and $ØØω_0$ using phenomenological templates?
• RQ5 Can the method be generalized to Kerr background EMRIs, given the similarity in early-phase frequency evolution?

Key findings

• The hierarchical search achieved relative measurement errors of less than 4% for the massive black hole mass, even without prior physical information.
• Relative errors for other EMRI parameters were kept as low as 0.5%, demonstrating high-precision signal identification.
• Phenomenological waveform parameters $ω_0$, $Øω_0$, and $ØØω_0$ were measured with precision down to $10^{-4}$, enabling accurate phase evolution reconstruction.
• The method successfully navigated the multi-peak posterior structure by using phenomenological search results to guide physical parameter inference.
• The phase evolution of EMRIs was accurately captured over short time segments in early inspiral, where phase data are sparse, due to cubic spline interpolation in FEW.
• The approach is extendable to more complex scenarios, including Kerr background EMRIs and Time Delay Interferometry, due to strong correlation between phenomenological and physical waveforms in early phases.