[Paper Review] Eccentric Massive Black Hole Binaries in LISA I : The Detection Capabilities of Circular Templates

E. K. Porter, Alberto Sesana|arXiv (Cornell University)|May 28, 2010

Particle physics theoretical and experimental studies11 citations

TL;DR

This paper investigates the inefficacy of circular gravitational wave templates in detecting eccentric massive black hole binaries expected to be observed by LISA. Using astrophysically motivated models and Markov chain Monte Carlo analysis, it demonstrates that circular templates recover only 5–13% of the optimal signal-to-noise ratio and fail to resolve sky position and luminosity distance, proving that eccentric templates are essential even for low final eccentricities.

ABSTRACT

One of the major assumptions in the search for gravitational wave signatures from massive and supermassive black hole binaries with LISA, is that these systems will have circularized before entering the LISA bandwidth. Current astrophysical simulations now suggest that systems could have a non-negligible eccentricity in the LISA band, and an important level of eccentricity in the Pulsar Timing regime. In this work, we use a set of source catalogues from astrophysically motivated models of massive black hole binary formation and assume a one year LISA mission lifetime. Depending on the model in question, the initial eccentricities in the final year of the inspiral can be as high as 0.6 for high mass seeds and 0.8 for low mass seeds. We show that restricted post-Newtonian circular templates are extremely inefficient in recovering eccentric binaries, with median optimal signal to noise ratio recoveries of approximately 10% for all models considered. This coupled with extremely large errors in parameter recovery from individual Markov chain Monte Carlo's demonstrate quite clearly that even to search for binaries with initial eccentricities as low as $10^{-4}$, we will require eccentric templates for LISA data analysis.

Motivation & Objective

• To assess the detection efficiency of circular gravitational wave templates for eccentric massive black hole binaries in the LISA frequency band.
• To evaluate the impact of initial eccentricity on template matching and parameter estimation accuracy.
• To determine whether circular templates remain viable for LISA data analysis despite astrophysical evidence of non-zero eccentricity in the final year of inspiral.
• To quantify the limitations of circular templates in recovering key source parameters such as chirp mass, reduced mass, sky position, and luminosity distance.
• To establish the necessity of developing and implementing eccentric waveform templates for future LISA data analysis pipelines.

Proposed method

• Utilized source catalogues from hybrid models of massive black hole binary formation with initial eccentricities of 0, 0.3, and 0.6 for high and low mass seed systems.
• Evolved binary systems into the LISA band using Peters and Mathews' secular decay equations for semi-major axis and eccentricity, transitioning to 2-PN equations for the final year of inspiral.
• Performed Monte Carlo simulations over extrinsic parameters (inclination, polarization, distance, sky position) to simulate realistic signal injections.
• Applied Markov Chain Monte Carlo (MCMC) techniques to estimate parameters and compute fitting factors (overlaps) between injected eccentric waveforms and recovered circular templates.
• Computed optimal signal-to-noise ratios (SNR) and fidelity metrics to assess detection efficiency and parameter estimation accuracy.
• Analyzed parameter estimation errors for chirp mass, reduced mass, luminosity distance, and sky position across multiple models and eccentricity levels.

Experimental results

Research questions

• RQ1 How effective are circular gravitational wave templates in detecting massive black hole binaries with non-zero eccentricity in the LISA frequency band?
• RQ2 What is the maximum recoverable signal-to-noise ratio when using circular templates for eccentric binaries with initial eccentricities up to 0.8?
• RQ3 To what extent do circular templates fail in estimating key astrophysical parameters such as sky position and luminosity distance for eccentric binaries?
• RQ4 How do fitting factors (overlaps) between eccentric and circular waveforms vary with initial eccentricity and binary mass?
• RQ5 What are the implications for LISA data analysis and numerical relativity if eccentric binaries are common in the LISA band?

Key findings

• For high mass seed systems, circular templates recover only about 5% of the optimal signal-to-noise ratio, with maximum overlaps (fitting factors) of approximately 0.15.
• For low mass seed systems, the recovered optimal SNR reaches a maximum of 13%, with fitting factors peaking at around 0.25, still far below the LISA confidence threshold.
• Sky position and luminosity distance are essentially unresolved in all models, leading to systematic misinterpretation of source parameters as lighter binaries at higher redshifts.
• Parameter estimation errors for chirp mass peak between 10⁻⁴ and 10⁻³, while reduced mass errors range from 10⁻² to 10⁻¹, indicating poor resolution despite some mass parameter recoverability.
• Even for final eccentricities as low as 10⁻⁴, circular templates fail to provide reliable detection and estimation, necessitating the use of eccentric waveforms in LISA data analysis.
• The long duration of LISA signals (months to years) increases the risk of de-phasing between circular and eccentric waveforms, making circular templates increasingly ineffective compared to shorter-duration LIGO-like signals.