[Paper Review] Parameter estimation for space-based gravitational wave detectors with ringdown signals

Chunyu Zhang, Yungui Gong+1 more|arXiv (Cornell University)|May 24, 2021

Pulsars and Gravitational Waves Research107 references16 citations

TL;DR

This paper derives analytical frequency-domain models for ringdown gravitational wave signals in space-based detectors, incorporating harmonic phases, detector rotation, and arm length effects. It demonstrates that networked space-based detectors significantly improve source localization for massive black hole mergers, with Fisher matrix results validated by Bayesian inference, especially for high-mass binaries at high redshifts.

ABSTRACT

Unlike ground-based gravitational wave detectors, space-based gravitational wave detectors can detect the ringdown signals from massive black hole mergers with large signal-to-noise ratios, help to localize sources and extract their parameters. To reduce the computation time in the Fisher information matrix analysis, we derive the analytical formulas of frequency-domain ringdown signals for both heliocentric and geocentric detectors by considering the effects of the harmonic phases, the rotation period of the geocentric detector, and the detector's arm length. We explore median errors of the parameter estimation and source localization with ringdown signals from binaries with different masses and different redshifts. Using a binary source with the total mass $M=10^7\ M_\odot$ at the redshift $z=1$, we analyze the dependence of these errors on the sky position. We find that the network of space-based gravitational wave detectors can significantly improve the source localization at the ringdown stage. The results of the Fisher matrix approximation are also checked by Bayesian inference method.

Motivation & Objective

• To develop analytical frequency-domain models for ringdown signals in space-based gravitational wave detectors, accounting for realistic instrumental effects.
• To improve parameter estimation and source localization accuracy for massive black hole binaries using ringdown signals.
• To validate Fisher matrix results with Bayesian inference, particularly for extrinsic parameters like sky position and luminosity distance.
• To investigate the impact of higher harmonics and detector network configurations on localization performance.
• To quantify the dependence of estimation errors on sky position and source redshift for binaries with varying total masses.

Proposed method

• Derives analytical expressions for frequency-domain ringdown signals in both heliocentric and geocentric reference frames.
• Incorporates the effects of harmonic phases, the Earth's rotation period, and detector arm length into the signal model.
• Applies the Fisher Information Matrix (FIM) method to estimate median parameter errors and source localization accuracy.
• Uses Bayesian inference with the dynesty sampler to validate FIM results, particularly for extrinsic parameters.
• Performs error propagation using the FIM on ringdown signals from binaries with total masses M = 10⁷ M⊙ and redshift z = 1, varying sky position.
• Compares localization performance across single detectors and networks of space-based detectors.

Experimental results

Research questions

• RQ1 How do harmonic phases, detector rotation, and arm length affect the accuracy of ringdown signal modeling in space-based detectors?
• RQ2 What are the median parameter estimation errors for massive black hole binaries (M = 10⁷ M⊙) at z = 1, and how do they vary with sky position?
• RQ3 To what extent can a network of space-based detectors improve source localization compared to single detectors?
• RQ4 How do Fisher matrix results compare with Bayesian inference for extrinsic parameters like sky location and luminosity distance?
• RQ5 What is the role of higher harmonics in breaking parameter degeneracies and enhancing localization for high-mass ringdown signals?

Key findings

• The analytical frequency-domain signal model accurately captures the effects of harmonic phases, detector rotation, and arm length, enabling faster parameter estimation than numerical integration.
• For a binary with total mass M = 10⁷ M⊙ at redshift z = 1, the median localization error varies with sky position, with the best performance achieved near the ecliptic poles.
• The network of space-based detectors improves source localization by a factor of ∼100 compared to single detectors, significantly enhancing the ability to identify electromagnetic counterparts.
• Fisher matrix results are validated by Bayesian inference, confirming improved accuracy for extrinsic parameters when higher harmonics are included.
• Higher harmonics of ringdown signals play a crucial role in breaking degeneracies between parameters, especially for massive black hole binaries.
• The study confirms that space-based detectors like LISA, TianQin, and Taiji can achieve high-precision parameter estimation for ringdown signals from supermassive black hole mergers, enabling cosmological applications such as Hubble tension tests.