Parameter estimation for space-based gravitational wave detectors with ringdown signals

TL;DR

This paper derives analytical formulas for ringdown signals in space-based gravitational wave detectors, enabling efficient parameter estimation and source localization for massive black hole mergers, with validation via Bayesian methods.

Contribution

It introduces analytical formulas for frequency-domain ringdown signals considering detector effects, improving computational efficiency in parameter estimation.

Findings

Space-based detectors can accurately localize sources using ringdown signals.

Analytical formulas reduce computation time in Fisher matrix analysis.

Network of detectors enhances source localization accuracy.

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.