Systematic bias in LISA ringdown analysis due to waveform inaccuracy

TL;DR

This paper evaluates how waveform modeling inaccuracies, especially mode truncation in ringdown signals, can cause biases in parameter estimation for LISA gravitational wave sources, emphasizing the need for including multiple modes.

Contribution

It establishes the minimum number of ringdown modes required to avoid parameter biases in LISA observations, based on a reference waveform with 13 modes.

Findings

3-6 modes are sufficient for typical sources

High-SNR events may require at least 10 modes

More modes might be needed depending on windowing choices

Abstract

Inaccurate modeling of gravitational-wave signals can introduce systematic biases in the inferred source parameters. As detector sensitivities improve and signals become louder, mitigating such waveform-induced systematics becomes increasingly important. In this work, we assess the systematic biases introduced by an incomplete description of the ringdown signal from massive black hole binaries in the LISA band. Specifically, we investigate the impact of mode truncation in the ringdown template. Using a reference waveform composed of 13 modes, we establish a mode hierarchy and determine the minimum number of modes required to avoid parameter biases across a wide range of LISA sources. For typical systems with masses $\sim 10^6$--$10^7\,M_\odot$ at redshifts $z \sim 2$--$6$, we find that at least 3--6 modes are needed for accurate parameter estimation, while high-SNR events may need at least 10 modes. Our results are a window-insensitive lower bound on the minimum number of modes, as more modes may be needed depending on the choice of time-domain windowing of the post-merger signal.