LISA detections of massive black hole inspirals: parameter extraction errors due to inaccurate template waveforms

TL;DR

This paper estimates the impact of waveform model inaccuracies on parameter extraction for massive black hole binaries detected by LISA, highlighting potential limitations in measurement precision due to theoretical errors.

Contribution

The authors develop mathematical tools to quantify theoretical waveform errors and apply them to a simplified MBHB inspiral model, providing insights into their significance.

Findings

Theoretical errors in sky position are comparable to statistical errors (~1 degree).

For mass and spin parameters, theoretical errors may surpass statistical errors by an order of magnitude.

Tools developed can be applied to estimate waveform error impacts in broader gravitational-wave studies.

Abstract

The planned Laser Interferometer Space Antenna (LISA) is expected to detect the inspiral and merger of massive black hole binaries (MBHBs) at z <~ 5 with signal-to-noise ratios (SNRs) of hundreds to thousands. Because of these high SNRs, and because these SNRs accrete over periods of weeks to months, it should be possible to extract the physical parameters of these systems with high accuracy; for instance, for a ~ 10^6 Msun MBHBs at z = 1 it should be possible to determine the two masses to ~ 0.1% and the sky location to ~ 1 degree. However, those are just the errors due to noise: there will be additional "theoretical" errors due to inaccuracies in our best model waveforms, which are still only approximate. The goal of this paper is to estimate the typical magnitude of these theoretical errors. We develop mathematical tools for this purpose, and apply them to a somewhat simplified version of the MBHB problem, in which we consider just the inspiral part of the waveform and neglect spin-induced precession, eccentricity, and PN amplitude corrections. For this simplified version, we estimate that theoretical uncertainties in sky position will typically be ~ 1 degree, i.e., comparable to the statistical uncertainty. For the mass and spin parameters, our results suggest that while theoretical errors will be rather small absolutely, they could still dominate over statistical errors (by roughly an order of magnitude) for the strongest sources. The tools developed here should be useful for estimating the magnitude of theoretical errors in many other problems in gravitational-wave astronomy.