Measuring test mass acceleration noise in space-based gravitational wave astronomy

TL;DR

This paper introduces an acceleration-based formalism for analyzing space-based gravitational wave detector data, improving noise characterization and systematic subtraction, demonstrated with LISA Pathfinder simulations.

Contribution

It develops an acceleration formalism for gravitational wave data analysis, enhancing systematic subtraction and noise marginalization in space-based detectors.

Findings

Effective systematic subtraction using acceleration formalism

Application of the method to LISA Pathfinder simulation data

Generalization of the $\\mathcal{F}$-statistic for noise and parameter marginalization

Abstract

The basic constituent of interferometric gravitational wave detectors -- the test mass to test mass interferometric link -- behaves as a differential dynamometer measuring effective differential forces, comprising an integrated measure of gravity curvature, inertial effects, as well as non-gravitational spurious forces. This last contribution is going to be characterised by the LISA Pathfinder mission, a technology precursor of future space-borne detectors like eLISA. Changing the perspective from displacement to acceleration can benefit the data analysis of LISA Pathfinder and future detectors. The response in differential acceleration to gravitational waves is derived for a space-based detector's interferometric link. The acceleration formalism can also be integrated into time delay interferometry by building up the unequal-arm Michelson differential acceleration combination. The differential acceleration is nominally insensitive to the system free evolution dominating the slow displacement dynamics of low-frequency detectors. Working with acceleration also provides an effective way to subtract measured signals acting as systematics, including the actuation forces. Because of the strong similarity with the equations of motion, the optimal subtraction of systematic signals, known within some amplitude and time shift, with the focus on measuring the noise provides an effective way to solve the problem and marginalise over nuisance parameters. The $\mathcal{F}$-statistic, in widespread use throughout the gravitation waves community, is included in the method and suitably generalised to marginalise over linear parameters and noise at the same time. The method is applied to LPF simulator data and, thanks to its generality, can also be applied to the data reduction and analysis of future gravitational wave detectors.