Adapting time-delay interferometry for LISA data in frequency

TL;DR

This paper addresses the challenge of residual noise in LISA's time-delay interferometry caused by Doppler shifts and proposes a scaling technique to improve laser noise suppression for gravitational wave detection.

Contribution

It introduces a novel scaling method in TDI to mitigate Doppler-induced residual noise, enhancing gravitational wave measurement accuracy.

Findings

The Doppler shift causes significant residual noise in frequency-based TDI measurements.

Including a scaling step in TDI effectively reduces residual noise.

The proposed method restores standard laser noise suppression levels.

Abstract

Time-delay interferometry (TDI) is a post-processing technique used to reduce laser noise in heterodyne interferometric measurements with unequal armlengths, a situation characteristic of space gravitational detectors such as Laser Interferometer Space Antenna (LISA). This technique consists in properly time-shifting and linearly combining the interferometric measurements in order to reduce the laser noise by several orders of magnitude and to detect gravitational waves. In this communication, we show that the Doppler shift due to the time evolution of the armlengths leads to an unacceptably large residual noise when using interferometric measurements expressed in units of frequency and standard expressions of the TDI variables. We also present a technique to mitigate this effect by including a scaling of the interferometric measurements in addition to the usual time-shifting operation when constructing the TDI variables. We demonstrate analytically and using numerical simulations that this technique allows one to recover standard laser noise suppression which is necessary to measure gravitational waves.