Geometric Time Delay Interferometry

TL;DR

This paper introduces Geometric TDI, a new approach to analyze and optimize Time Delay Interferometry observables for LISA, enhancing sensitivity and robustness against noise and instrumental issues.

Contribution

It presents a combinatorial algorithm for exploring second-generation TDI observables, identifying improved forms with better sensitivity and noise resilience.

Findings

Identified alternative TDI observables with fewer nulls in response functions.

Discovered TDI forms less susceptible to instrumental gaps and glitches.

Enhanced high-frequency gravitational-wave sensitivity.

Abstract

The space-based gravitational-wave observatory LISA, a NASA-ESA mission to be launched after 2012, will achieve its optimal sensitivity using Time Delay Interferometry (TDI), a LISA-specific technique needed to cancel the otherwise overwhelming laser noise in the inter-spacecraft phase measurements. The TDI observables of the Michelson and Sagnac types have been interpreted physically as the virtual measurements of a synthesized interferometer. In this paper, I present Geometric TDI, a new and intuitive approach to extend this interpretation to all TDI observables. Unlike the standard algebraic formalism, Geometric TDI provides a combinatorial algorithm to explore exhaustively the space of second-generation TDI observables (i.e., those that cancel laser noise in LISA-like interferometers with time-dependent armlengths). Using this algorithm, I survey the space of second-generation TDI observables of length (i.e., number of component phase measurements) up to 24, and I identify alternative, improved forms of the standard second-generation TDI observables. The alternative forms have improved high-frequency gravitational-wave sensitivity in realistic noise conditions (because they have fewer nulls in the gravitational-wave and noise response functions), and are less susceptible to instrumental gaps and glitches (because their component phase measurements span shorter time periods).