Higher-order Time-Delay Interferometry

TL;DR

This paper extends Time-Delay Interferometry (TDI) to higher orders, enabling exact cancellation of laser noise including acceleration effects, which is crucial for future space-based gravitational wave detectors with large and varying inter-spacecraft distances.

Contribution

The paper introduces a higher-order TDI framework that cancels laser noise up to acceleration and higher derivatives, advancing previous first- and second-order methods.

Findings

Higher-order TDI cancels laser noise including acceleration effects.

Method involves lifting basis elements to higher-order spaces and linear combinations.

Applicable to future missions with large, varying inter-spacecraft distances.

Abstract

Time-Delay Interferometry (TDI) is the data processing technique that cancels the large laser phase fluctuations affecting the one-way Doppler measurements made by unequal-arm space-based gravitational wave interferometers. In a previous publication we derived TDI combinations that exactly cancel the laser phase fluctuations up to first order in the inter-spacecraft velocities. This was done by interfering two digitally-synthesized optical beams propagating a number of times clock- and counter-clock-wise around the array. Here we extend that approach by showing that the number of loops made by each beam before interfering corresponds to a specific higher-order TDI space. In it the cancellation of laser noise terms that depend on the acceleration and higher-order time derivatives of the inter-spacecraft light-travel-times is achieved exactly. Similarly to what we proved for the second-generation TDI space, elements of a specific higher-order TDI space can be obtained by first ``lifting'' the basis ($\a, \b, \g, X$) of the $1^{\rm st}$-generation TDI space to the higher-order space of interest and then taking linear combinations of them with coefficients that are polynomials of the six delays operators. Higher-Order TDI might be required by future interplanetary gravitational wave missions whose inter-spacecraft distances vary appreciably with time, in particular, relative velocities are much larger than those of currently planned arrays.