TDIR: Time-Delay Interferometric Ranging for Space-Borne Gravitational-Wave Detectors

TL;DR

This paper introduces TDIR, a novel method for estimating light-travel time delays in space-based gravitational-wave detectors using TDI combinations themselves, enabling laser noise cancellation without dedicated ranging systems.

Contribution

The paper proposes a high-accuracy, TDI-based ranging technique called TDIR, simplifying LISA's design by eliminating the need for separate inter-spacecraft ranging hardware.

Findings

TDIR achieves delay estimates accurate enough to cancel laser noise below secondary noise levels.

Simulation results demonstrate TDIR's effectiveness in the Synthetic LISA environment.

TDIR can potentially streamline the LISA mission design by removing dedicated ranging systems.

Abstract

Space-borne interferometric gravitational-wave detectors, sensitive in the low-frequency (mHz) band, will fly in the next decade. In these detectors, the spacecraft-to-spacecraft light-travel times will necessarily be unequal and time-varying, and (because of aberration) will have different values on up- and down-links. In such unequal-armlength interferometers, laser phase noise will be canceled by taking linear combinations of the laser-phase observables measured between pairs of spacecraft, appropriately time-shifted by the light propagation times along the corresponding arms. This procedure, known as time-delay interferometry (TDI), requires an accurate knowledge of the light-time delays as functions of time. Here we propose a high-accuracy technique to estimate these time delays and study its use in the context of the Laser Interferometer Space Antenna (LISA) mission. We refer to this ranging technique, which relies on the TDI combinations themselves, as Time-Delay Interferometric Ranging (TDIR). For every TDI combination, we show that, by minimizing the rms power in that combination (averaged over integration times $\sim 10^4$ s) with respect to the time-delay parameters, we obtain estimates of the time delays accurate enough to cancel laser noise to a level well below the secondary noises. Thus TDIR allows the implementation of TDI without the use of dedicated inter-spacecraft ranging systems, with a potential simplification of the LISA design. In this paper we define the TDIR procedure formally, and we characterize its expected performance via simulations with the \textit{Synthetic LISA} software package.