Bayesian Time Delay Interferometry

TL;DR

This paper develops Bayesian methods for accurately estimating spacecraft delays in LISA's TDI process, enabling better suppression of laser frequency noise and improved gravitational wave detection.

Contribution

It introduces a Bayesian TDI ranging approach integrated into the LISA data analysis pipeline, allowing for joint delay estimation and gravitational wave inference.

Findings

Delay estimation achieves ~30 cm accuracy over 2.5 Gm baseline.

LFN suppression is below secondary noise levels.

MCMC methods effectively infer spacecraft delays from simulated data.

Abstract

Laser frequency noise (LFN) is the dominant source of noise expected in the Laser Interferometer Space Antenna (LISA) mission, at $\sim$7 orders of magnitude greater than the typical signal expected from gravitational waves (GWs). Time-delay interferometry (TDI) suppresses LFN to an acceptable level by linearly combining measurements from individual spacecraft delayed by durations that correspond to their relative separations. Knowledge of the delay durations is crucial for TDI effectiveness. The work reported here extends upon previous studies using data-driven methods for inferring the delays during the post-processing of raw phasemeter data, also known as TDI ranging (TDIR). Our TDIR analysis uses Bayesian methods designed to ultimately be included in the LISA data model as part of a "Global Fit" analysis pipeline. Including TDIR as part of the Global Fit produces GW inferences which are marginalized over uncertainty in the spacecraft separations and allows for independent estimation of the spacecraft orbits. We demonstrate Markov Chain Monte Carlo (MCMC) inferences of the six time-independent delays required in the rigidly rotating approximation of the spacecraft configuration (TDI 1.5) using simulated data. The MCMC uses fractional delay interpolation (FDI) to digitally delay the raw phase meter data, and we study the sensitivity of the analysis to the filter length. Varying levels of complexity in the noise covariance matrix are also examined. Delay estimations are found to result in LFN suppression well below the level of secondary noises and constraints on the armlengths to $\mathcal{O}(30)\ {\rm cm}$ over the ${\sim}2.5\ {\rm Gm}$ baseline.