Bayesian Time Delay Interferometry for Orbiting LISA: Accounting for the Time Dependence of Spacecraft Separations

TL;DR

This paper extends Bayesian time delay interferometry techniques to orbiting LISA, accounting for time-dependent spacecraft separations, enabling effective laser noise suppression and gravitational wave analysis in realistic orbital conditions.

Contribution

It introduces a novel Taylor-expanded fractional delay interpolation filter for efficient arm-length estimation in orbiting LISA data analysis.

Findings

Feasibility of arm-length estimation on day-long timescales.

Effective laser frequency noise suppression using Keplerian orbital parameters.

Potential extension to arbitrary numerical orbits.

Abstract

Previous work demonstrated effective laser frequency noise (LFN) suppression for Laser Interferometer Space Antenna (LISA) data from raw phasemeter measurements using a Markov Chain Monte Carlo (MCMC) algorithm with fractional delay interpolation (FDI) techniques to estimate the spacecraft separation parameters required for time-delay interferometry (TDI) under the assumption of a rigidly rotating LISA configuration. Including TDI parameters in the LISA data model as part of a global fit analysis pipeline enables gravitational wave inferences to be marginalized over uncertainty in the spacecraft separations. Here we extend the algorithm's capability to perform data-driven TDI on LISA in Keplerian orbits, which introduce a time-dependence in the arm-length parameters and at least $\mathcal{O}$(M) times greater computational cost since the filter must be applied for every sample in the time series of sample size M. We find feasibility of arm-length estimation on $\sim$day-long time scales by using a novel Taylor-expanded version of the fractional delay interpolation filter that allows half of the filter computation to be calculated and stored before MCMC iterations and requires shorter filter lengths than previously reported. We demonstrate LFN suppression for orbiting LISA using accurate arm-length estimates parameterized by Keplerian orbital parameters under the assumption of unperturbed analytical Keplerian orbits, and explore the potential extension of these methods to arbitrary numerical orbits.