Numerical simulation of time delay interferometry for a LISA-like mission with the simplification of having only one interferometer

TL;DR

This paper performs a detailed numerical simulation of time delay interferometry for a LISA-like mission with a single interferometer, accounting for planetary perturbations, to ensure laser noise suppression meets sensitivity requirements.

Contribution

It introduces a numerical approach to simulate TDI residuals considering planetary perturbations for a simplified single-interferometer LISA-like mission.

Findings

Residual optical path differences are below 1 meter, well within noise suppression limits.

Numerical accuracy of residual path difference calculation is better than 1 cm.

Simulation framework can be applied to other space-borne gravitational wave detectors.

Abstract

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper (Dhurandhar et al., Class. Quantum Grav., 27, 135013, 2010), we have found a large family of second-generation analytic solutions of time delay interferometry with one arm dysfunctional, and we also estimated the laser noise due to residual time-delay semi-analytically from orbit perturbations due to Earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry (TDI), we simulate the time delay numerically in this paper for all solutions with the generation number n \leq 3. We have worked out a set of 3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021 using the CGC2.7 ephemeris framework. We then use this numerical solution to calculate the residual optical path differences in the second-generation solutions of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1 cm (or 30 ps). The maximum path length difference, for all configuration calculated, is below 1 m (3 ns). This is well below the limit under which the laser frequency noise is required to be suppressed. The numerical simulation in this paper can be applied to other space-borne interferometers for gravitational wave detection with the simplification of having only one interferometer.