General relativistic treatment of LISA optical links

TL;DR

This paper presents a fully general relativistic numerical model for calculating LISA's optical links, accounting for gravitational effects of the Sun and Earth, to improve time-delay interferometry and suppress laser noise.

Contribution

It introduces a high-accuracy, general relativistic numerical code for computing LISA's optical links, including effects like Sagnac and Shapiro delay, enhancing TDI performance.

Findings

Numerical code achieves ~10^{-2} m accuracy in optical link calculations.

Relativistic effects and symmetries can be used to suppress residual laser noise.

Analysis demonstrates improved TDI variable performance with the proposed model.

Abstract

LISA is a joint space mission of the NASA and the ESA for detecting low frequency gravitational waves in the band $10^{-5} - 1$ Hz. In order to attain the requisite sensitivity for LISA, the laser frequency noise must be suppressed below the other secondary noises such as the optical path noise, acceleration noise etc. This is achieved by combining time-delayed data for which precise knowledge of time-delays is required. The gravitational field, mainly that of the Sun and the motion of LISA affect the time-delays and the optical links. Further, the effect of the gravitational field of the Earth on the orbits of spacecraft is included. This leads to additional flexing over and above that of the Sun. We have written a numerical code which computes the optical links, that is, the time-delays with great accuracy $\sim 10^{-2}$ metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with sufficient accuracy within $\sim 10$ metres for an integrated time window of about six days, when one of the arms tends to be tangent to the orbit. Our analysis of the optical links is fully general relativistic and the numerical code takes into account effects such as the Sagnac, Shapiro delay, etc.. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the configuration of LISA and in the physics, which may be used effectively to suppress the residual laser noise in the modified first generation TDI. We demonstrate our results for some important TDI variables.