Time scales in LISA

TL;DR

This paper analyzes the relationship between station proper time and Barycentric Coordinate Time (TCB) for the LISA mission, providing necessary transformations to improve gravitational wave detection accuracy.

Contribution

It derives the proper time versus BCRS time transformation for LISA, quantifying the rate difference and oscillatory behavior of station proper times relative to TCB.

Findings

Rate difference of about 5×10^{-8} between proper time and TCB.

Oscillatory trend in proper time difference with amplitude ~10^{-3} seconds.

Provides essential time transformation for LISA data analysis.

Abstract

The LISA mission is a space interferometer aiming at the detection of gravitational waves in the [$10^{-4}$,$10^{-1}$] Hz frequency band. In order to reach the gravitational wave detection level, a Time Delay Interferometry (TDI) method must be applied to get rid of (most of) the laser frequency noise and optical bench noise. This TDI analysis is carried out in terms of the coordinate time corresponding to the Barycentric Coordinate Reference System (BCRS), TCB, whereas the data at each of the three LISA stations is recorded in terms of each station proper time. We provide here the required proper time versus BCRS time transformation. We show that the difference in rate of station proper time versus TCB is of the order of $5 10^{-8}$. The difference between station proper times and TCB exhibits an oscillatory trend with a maximum amplitude of about $10^{-3}$ s.