Proper time versus TCB used for Time Delay Interferometry in the LISA mission

Astronomy and Astrophysics – Astrophysics

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The three spacecraft i,j,k=1,2,3 of the LISA (Laser Interferometer Space Antenna) joint ESA-NASA mission aim at the detection of gravitational waves (GW). They are to be launched in 2015, L_{ij}˜ 5\cdot10^{6} kilometers apart, in a triangular configuration, each following a free-falling test mass. The test masses are inter-connected by double laser links forming an interferometer. Laser frequency (LF) and optical bench (OB) noises are several orders of magnitude larger than GW signals to be detected. Hence, Time Delay Interferometry (TDI) data pre-processing (summarized here) was developed to reach the gravitational wave detection level, allowing to get rid of (most of) LF and OB noises. TDI combination algebra, to be applied on the data, is given in terms of the coordinate time, t, corresponding to the Barycentric Coordinate Reference System (BCRS) and called TCB. However, local data at each spacecraft is recorded in terms of spacecraft proper time, k/τ, requiring the use of relativistic time transformations k/τ -t provided here.

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