TDI and clock noise removal for the split interferometry configuration of LISA

Abstract

Laser phase noise is the dominant noise source in the on-board measurements of the space-based gravitational wave detector LISA (Laser Interferometer Space Antenna). A well-known data analysis technique, the so-called time-delay interferometry (TDI), provides synthesized data streams free of laser phase noise. At the same time, TDI also removes the next largest noise source: phase fluctuations of the on-board clocks which distort the sampling process. TDI needs precise information about the spacecraft separations, sampling times and differential clock noise between the three spacecrafts. These are measured using auxiliary modulations on the laser light. Hence, there is a need for algorithms that account for clock noise removal schemes combined with TDI while preserving the gravitational wave signal. In this paper, we will present the mathematical formulation of the LISA-like data streams and discuss a compliant algorithm that corrects for both clock and laser noise in the case of a rotating, non-breathing LISA constellation. In contrast to previous papers, we consider the current optical bench design (split interferometry configuration), i.e. the test mass readout is done by the local oscillators only, instead of reflecting the weak inter-spacecraft light off the test mass. Furthermore, the absolute order of laser frequencies is taken into account and it can be shown that the TDI equations remain invariant. This is a crucial issue and was, up to now, completely neglected in the analysis.