Time-delay analysis of LISA gravitational wave data: Elimination of spacecraft motion effects

LISA (Laser Interferometer Space Antenna) is a proposed mission which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. Modeling each spacecraft as moving almost inertially, rigidly carrying a laser, beam splitters and photodetectors, we previously showed how the measured time series of Doppler shifts of the six one-way laser beams between spacecraft pairs could be combined, with suitable time delays, to cancel exactly the otherwise overwhelming phase noise of the lasers. Three of the combinations synthesized data that could in principle be obtained if the spacecraft separations were very precisely equal, as in Michelson interferometry; seven other combinations offered possible design advantages and useful redundancy. Here we extend those results by presenting time-delay equations for Doppler data from the actual drag-free configuration envisaged for the LISA mission. Each spacecraft will carry two proof-masses, shielded within two non-inertial optical benches carrying lasers and photodetectors. In this full drag-free configuration there are now twelve Doppler data streams, six measured with beams between the three vertex spacecraft and two with beams between each of the optical bench pairs on the three spacecraft. We show that generalizations of our previous linear data combinations, now using these twelve one-way Doppler measurements, can cancel the noises of all six lasers and also remove Doppler shifts due to the non-inertial motions of the six optical benches. It is noteworthy that adjacent optical benches need not be rigidly connected and that no phase locking of their lasers is required. From the latest LISA estimates for power spectra of remaining Doppler noises (very-low-level proof-mass “acceleration” noise, photodetector shot noise, and beam pointing noise) we compute the sensitivities of the generalized data combinations X and P. In the Appendix we give defining equations and sensitivity results for two additional data combinations, denoted E and U. Like X and P, these combinations only require data from four one-way laser links between the LISA spacecraft. LISA can achieve the desired gravitational wave strain performance of $\sim {10}^{-23}$ with any of these combinations.