Time-delay interferometry for space-based gravitational wave searches

Ground-based, equal-arm-length laser interferometers are being built to measure high-frequency astrophysical gravitational waves. Because of the arm-length equality, laser light experiences the same delay in each arm and thus phase or frequency noise from the laser itself precisely cancels at the photodetector. This laser noise cancellation is crucial. Raw laser noise is orders of magnitude larger than other noises and the desired sensitivity to gravitational waves cannot be achieved without very precise cancellation. Laser interferometers in space, e.g., the proposed three-spacecraft LISA detector, will have much longer arm lengths and will be sensitive to much lower frequency gravitational radiation. In contrast with ground-based interferometers, it is impossible to maintain equal distances between spacecraft pairs; thus laser noise cannot be cancelled by direct differencing of the beams. We analyze here an unequal-arm three-spacecraft gravitational wave detector in which each spacecraft has one free-running laser used both as a transmitter (to send to the other two spacecraft) and as a local oscillator (to monitor the frequencies of beams received from the other two spacecraft). This produces six data streams, two received time series generated at each of the three spacecraft. We describe the apparatus in terms of Doppler transfer functions of signals and noises on these one-way transits between pairs of test masses. Accounting for time-delays of the laser light and gravitational waves propagating through the apparatus, we discuss several simple and potentially useful combinations of the six data streams, each of which exactly cancels the noise from all three lasers while retaining the gravitational wave signal. Three of these combinations are equivalent to unequal-arm interferometers, previously analyzed by Tinto & Armstrong. The other combinations are new and may provide design and operational advantages for space-based detectors. Since at most three laser-noise-free data streams can be independent, we provide equations relating the combinations reported here. We give the response functions of these laser-noise-canceling data combinations for both a gravity wave signal and for the remaining noncancelled noise sources. Finally, using spacecraft separations and noise spectra appropriate for the LISA mission, we calculate the expected gravitational wave sensitivities for each laser-noise-canceling data combination.