SyZyGy: A straight interferometric spacecraft system for gravity wave observations

We consider a spaceborne gravitational wave (GW) detector formed by three spacecraft in a linear array, coherently exchanging laser beams and using the data combinations of time-delay interferometry (TDI). We previously showed how the measured time series of Doppler shifts in the six one-way laser links between spacecraft pairs in a general unequal-arm triangular configuration can be combined, using TDI, to exactly cancel the otherwise overwhelming phase noise of the lasers while retaining sensitivity to GWs. Here we apply TDI, unfolding the general triangular configuration, to the special case of a linear array of three spacecraft. We show that such an array (``SyZyGy'') has, compared with an equilateral triangle GW detector of the same scale, a degraded (but non-zero) sensitivity at low frequencies $[f\ensuremath{\ll}c/(\mathrm{array}\mathrm{}\mathrm{size})]$ but similar peak and high-frequency sensitivities to GWs. We develop the GW and noise responses, noting that in this geometrical case only one TDI combination is GW sensitive showing a relatively simple 6-pulse response to an incident GW burst. Sensitivity curves are presented for SyZyGys having various arm lengths. A number of technical simplifications result from the linear configuration. These include only one faceted (e.g. cubical) proof mass per spacecraft, intraspacecraft laser metrology needed only at the central spacecraft, placement in an appropriate orbit can reduce Doppler drifts so that no laser beam modulation is required for ultrastable oscillator noise calibration, and little or no time-dependent articulation of the telescopes to maintain pointing. Because SyZyGy's sensitivity falls off more sharply at low frequency than that of an equilateral triangular array, it may be most useful for GW observations in the band between those of ground-based interferometers $(\ensuremath{\sim}10\char21{}2000\mathrm{Hz})$ and the Laser Interferometer Space Antenna $(\ensuremath{\sim}{10}^{\ensuremath{-}4}\char21{}{10}^{\ensuremath{-}1}\mathrm{Hz}).$ SyZyGy with $\ensuremath{\sim}1$ light-second scale could, for the same instrumental assumptions as LISA, make observations in this intermediate frequency GW band with $5\ensuremath{\sigma}$ sensitivity to sinusoidal waves $\ensuremath{\simeq}2.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}23}$ in a year's integration.