Massimo Tinto

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.

Time-Delay Interferometry

Equal-arm detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set the overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called time-delay interferometry (TDI).This article provides an overview of the theory, mathematical foundations, and experimental aspects associated with the implementation of TDI. Although emphasis on the application of TDI to the Laser Interferometer Space Antenna (LISA) mission appears throughout this article, TDI can be incorporated into the design of any future space-based mission aiming to search for gravitational waves via interferometric measurements. We have purposely left out all theoretical aspects that data analysts will need to account for when analyzing the TDI data combinations.

The LISA Optimal Sensitivity

The multiple Doppler readouts available on the Laser Interferometer Space Antenna (LISA) permit simultaneous formation of several interferometric observables. All these observables are independent of laser frequency fluctuations and have different couplings to gravitational waves and to the various LISA instrumental noises. Within the functional space of interferometric combinations LISA will be able to synthesize, we have identified a triplet of interferometric combinations that show optimally combined sensitivity. As an application of the method, we computed the sensitivity improvement for sinusoidal sources in the nominal, equal-arm LISA configuration. In the part of the Fourier band where the period of the wave is longer than the typical light travel-time across LISA, the sensitivity gain over a single Michelson interferometer is equal to

LISA and its in-flight test precursor SMART-2

\sqrt{2}

Data Combinations Accounting for LISA Spacecraft Motion

. In the mid-band region, where the LISA Michelson combination has its best sensitivity, the improvement over the Michelson sensitivity is slightly better than

Algorithms for unequal-arm Michelson interferometers

\sqrt{2}

Bayesian detection of unmodeled bursts of gravitational waves

, and the frequency band of best sensitivity is broadened. For frequencies greater than the reciprocal of the light travel-time, the sensitivity improvement is oscillatory and

Robust Bayesian detection of unmodelled bursts

\sim \sqrt{3}

The CASSINI Ka-band gravitational wave experiments

, but can be greater than

Pulsar timing sensitivities to gravitational waves from relativistic metric theories of gravity

\sqrt{3}