Both NASA and ESA perform experiments in which they monitor the return time of communication signals with interplanetary spacecraft for the characteristic effect of gravitational waves. For missions to Jupiter and Saturn, for example, the return times are of order 2–4 × 103 s. Any gravitational wave event shorter than this will, by Equation (43), appear three times in the time delay: once when the wave passes the Earth-based transmitter, once when it passes the spacecraft, and once when it passes the Earth-based receiver. Searches use a form of data analysis using pattern matching. Using two transmission frequencies and very stable atomic clocks, it is possible to achieve sensitivities for of order 10–13, and even 10–15 may soon be reached .
Many pulsars, particularly the old millisecond pulsars, are extraordinarily regular clocks when averaged over timescales of a few years, with random timing irregularities too small for the best atomic clocks to measure. If one assumes that they emit pulses perfectly regularly, then one can use observations of timing irregularities of single pulsars to set upper limits on the background gravitational-wave field. Here, the one-way formula Equation (42) is appropriate. The transit time of a signal to the Earth from the pulsar may be thousands of years, so we cannot look for correlations between the two terms in a given signal. Instead, the delay is a combination of the effects of waves at the pulsar when the signal was emitted and waves at the Earth when it is received. If one observes a single pulsar, then because not enough is known about the intrinsic irregularity in pulse emission, the most one can do is to set upper limits on a background of gravitational radiation at very low frequencies [244, 347].
If one simultaneously observes two or more pulsars, then the Earth-based part of the delay is correlated, and this offers, in addition, a means of actually detecting strong gravitational waves with periods of several years that pass the Earth (in order to achieve the long-period stability of pulse arrival times). Observations are currently underway at a number of observatories. The most stringent limits to date are from the Parkes Pulsar Timing Array , which sets an upper limit on a stochastic background of . Two further collaborations for timing have been formed: the European Pulsar Timing Array (EPTA)  and NanoGrav . Astrophysical backgrounds in this frequency band are likely (see Section 8.2.2), so these arrays have a good chance of making early detections. Future timing experiments will be even more powerful, using new phased arrays of radio telescopes that can observe many pulsars simultaneously, such as the Low Frequency Array (LOFAR)  and the Square Kilometer Array .
Pulsar timing can also be used to search for individual events, not just a stochastic signal. The first example of an upper limit from such a search was the exclusion of a black-hole–binary model for 3C66B .
Gravity-gradient noise on the Earth is much larger than the amplitude of any expected waves from astronomical sources at frequencies below about 1 Hz, but this noise falls off rapidly as one moves away from the Earth. A detector in space would not notice the Earth’s noisy environment. The Laser Interferometer Space Antenna (LISA) project, currently being developed in collaboration by ESA and NASA with a view toward launching in 2018, would open up the frequency window between 0.1 mHz and 0.1 Hz for the first time [198, 145]. There are several websites that provide full information about this project [234, 235, 236].
We will see below that there are many exciting sources expected in this wave band, for example the coalescences of giant black holes in the centers of galaxies. LISA would see such events with extraordinary sensitivity, recording typical SNRs of 1000 or more for events at redshift one.
A space-based interferometer can have arm lengths much greater than a wavelength. LISA, for example, would have arms 5 × 106 km long, and that would be longer than half a wavelength for any gravitational waves above 30 mHz. In this regime, the response of each arm will follow the three-term formula we encountered earlier. The short-arm approximation we used for ground-based interferometers works for LISA only at the lowest frequencies in its observing band.
LISA will consist of three free-flying spacecraft, arranged in an array that orbits the sun at 1 AU, about 20 degrees behind the Earth in its orbit. They form an approximately equilateral triangle in a plane tilted at 60° to the ecliptic, and their simple Newtonian elliptical orbits around the sun preserve this arrangement, with the array rotating backwards once per year as the spacecraft orbit the sun. By passing light along each of the arms, one can construct three different Michelson-type interferometers, one for each vertex. With this array one can measure the polarization of a gravitational wave directly. The spacecraft are too far apart to use simple mirrors to reflect light back along an arm: the reflected light would be too weak. Instead, LISA will have optical transponders: light from one spacecraft’s on-board laser will be received at another, which will then send back light from its own laser locked exactly to the phase of the incoming signal.
The main environmental disturbances to LISA are forces from the sun: solar radiation pressure and pressure from the solar wind. To minimize these, LISA incorporates drag-free technology. Interferometry is referenced to an internal proof mass that falls freely, unattached to the spacecraft. The job of the spacecraft is to shield this mass from external disturbances. It does this by sensing the position of the mass and firing its own jets to keep itself (the spacecraft) stationary relative to the proof mass. To do this, it needs thrusters of very small thrust that have accurate control. The key technologies that have enabled the LISA mission are the availability of such thrusters, accelerometers needed to sense disturbances to the spacecraft, and lasers capable of continuously emitting 1 W of infrared light for many years. ESA is planning to launch a satellite called LISA Pathfinder to test all of these technologies in 2010 .
LISA is not the only proposal for an interferometer in space for gravitational wave detection. The DECIGO proposal is a more ambitious design, positioned at a higher frequency to fill the gap between LISA and ground-based detectors . Even more ambitious, in the same frequency band, is the Big Bang Observer, a NASA concept study to examine what technology would be needed to reach the ultimate sensitivity of detecting a gravitational wave background from inflation at these frequencies .
This work is licensed under a Creative Commons License.