relevant thing: interferometers basically compare two return times, and as long as light travels up and down the arms on a null worldline, it does not matter at all what the wavelength is doing along the way.1

Interferometer observations

Interferometers are now (2008) the most sensitive operating detectors, and they are the most likely instruments to make the first direct detections. They have two major advantages over bar detectors: their sensitivity can be increased considerably without running into fundamental problems of materials or physics, and (because they do not depend on any resonant vibration) they operate over a broad spectrum of frequencies.

In designing an interferometer for gravitational waves, scientists face the same basic options as for bar detectors: try to increase the size of the signal and try to reduce the extraneous noise. Unlike bars, interferometers have a natural way of increasing the signal: extending their length. The longer the arm, the larger will be the difference in return times for a given gravitational wave amplitude. The largest earth-bound detectors are the two 4-km LIGO detectors in the USA, closely followed by 3-km VIRGO in Italy. But physical length is only the first step. The light beams inside the arms can be folded over multiple passes up and down or contained within resonating light cavities, so that the residence time of light in each arm is longer; this again increases the difference in return times when there is a gravitational wave. A simplified sketch of the optical design of the LIGO or VIRGO detector is shown in Fig. (9.3).

But even with long arms, the signal can be masked by a variety of instrumental sources of noise (Saulson 1994, Hough and Rowan 2000). To filter out vibrations from ground disturbances, interferometers use the same strategy as bar detectors: the optical components are suspended. Twoor three-stage suspensions are normal, but VIRGO uses seven pendulums, each hanging from the one above; this is designed to allow the instrument to observe at lower frequencies, where seismic vibration noise is stronger. Thermal vibrations of mirrors and their suspensions are, as for bars, a serious problem, but interferometers do not have the option to operate at temperatures as low as 4K, because the heat input from the laser beam on the mirrors would be impossible to remove. Current interferometers (as of 2008) all operate at room temperature, although there are plans in Japan to pioneer operation at 40K. (The project is known as LCGT.) Thermal noise is controlled by using ultra-high-Q materials for the mirrors and suspension wires; this confines the thermal noise to narrow bands around the resonant frequencies of the mirror vibrations and pendulum modes, and these are designed to be well outside the observation band of the instruments. This approach, which includes using optical fiber as the suspension wire and bonding it to mirrors without glue, has been pioneered in the GEO600 detector. As interferometers become more advanced, they will also have to contend with quantum sources of noise and

1In fact, the wavelength and frequency of light depend in any case on the observer, so the question cannot be posed in a frame-invariant way. This is another reason not to introduce them into discussions of how interferometers measure gravitational waves!

Between mid-2005 and late 2007, the LIGO detectors logged operation in coincidence (all three detectors) for more than a year at a sensitivity better than 10−21 for broadband bursts of gravitational waves. From what astronomers know about potential sources of gravitational waves (see below), it is certainly possible that signals of this strength would arrive once or twice per year, but it is also possible that they are as rare as once per hundred years! GEO600 has operated for more than half of this same period in coincidence as well. VIRGO began operation at a similar sensitivity in early 2007. The LIGO and GEO detectors pool their data and analyze them jointly in an organization called the LIGO Scientific Collaboration (LSC). VIRGO also shares its data, which are then analyzed jointly with LSC data. If further large-scale detectors are brought into operation (there are advanced plans in Japan, as mentioned earlier, and in Australia), then they will presumably also join these efforts. Each new detector improves the sensitivity of all existing detectors.

The existing detector groups plan modest incremental upgrades in sensitivity during the remainder of the first decade of the twenty-first century, and then LIGO and VIRGO expect to upgrade to sensitivities better than 10−22 and to push their lower frequency limit closer to 10 Hz. These major upgrades, called Advanced LIGO and Advanced VIRGO, will involve many new components and much more powerful lasers. As we will see below, regular detections of gravitational waves are almost guaranteed at that point. But the first detection could of course come at any time during this development schedule.

Even more ambitious than the ground-based detector projects is the LISA mission, a joint undertaking of the European Space Agency (ESA) and the US space agency NASA that is currently planned for launch around 2018. Going into space is necessary if we want to observe at frequencies below about 1 Hz. At these low frequencies, the Earth’s Newtonian gravitational field is too noisy: any change in gravity will be registered by detectors, and even the tiny changes in gravity associated with the density changes of seismic waves and weather systems are larger than the expected amplitudes of gravitational waves. So low-frequency observing needs to be done far from the Earth.

LISA will consist of three spacecraft in an equilateral triangle, all orbiting the Sun at a distance of 1 AU, the same as the Earth, and trailing the Earth by 20o. Their separation will be 5 × 106 km, well-matched to detecting gravitational waves in the millihertz frequency range. The three arms can be combined in various ways to form three different two-armed interferometers, which allows LISA to measure both polarizations of an incoming wave and to sweep the sky with a fairly uniform antenna pattern. As with ground-based instruments, LISA must contend with noise. Thermal noise is not an issue because its large armlength means that the signal it is measuring – the time-difference between arms – is much larger than would be induced by vibrations of materials. But external disturbances, caused by the Sun’s radiation pressure and the solar wind, are significant, and so the LISA spacecraft must be designed to fall freely to high accuracy. Each spacecraft contains two free masses (called proof masses) that are undisturbed and able to follow geodesics. The spacecraft senses the positions of the masses and uses very weak jets to adjust its position so it does not disturb the proof masses. The proof masses are used as the reference points for the interferometer arms. This technique is called drag-free operation, and is one of a number of fascinating technologies that LISA will pioneer.