Gravitational Wave Detectors

Gravitational wave detectors have been in operation for over forty years now. However, it is only in the last five years or so that detectors with a non-negligible chance of detecting gravitational waves from astrophysical sources have been in operation. The first gravitational wave detector to operate was built by Joseph Weber [43]. It consisted of a large cylinder of aluminum, two meters long and a meter in diameter, with piezoelectric crystals affixed to either end.

The fundamental idea for such detectors is that if a strong enough gravitational wave was to pass by, that it would momentarily reduce the interatomic distances, essentially compressing the bar, and setting it ringing, like a tuning fork. The ringing would create electric voltages in the piezoelectric crystals which could then be read off. Of course, as with a tuning fork, the response of the apparatus is greatly increased if it is driven at its resonant frequency (about 1660Hz, for Weber's bars).

Weber's bar was isolated from seismic and electromagnetic disturbances and housed in a vacuum. He attributed the remaining noise in his instrument to thermal motion of the aluminum atoms. This noise limited Weber's measurements to strains of h^10~16, about five orders of magnitude less sensitive than the level now believed necessary to make the probability of detection non-negligible. Nonetheless, by 1969, Weber had constructed two bars and had observed coincident events in them although they were housed approximately 1000 miles apart. He calculated that his noise would create some of these events at rates as low as one per thousand years, and subsequently published his findings as "good evidence" for gravitational waves [44].

Many groups followed up on this and subsequent claims of gravitational wave detections made by Weber. No other group was ever able to reproduce these observations, and it is now generally agreed that Weber's events were spurious. Nonetheless, this launched the era of gravitational wave detectors, as resonant mass detectors (as Weber-like bars are now called) began operating in countries around the globe. Today, there is a network of these detectors operated under the general coordination of the International Gravitational Event Collaboration [45]. Technical advances have led to considerable improvements in sensitivity over the past decades. They continue to be rather narrow band detectors, however, and they are not the most sensitive instruments in operation today.

That distinction belongs to interferometric gravitational wave detectors [2]. The basic components of these detectors are a laser, a beam splitter to divide o

Mirror

Diode

1 Laser Beam

Mirror

Beam Splitter

Laser

Fig. 2. Schematic diagram of an interferometric gravitational wave detector. The beam splitter is coated to allow half the light to be transmitted to one of the mirrors, and the other to be reflected to the other mirror. Real interferometric gravitational wave detectors are much more sophisticated, including frequency stabilization of the laser, a second mirror on each arm between the beam splitter and the end mirror to create Fabry-Perot cavities, and control feedback loops which "lock" the interferometer onto an interference fringe. Thus, rather than measuring the current from the photo-diode directly, the gravitational wave signals are encoded in the feedback loop voltages needed to maintain the lock of the interferometer. These and many other enhancements are necessary to reach the required sensitivity level.

the laser light into two coherent beams, hanging mirrors to reflect the laser beams, and a light sensing diode, as shown in Fig. 2. The mirrors act essentially as freely moving particles in the horizontal directions. If a sufficiently strong gravitational wave with a vertical wave-vector component impinges, it shortens the distance between the beam splitter and one of the mirrors, and lengthens the distance between the beam splitter and the other mirror. This is registered as a shifting interference pattern by the light sensing diode, thus detecting the gravitational wave.

More specifically, what is measured is a quantity proportional to the strain on the detector, s := (Sx — Sy)/i, where 5x and 5y are the length changes in the two equal length arms of the interferometer, traditionally called the x and y arms, and I is the unperturbed length of each arm. If there were no noise, then in the special case that h+ or hx was aligned with the arms, we would have Sx = —Sy = Si and the measured quantity would be proportional to 2Si/i. For a more general alignment, but still in the absence of noise, some linear combination of h+ and hx is measured h(t) := F+(9,j>,-) h+ (t) + Fx(9,j>,-) hx(t), (4)

where F+ and Fx are called beam pattern functions. They project the gravitational wave components, h+ and hx, onto a coordinate system defined by the detector, and are functions of the Euler angles (9, —) which relate this coordinate system to coordinates which are aligned with the propagating GW.

In the case where there is noise, 5x and 5y are sums of the gravitational wave displacements and the noise displacements, so that the detector strain is s(t) = h(t)+n(t) (5)

where n(t) is the noise contribution. If the noise component can be kept from dominating the signal component, there is a reasonable chance that the gravitational wave can be detected. For a more complete and detailed account of interferometric detection of gravitational waves, as well as many other aspects of gravitational wave physics, we recommend [1].

The idea of using an interferometer as a gravitational wave detectors was explored repeatedly but independently by several different researchers over approximately 15 years [46-49]. The first prototype of an interferometric gravitational wave detector was built by one of Weber's students, Robert Forward, and collaborators in 1971 [50,51]. The advantages of this idea were immediately understood, but, as mentioned above, an understanding also emerged that kilometer-scale interferometry would be needed. Thus, these detectors needed to be funded, built and operated as coordinated efforts at the national or international level.

To date, there have been six large-scale (100 m plus) interferometers operated at five sites. Three of the these are located in the United States and constitute the Laser Interferometer Gravitational-wave Observatory (LIGO) [52, 53]. There is one four kilometer instrument at each of the LIGO-Hanford site in Washington State [54] and LIGO-Livingston site in Louisiana [55] (H1 and L1 respectively), and a two kilometer instrument, housed in the same enclosure, at the LIGO-Hanford Observatory (H2). The other interferometers are the three kilometer Virgo instrument, built in Italy by a French-Italian collaboration [56], the 600 meter German-English Observatory (GEO600) in Germany [57], and the TAMA observatory, a 300 meter instrument located in and funded by Japan [58].

Other large-scale interferometers are in various stages of planning, although funding has not been secured for them. One of the most interesting is LISA, a planned joint NASA-ESA mission, which would consist of two independent million-kilometer-scale interferometers created by three satellites in solar orbit [59, 60]. The larger scale and freedom from seismic noise will make this instrument sensitive at much lower frequencies than its Earth-based brethren.

Because they are currently the most sensitive gravitational wave detectors in the world, and the ones with which we are most familiar, this article will often use the particular example of LIGO and its methods to illustrate our discussion. LIGO began construction in 1994 and was commissioned in 1999. It began taking scientific data on 23 August, 2002. That data taking run, called Science Run One (or S1 for short), ended 9 Sept., 2002. There have been four subsequent science runs: S2 from 14 Feb. to 14 Apr. 2003, S3 from 31 Oct. 2003 to 9 Jan. 2004, S4 from 22 Feb. to 23 Mar. 2005, and finally S5 has been ongoing from Nov. 2005 and is expected to end in fall, 2007. At the conclusion of S5, the LIGO interferometers are scheduled for component enhancements which are expected to double the sensitivity of the instrument [61,62]. The upgrade process is scheduled to last approximately a year.

As with all the new interferometers, initial runs were short and periods between them were long because scientists and engineers were still identifying and eliminating technical and environmental noise sources which kept the instruments from running at their design sensitivity. As designed, interferometer sensitivity is expected to be bounded by three fundamental noise sources [49]. Below approximately 40 Hz, seismic noise transmitted to the mirrors through housing and suspension dominates. Between approximately 40 and 200 Hz, thermal vibrations in the suspension system for the mirrors dominates. Finally, above approximately 200 Hz, the dominant contribution comes from photon shot noise associated with counting statistics of the photons at the photodiode. These three fundamental noise regimes, which contribute to the "noise floor" of a detector, are described in the caption of Fig. 3.

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