# Gravitational-wave detector

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A gravitational-wave detector is any device designed to measure gravitational waves, minute distortions of spacetime that are predicted by Einstein's theory of general relativity. The existence of gravitational radiation is a prediction of general relativity. Gravitational waves are perturbations in the curvature of spacetime caused by accelerated masses. Since the 1960s gravitational-wave detectors have been built and constantly improved. The present-day generation of resonant mass antennas and laser interferometers has reached the necessary sensitivity to detect gravitational waves from sources in the Milky Way. As of late 2013, no direct detection of gravitational waves has yet been accomplished, although a number of experiments have now added to the evidence that gravitational waves are more than mathematical anomalies of relativity calculations (ref. the 1993 Nobel Prize in Physics).

## Complications

The direct detection of gravitational waves is complicated by the extraordinarily small effect the waves would produce on a detector. The amplitude of a spherical wave will fall off as the inverse of the distance from the source. Thus, even waves from extreme systems like merging binary black holes die out to very small amplitude by the time they reach the Earth. Astrophysicists expect that some gravitational waves passing the Earth may be as large as $h\approx 10^{-18}$, but generally no bigger.[citation needed]

## Weber bars

A simple device to detect the expected wave motion is called a Weber bar – a large, solid bar of metal isolated from outside vibrations. This type of instrument was the first type of gravitational-wave detector. Strains in space due to an incident gravitational wave excite the bar's resonant frequency and could thus be amplified to detectable levels. Conceivably, a nearby supernova might be strong enough to be seen without resonant amplification. Modern forms of the Weber bar are still operated, cryogenically cooled, with superconducting quantum interference devices to detect vibration (see for example, ALLEGRO). Weber bars are not sensitive enough to detect anything but extremely powerful gravitational waves.[1]

MiniGRAIL is a spherical gravitational-wave antenna using this principle. It is based at Leiden University, consisting of an exactingly machined 1150 kg sphere cryogenically cooled to 20 mK.[2] The spherical configuration allows for equal sensitivity in all directions, and is somewhat experimentally simpler than larger linear devices requiring high vacuum. Events are detected by measuring deformation of the detector sphere. MiniGRAIL is highly sensitive in the 2–4 kHz range, suitable for detecting gravitational waves from rotating neutron star instabilities or small black hole mergers.[3]

AURIGA is an ultracryogenic resonant bar gravitational wave detector based at INFN in Italy. It is based on a cylindrical bar detector. The AURIGA and LIGO teams have collaborated in joint observations.[4]

## Interferometers

A schematic diagram of a laser interferometer.
Atomic interferometry.

A more sensitive detector uses laser interferometry to measure gravitational-wave induced motion between separated 'free' masses.[5] This allows the masses to be separated by large distances (increasing the signal size); a further advantage is that it is sensitive to a wide range of frequencies (not just those near a resonance as is the case for Weber bars). Ground-based interferometers are now operational. Currently, the most sensitive is LIGO – the Laser Interferometer Gravitational Wave Observatory. LIGO has three detectors: one in Livingston, Louisiana; the other two (in the same vacuum tubes) at the Hanford site in Richland, Washington. Each consists of two light storage arms which are 2 to 4 kilometers in length. These are at 90 degree angles to each other, with the light passing through 1m diameter vacuum tubes running the entire 4 kilometers. A passing gravitational wave will slightly stretch one arm as it shortens the other. This is precisely the motion to which an interferometer is most sensitive.

Even with such long arms, the strongest gravitational waves will only change the distance between the ends of the arms by at most roughly 10−18 meters. LIGO should be able to detect gravitational waves as small as $h \approx 5\times 10^{-22}$. Upgrades to LIGO and other detectors such as VIRGO, GEO 600, and TAMA 300 should increase the sensitivity still further; the next generation of instruments (Advanced LIGO and Advanced Virgo) will be more than ten times more sensitive. Another highly sensitive interferometer (LCGT) is currently in the design phase. A key point is that a ten-times increase in sensitivity (radius of "reach") increases the volume of space accessible to the instrument by one thousand. This increases the rate at which detectable signals should be seen from one per tens of years of observation, to tens per year.

Interferometric detectors are limited at high frequencies by shot noise, which occurs because the lasers produce photons randomly; one analogy is to rainfall – the rate of rainfall, like the laser intensity, is measurable, but the raindrops, like photons, fall at random times, causing fluctuations around the average value. This leads to noise at the output of the detector, much like radio static. In addition, for sufficiently high laser power, the random momentum transferred to the test masses by the laser photons shakes the mirrors, masking signals at low frequencies. Thermal noise (e.g., Brownian motion) is another limit to sensitivity. In addition to these "stationary" (constant) noise sources, all ground-based detectors are also limited at low frequencies by seismic noise and other forms of environmental vibration, and other "non-stationary" noise sources; creaks in mechanical structures, lightning or other large electrical disturbances, etc. may also create noise masking an event or may even imitate an event. All these must be taken into account and excluded by analysis before a detection may be considered a true gravitational-wave event.

Space-based interferometers, such as LISA and DECIGO, are also being developed. LISA's design calls for three test masses forming an equilateral triangle, with lasers from each spacecraft to each other spacecraft forming two independent interferometers. LISA is planned to occupy a solar orbit trailing the Earth, with each arm of the triangle being five million kilometers. This puts the detector in an excellent vacuum far from Earth-based sources of noise, though it will still be susceptible to shot noise, as well as artifacts caused by cosmic rays and solar wind.

## High frequency detectors

There are currently two detectors focusing on detections at the higher end of the gravitational-wave spectrum (10−7 to 105 Hz)[citation needed]: one at University of Birmingham, England, and the other at INFN Genoa, Italy. A third is under development at Chongqing University, China. The Birmingham detector measures changes in the polarization state of a microwave beam circulating in a closed loop about one meter across. Two have been fabricated and they are currently expected to be sensitive to periodic spacetime strains of $h\sim{2 \times 10^{-13}/\sqrt{\mathit{Hz}}}$, given as an amplitude spectral density. The INFN Genoa detector is a resonant antenna consisting of two coupled spherical superconducting harmonic oscillators a few centimeters in diameter. The oscillators are designed to have (when uncoupled) almost equal resonant frequencies. The system is currently expected to have a sensitivity to periodic spacetime strains of $h\sim{2 \times 10^{-17}/\sqrt{\mathit{Hz}}}$, with an expectation to reach a sensitivity of $h\sim{2 \times 10^{-20}/\sqrt{\mathit{Hz}}}$. The Chongqing University detector is planned to detect relic high-frequency gravitational waves with the predicted typical parameters ?g ~ 1010 Hz (10 GHz) and h ~ 10−30–10−31.

## Pulsar timing arrays

A different approach to detecting gravitational waves is used by pulsar timing arrays, such as the European Pulsar Timing Array,[6] the North American Nanohertz Observatory for Gravitational Waves,[7] and the Parkes Pulsar Timing Array.[8] These projects propose to detect gravitational waves by looking at the effect these waves have on the incoming signals from an array of 20–50 well-known millisecond pulsars. As a gravitational wave passing through the Earth contracts space in one direction and expands space in another, the times of arrival of pulsar signals from those directions are shifted correspondingly. By studying a fixed set of pulsars across the sky, these arrays should be able to detect gravitational waves in the nanohertz range. Such signals are expected to be emitted by pairs of merging supermassive black holes.[9]

## Einstein@Home

In some sense, the easiest signals to detect should be constant sources. Supernovae and neutron star or black hole mergers should have larger amplitudes and be more interesting, but the waves generated will be more complicated. The waves given off by a spinning, bumpy neutron star would be "monochromatic" – like a pure tone in acoustics. It would not change very much in amplitude or frequency.

The Einstein@Home project is a distributed computing project similar to SETI@home intended to detect this type of simple gravitational wave. By taking data from LIGO and GEO, and sending it out in little pieces to thousands of volunteers for parallel analysis on their home computers, Einstein@Home can sift through the data far more quickly than would be possible otherwise.[10]

## References

1. ^ For a review of early experiments using Weber bars, see Levine, J. (April 2004). "Early Gravity-Wave Detection Experiments, 1960-1975". Physics in Perspective (Birkhäuser Basel) 6 (1): 42–75. Bibcode:2004PhP.....6...42L. doi:10.1007/s00016-003-0179-6.
2. ^ Gravitational Radiation Antenna In Leiden
3. ^ de Waard, Arlette; Luciano Gottardi, and Giorgio Frossati (Italy). "Spherical Gravitational Wave Detectors: cooling and quality factor of a small CuAl6% sphere". Marcel Grossman meeting on General Relativity (PDF). Rome
4. ^ AURIGA Collaboration; LIGO Scientific Collaboration; Baggio et al; Cerdonio, M; De Rosa, M; Falferi, P; Fattori, S; Fortini, P et al. (2008). "A Joint Search for Gravitational Wave Bursts with AURIGA and LIGO". Classical and Quantum Gravity 25 (9): 095004. arXiv:0710.0497. Bibcode:2008CQGra..25i5004B. doi:10.1088/0264-9381/25/9/095004.
5. ^ The idea of using laser interferometry for gravitational-wave detection was first mentioned by Gerstenstein and Pustovoit 1963 Sov. Phys.–JETP 16 433. Weber mentioned it in an unpublished laboratory notebook. Rainer Weiss first described in detail a practical solution with an analysis of realistic limitations to the technique in R. Weiss (1972). "Electromagnetically Coupled Broadband Gravitational Antenna". Quarterly Progress Report, Research Laboratory of Electronics, MIT 105: 54.
6. ^ Janssen, G. H.; Stappers, B. W.; Kramer, M.; Purver, M.; Jessner, A.; Cognard, I.; Bassa, C.; Wang, Z.; Cumming, A.; Kaspi, V. M. (2008). "European Pulsar Timing Array". AIP Conference Proceedings 983. pp. 633–635. doi:10.1063/1.2900317. edit
7. ^ North American Nanohertz Observatory for Gravitational Waves (NANOGrav) homepage
8. ^ Parkes Pulsar Timing Array homepage
9. ^ Hobbs, G. B.; Bailes, M.; Bhat, N. D. R.; Burke-Spolaor, S.; Champion, D. J.; Coles, W.; Hotan, A.; Jenet, F. et al. (2008). "Gravitational wave detection using pulsars: status of the Parkes Pulsar Timing Array project". arXiv:0812.2721 [astro-ph].
10. ^ Einstein@Home