Catching a gravitational wave

13 January 2017

The technology behind LIGO’s epochal discovery.

Gravitational waves alternatively compress and stretch space–time as they propagate, exerting tidal forces on all objects in their path. Detectors such as Advanced LIGO (aLIGO) search for this subtle distortion of space–time by measuring the relative separation of mirrors at the ends of long perpendicular arms, which form a simple Michelson interferometer with Fabry–Perot cavities in the arms: a beam splitter directs laser light to mirrors at the ends of the arms and the reflected light is recombined to produce an interference pattern. When a gravitational wave passes through the detector, the strain it exerts changes the relative lengths of the arms and causes the interference pattern to change.

The arms of the aLIGO detectors are each 4 km long to help maximise the measured length change. Even on this scale, however, the induced length changes are tiny: the first detected gravitational waves, from the merger of two black holes, changed the arm length of the aLIGO detectors by just 4 × 10–18 m, which is approximately 200 times smaller than the proton radius. Achieving the fantastically high sensitivity required to detect this event was the culmination of decades of research and development.

Battling noise

The idea of using an interferometer to detect gravitational waves was first concretely proposed in the 1970s and full-scale detectors began to be constructed in the mid-1990s, including GEO600 in Germany, Virgo in Italy and the LIGO project in the US. LIGO consists of detectors at two sites separated by about 3000 km – Hanford (in Washington state) and Livingston in Louisiana – and undertook its first science runs in 2002–2008. Following a major upgrade, the observatory restarted in September 2015 as aLIGO with an initial sensitivity four times greater than its predecessor. Since the detectors measure strain in space–time, the effective increase in volume, or event rate, of aLIGO is a factor 43 higher.

A major issue facing aLIGO designers is to isolate the detectors from various noise sources. At a frequency of around 10 Hz, the motion of the Earth’s surface or seismic noise is about 10 orders of magnitude larger than required, with the seismic noise falling off at higher frequencies. A powerful solution is to suspend the mirrors as pendulums: a pendulum acts as a low-pass filter, providing significant reductions in motion at frequencies above the pendulum frequency. In aLIGO, a chain of four suspended masses is used to provide a factor 107 reduction in seismic motion. In addition, the entire suspension is attached to an advanced seismic isolation system using a variety of active and passive techniques, which further isolate noise by a factor 1000. At 10 Hz, and in the absence of other noise sources, these systems could already increase the sensitivity of the detectors to roughly 10–19 m/(Hz). At even lower frequencies (10 μHz), the daily tides stretch and shrink the Earth by the order of 0.4 mm over 4 km.

Another source of low-frequency noise arises from moving mass interacting with the detector mirrors via the Newtonian inverse square law. The dominant source of this noise is from surface seismic waves, which can produce density fluctuations of the Earth’s surface close to the interferometer mirrors and result in a fluctuating gravitational force on them. While methods of monitoring and subtracting this noise are being investigated, the performance of Earth-based detectors is likely to always be limited at frequencies below 1 Hz by this noise source.

Thermal noise associated with the thermal energy of the mirrors and their suspensions can also cause the mirrors to move, providing a significant noise source at low-to-mid-range frequencies. The magnitude of thermal noise is related to the mechanical loss of the materials: similar to a high-quality wine glass, a material with a low loss will ring for a long time with a pure note because most of the thermal motion is confined to frequencies close to the resonance. For this reason, aLIGO uses fibres fabricated from fused silica – a type of very pure glass with very low mechanical loss – for the final stage of the mirror suspension. Pioneered in the GEO600 detector near Hanover in Germany, the use of silica fibres in place of the steel wires used in the initial LIGO detectors significantly reduces thermal noise from suspension.

aLIGO also has much reduced quantum noise compared with the original LIGO.

Low-loss fused silica is also used for the 40 kg interferometer mirrors, which use multi-layered optical coatings to achieve the high reflectivity required. For aLIGO, a new optical coating was developed comprising a stack of alternating layers of silica and titania-doped “tantala”, reducing the coating thermal noise by about 20%. However, at the aLIGO design sensitivity (which is roughly 10 times higher than the initial aLIGO set-up) thermal noise will be the limiting noise source at frequencies of around 60 Hz – close to the frequency at which the detectors are most sensitive.

aLIGO also has much reduced quantum noise compared with the original LIGO. This noise source has two components: radiation-pressure noise and shot noise. The former results from fluctuations in the number of photons hitting the detector mirrors, which is more significant at lower frequencies, and has been reduced by using mirrors four times heavier than the initial LIGO mirrors. Photon shot noise, resulting from statistical fluctuations in the number of photons at the output of the detector, limits sensitivity at higher frequencies. Since shot noise is inversely proportional to the square root of the power, it can be reduced by using higher laser power. In the first observing run of aLIGO, 100 kW of laser power was circulating in the detector arms, with the potential to increase it to up to 750 kW in future runs. Optical cavities are also used to store light in the arms and build up laser power.

In addition to reductions in these fundamental noise sources, many other technological improvements were required to reduce more technical noise sources. Improvements over the initial LIGO detector included a thermal compensation system to reduce thermal lensing effects in the optics, reduced electronic noise in control circuits and finer polishing of the mirror substrates to reduce the amount of scattered light in the detectors.

Upgrades on the ground

Having detected their first gravitational wave almost as soon as they switched on in September 2015, followed by a further event a few months later, the aLIGO detectors began their second observation run on 30 November. Dubbed “O2”, it is scheduled to last for six months. More observation runs are envisaged, with more upgrades in sensitivity taking place between them.

The next major upgrade, expected in around 2018, will see the injection of “squeezed light” to further reduce quantum noise. However, to gain the maximum sensitivity improvement from squeezing, a reduction in coating thermal noise is also likely to be required. With these and other relatively short-term upgrades, it is expected that a factor-two improvement over the aLIGO design sensitivity could be achieved. This would allow events such as the first detection to be observed with a signal-to-noise ratio almost 10 times better than the initial result. Further improvements in sensitivity will almost certainly require more extensive upgrades or new facilities, possibly involving longer detectors or cryogenic cooling of the mirrors.

aLIGO is expected to soon be joined in observing runs by Advanced Virgo, giving a network of three geographically separated detectors and thus improving our ability to locate the position of gravitational-wave sources on the sky. Discussions are also under way for an aLIGO site in India. In Japan, the KAGRA detector is under construction: this detector will use cryogenic cooling to reduce thermal noise and is located underground to reduce seismic and gravity gradient effects. When complete, KAGRA is expected to have similar sensitivity to aLIGO.

Longer term, in Europe a detector known as the Einstein Telescope (ET) has been proposed to provide a factor 10 more sensitivity than aLIGO. ET would not only have arms measuring 10 km long but would take a new approach to noise reduction using two very different detectors: a high-power room-temperature interferometer optimised for sensitivity at high frequencies, where shot noise limits performance, and a low-power cryogenic interferometer optimised for sensitivity at low frequencies (where performance is limited by thermal noise). ET would require significant changes in detector technology and also be constructed underground to reduce the effect of seismic noise and gravity-gradient noise on low-frequency sensitivity.

The final frontier

Obtaining significantly improved sensitivity at lower frequencies is difficult on Earth because they are swamped by local mass motion. Gaining sensitivity at very low frequencies, which is where we must look for signals from massive black-hole collisions and other sources that will provide exquisite science results, is only likely to be achieved in space. This concept has been on the table since the 1970s and has evolved into the Laser Interferometer Space Antenna (LISA) project, which is led by the European Space Agency (ESA) with contributions from 14 European countries and the US.

A survey mission called LISA Pathfinder was launched on 3 December 2015 from French Guiana. It is currently located 1.5 million  km away at the first Earth–Sun Lagrange point, and will take data until the end of May 2017. The aim of LISA Pathfinder was to demonstrate technologies for a space-borne gravitational-wave detector based on the same measurement philosophy as that used by ground-based detectors. The mission has clearly demonstrated that we can place test masses (gold–platinum cubes with 46 mm sides separated by 38 cm) into free fall, such that the only varying force acting on them is gravity. It has also validated a host of complementary techniques, including: operating a drag-free spacecraft using cold gas thrusters; electrostatic control of free-floating test masses; short-arm interferometry and test-mass charge control. When combined, these novel features allow differential accelerometry at the 10–15 g level, which is the sensitivity needed for a space-borne gravitational-wave detector. Indeed, if Pathfinder test-mass technology were used to build a full-scale LISA detector, it would recover almost all of the science originally anticipated for LISA without any further improvements.

The success of Pathfinder, coming hot on the heels of the detection of gravitational waves, is a major boost for the international gravitational-wave community. It comes at an exceptional time for the field, with ESA currently inviting proposals for the third of its Cosmic Vision “large missions” programme. Developments are now needed to move from LISA Pathfinder to LISA proper, but these are now well understood and technology development programmes are planned and under way. The timeline for this mission leads to a launch in the early 2030s and the success of Pathfinder means we can look forward with excitement to the fantastic science that will result.

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