In the past ten years,several giant interferometers have been built around the world with the goal ofa first direct detection ofgravitational waves.The most sensitive detectors,2 interferometers for the US LIGO collaboration and the detector built by the Italo-French collaboration Virgo (fig.1) are approaching their design sensitivity. Scientific exploitation ofthese instruments is now starting ..

Clapson, A.C.

Hello, P.

Europhysics News

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Virgo and the quest for gravitational waves

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Virgo and the quest for gravitational wavesA.C. Clapson, P. HelloTo cite this version:A.C. Clapson, P. Hello. Virgo and the quest for gravitational waves. Europhysics News, EDPSciences, 2006, 37, pp.14-16. <in2p3-00101548>HAL Id: in2p3-00101548http://hal.in2p3.fr/in2p3-00101548Submitted on 27 Sep 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.In the past ten years, several giant interferometers have been builtaround the world with the goal of a first direct detection of gravi-tational waves.The most sensitive detectors,2 interferometers for theUS LIGO collaboration and the detector built by the Italo-Frenchcollaboration Virgo (fig. 1) are approaching their design sensitivity.Scientific exploitation of these instruments is now starting …What is a Gravitational Wave?Basically, Gravitational Waves (GW) are ripples of space-time,which propagate at the speed of light. They are predicted by generalrelativity and other, alternative, modern theories of gravitation, asan effect of accelerated motions of matter. This is somewhat simi-lar to electromagnetic waves, produced by the motion ofaccelerated charges. A difference is that GW production requiresnon symmetrical distributions of matter. Thus a star collapsingwith perfect spherical symmetry emits no GW.Another differenceis that at the lowest order GW are quadrupolar waves while elec-tromagnetic waves are dipolar.An observable indication of the passage of these ripples ofspace-time is a modification of the measures of distance. Moreprecisely, consider a circle of test masses at rest (Fig. 2). As a GWwith normal incidence passes through the circle distances in onedirection seem to expand while in a perpendicular one they seemto shrink, owing to the quadrupolar nature of GW. This relative dis-tance modification is used in the definition of the GWdimensionless amplitude: h(t) ≈ 1—2 δL—L where L is the distance mea-sured in the absence of GW (the ordinary flat space-time). Theproblem is that h is in general so weak that detecting a GW seemshopeless.Astrophysical sourcesIn fact, only sources involving relativistic (compact) stars such asblack holes or neutron stars may emit GW that can be detectableon Earth. The most promising sources are thought to be binarysystems of inspiralling neutron stars or black holes. In such asystem emitted GW carry away part of the orbital energy. Thisloss entails a decrease of the orbital radius: with time the two starsbecome closer and closer and as they get closer the GW emissionbecomes more and more intense. The resulting GW signal h(t) iscalled a chirp, a sinusoid with increasing amplitude and frequencythat ends when the two objects merge. Collapses of massive starsinto neutron stars or black holes (gravitational supernovae) are alsosources of GW that must be considered. Here typical GW signals(though very difficult to model) are bursts with estimated typicalduration of the order of a few milliseconds. Finally let’s mentionother kinds of sources, such as isolated rotating neutron stars orpulsars that can emit weak continuous signals if the star is notperfectly symmetric or cosmological backgrounds.A survey of potential GW sources, orders of magnitude foramplitudes and rates, leads to a simple conclusion. A grounddetector of GW must be designed to be sensitive to GW ampli-tudes of typically h ~10-21 or less, in a bandwidth from 10 Hz up toa few thousands Hz to be able to observe these waves one day.This is the goal of the first generation GW interferometers that arein (or are entering into) operation today.The interferometric detection of Gravitational WavesThe hunt for Gravitational Waves is not a recent story. It began atthe end of the 50’s under the impulse of the American physicist JoeWeber. The GW detector he invented was a cylindrical bar about1.5 meters long equipped with piezo-electric transducers torecord the vibrations of the bar, to be excited by the passing GW.This setup spawned several modern descendants: aluminium bars(and more recently spheres) cooled below 1 K. The main limitationof this kind of detector is its very narrow bandwidth (typically afew Hz). Detectors based on optical interferometry are not limitedin this way.Interferometric detection relies on the Michelson interfero-meter scheme (see fig. 3). The output port power is given by   Pmich = P0—2 [1+Ccos(2ω0—c ∆larms)] with P0 the input laser power, ω0the laser angular frequency,∆larms the optical path difference betweenthe arms and C the interference contrast, as set by the parameters ofthe optical cavity. The interferometer must be tuned in order tooptimize the sensitivity to a gravitational wave, that is to say to smallvariations in ∆larms. The main fundamental noise limiting the sensi-tivity is shot noise. It imposes the dark fringe, where Pmich isminimized, as the best configuration. In order to improve sensitivi-ty,we can lower the shot noise.Only two parameters are effective: theoptical length of the interferometer arms and the power circulatingin the interferometer.This is why interferometric detectors have kilo-metric arms (3 km in the case of Virgo).An optical path of about 100km can then be obtained by placing a Fabry-Perot cavity in the arms.Concerning the light power, as continuous laser sources providelimited power, the trick consists in the addition of an extra mirror atthe input of the interferometer. This mirror and the rest of the inter-ferometer create a new cavity (power-recycling cavity) where thestored light power is enhanced at resonance (See fig. 3 for the finaloptical design of a Virgo-like detector).A shot-noise limited spectral sensitivity of the order of 10-23 Hz-1/2can be achieved using the complete setup with Virgo dimensions: 3km Fabry-Perot arm cavities with a finesse of 50, a 10 W input laserbeam and a recycling power gain of the order of 50.Of course othernoises are likely to limit the sensitivity in diverse spectral zones.14 • volume 37 • number 3 europhysicsnewsfeaturesVirgo and the quest for gravitational wavesAndré-Claude Clapson and Patrice Hello,Laboratoire de l’Accélérateur Linéaire IN2P3/CNRS and Université de Paris XI Campus d’Orsay • 91898 Orsay Cedex • Franceb Fig. 1: Aerial view of the virgo detector, near Pisa (Italy).Fundamental, environmental and technological noisesThe first obvious obstacle to low frequency measurements in aMichelson interferometer is seismic noise. Measurements ofdisplacement spectral densities in quiet sites typically give ~x( f ) ≈ 10-6 / f 2 meters / √—Hz.The mirrors must therefore be isolated from ground motions.This can be achieved by suspending them. Basically the suspendedmirrors then behave like harmonic pendulums with a naturalangular frequency of oscillation ω0 = √—g /l, where g is the gravita-tional acceleration and l the pendulum length. While groundmotion is amplified at the natural frequency, it is by contrastdamped by ω0 2 / ω 2 at higher frequencies. In Virgo the mirrors aresuspended in a multiple-stages pendulum (fig. 4) with a fundamentalresonance below 1 Hz and a resulting seismic attenuation factor ofthe order of 1010 at 10 Hz.Thermal noise is another annoying source of noise. Indeedmirrors and their suspensions all are mechanical resonators, whosedegrees of freedom are excited at ambient temperature. The alter-native to cooling the whole instrument is to select highquality-factor materials, in particular for the mirror substrates andsuspension wires, in order to limit the spectral spread of the noise.Besides, sources of mechanical losses must be hunted.Laser noises must be also controlled. In particular fluctuationsin laser frequency or power can couple to interferometer lengthasymmetries to give dangerous phase noises than can competewith the shot noise. The laser is therefore actively servoed on alength reference, provided by an Ultra Low Expansion (ULE) cavity,and therefore frequency-stabilised. Before entering the interferom-eter itself, the laser beam passes through another Fabry-Perotcavity, named the Mode-Cleaner. A cavity is indeed an opticalresonator so it filters off-resonance beam fluctuations (moreprecisely it is a low-pass filter). This helps to attenuate the laser fluc-tuations, including beam jitters.Ultra high vacuum is of course required in order to avoid spurioussignals due to residual gas index fluctuations in the interferometerarms. The vacuum level specification corresponds to a residualpressure below10-7 mbar. The interferometer must be entirelyunder vacuum. Hence the mirrors and their suspensions are locat-ed in towers and the kilometric arms are in the material form oftubes (120 cm diameter in Virgo).The inner parts of the tubes and towers are equipped with baffles,whose function is to remove the light scattered by mirrors in off-axis directions. Mirrors always have some residual rugosity, in spiteof their very good quality. This rugosity causes a small part of thebeam photons to travel off-axis and eventually reflect on the infra-structure (tubes, towers) which is not isolated from seismic noise.These photons then get random phases and the recombination ofsome of them with the main beam produces an extra phase noisewhich would be at the level of the shot noise if nothing were done!The design sensitivity curve of Virgo is shown in figure 5. Alltechnological noises are supposedly under control. The sensitivityis then limited at low frequency by the seismic wall (seismic noisebelow 4 Hz, not filtered by the super attenuator), at intermediaryfrequencies by the thermal noise (the high frequency tail of thependulum thermal noise, the low-frequency tail of the mirrors’thermal noise plus the many resonances due to the suspensionwires) and in the high frequency region by the shot noise.Where are we?The construction of Virgo was achieved in fall 2003. Since thenthe detector has been in the commissioning phase. Virgo is a verycomplex instrument and reaching the design sensitivity takes time.One of the main tasks is the control of the interferometer itself.When free, suspended mirrors oscillate continuously at the pendu-lum resonance frequency. The working point of the detector isobtained when arm cavities are locked at resonance for the laserbeam, the Michelson interferometer tuned at a dark fringe and therecycling cavity also resonant for the laser beam. This gives fouroptical lengths to be controlled, plus the mirror rotation degrees offreedom.We see that Virgo needs an active servo-system to controllengths and angular tilts of mirrors as far as 3 km apart, on a timescale of a fraction of second.The commissioning has been carried out step by step, lockingfirst the one-arm cavities, then the two arms plus the Michelsoninterferometer and finally the complete configuration. The auto-matic alignment (angular control) has been built and tested inparallel.To date the Virgo sensitivity is roughly one order of magnitudeabove the design curve. Meanwhile the two 4 km detectors of theUS LIGO collaboration have reached more or less their designsensitivity above 100 Hz (commissioning started earlier for LIGO).Since the data produced by these instruments are mostly com-posed of noise, with hopefully someday an astrophysical signal, thefirst challenge for analysis is to distinguish signal from noise.Otherwise, we would be swamped by false GW detections, to beidentified as such by eye. Most of the efforts so far have focussed oninspiral and burst scenarios, though all avenues are explored. Manytypes of algorithms have been tested, some looking for specificwaveforms that general relativity may provide, others aiming atgeneric signal signatures. As short duration signals are easilymimicked by the instrument, successful analysis is strongly cou-pled to an understanding of the behaviour of the instrument.europhysicsnews number 3 • volume 37 • 15featuresm Fig. 2: Effect of a GW passing through a circle of test masses. Thewave incidence is normal to the mass plane. (a) the effect of a “+”polarised wave. (b) the effect of a “x” polarised wave. The amplitudeof the GW h(t) is shown as a function of time t.m Fig. 3: The optical scheme of a GWinterferometer detector. We show thekilometric cavities as arms and thepower-recycling mirror. The futureThe question is not if we will detect GW but rather when! Evidencefor their existence is provided by the study of the binary pulsar PSRB1913+16 discovered by the Nobel laureates Hulse and Taylor inthe seventies. This inspiralling system consists of two neutron stars,one being a pulsar detected by radio-telescopes. This is a perfectexample of a GW emitter. Astrophysicists have been able to com-pare the behaviour of the binary pulsar to the predictions ofgeneral relativity.Concerning the orbital decay due to GW emission,measurements and theory agree within less than 1%. This is abeautiful proof that GW exist!Of course physicists are now waiting for a direct detection. Forthe very near future it is likely that three (two for LIGO and one forVirgo) detectors with similar sensitivities will be on watch for awave to come. With some luck, smaller instruments (the Anglo-German GEO 600 or the Japanese TAMA 300) may also contributeto the discovery.To increase the chance of detection and to confirm detection, anetwork of detectors is necessary. Validation of detection can beachieved by studying coincident events with other types ofdetectors, such asneutrino detectorsor Gamma-Raysatellites, sincethese signals arelikely to be thecounterparts ofGW emitters, neu-trinos in the caseof a supernovaevent or GammaRay bursts in thecase of the mergerof neutron stars.However, to obtaina complete recon-struction of thepassing waveform(amplitude,polari-sation, location ofthe source …) at least three GW detectors are mandatory. Virgo-type instruments are indeed not directional as traditionaltelescopes. Their antenna pattern looks somewhat like a peanut,symmetrical with respect to the interferometer plane. With coin-cident events from three GW detectors at separate locations,source location can be reconstructed using triangulation. Moredetails could be obtained through sophisticated coherent analysismethods.Nevertheless even with three detectors (LIGO and Virgo)working at their design sensitivity a first direct detection in thenear future is not guaranteed. Due to the uncertainties in rates ofevents (binary inspirals) or in waveform amplitudes (super-novae), it is believed today that to be sure to “see” several eventsper year the sensitivity of current interferometers has to beimproved by about one order of magnitude. Work has alreadystarted on second generation detectors. An advanced LIGO hasbeen funded by the NSF. R&D for the next generation is alsogoing on in Europe and plans for future detectors are being dis-cussed. Of course second-generation detectors are for the nextdecade. Today, the GW observation field is very active. We arereally at the birth of GW astronomy and a new window is aboutto open on the Universe. nAbout the authorsAndré-Claude Clapson is currently finishing his  PhD thesis andPatrice Hello is Maître de Conférences at the Orsay Campus nearParis. They are both hosted by the Laboratoire de l’AccélérateurLinéaire and members of the Italian-French Virgo collaboration.They are working together mainly on Gravitational Wave DataAnalysis issues. Patrice Hello has also an interest in R&D for futureAdvanced Detectors of Gravitational Waves.Usefull links :Virgo collaboration:www.cascina.virgo.infn.itLIGO collaboration:www.ligo.caltech.eduGEO600 collaboration:www.geo600.uni-hannover.de16 • volume 37 • number 3 europhysicsnewsfeaturesb Fig. 4: The Virgosuper attenuator.m Fig. 5: The Virgo design sensitivity. The sensitivity is limited in theeffective bandwidth by thermal noise and shot noise.

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