LCGT and the global network of gravitational wave detectors
aa r X i v : . [ a s t r o - ph . I M ] D ec The 11 th Asian-Pacific Regional IAU Meeting 2011NARIT Conference Series, Vol. 1, c (cid:13) LCGT and the global network ofgravitational wave detectors
Nobuyuki Kanda and LCGT collaboration Department of Physics, Graduate School of Science, Osaka City University,Sugimoto 3-3-138, Sumiyoshi-ku, Osaka 558-8585, JapanE-mail: [email protected]
Abstract.
Gravitational wave is a propagation of space-time distortion,which is predicted by Einstein in general relativity. Strong gravitationalwaves will come from some drastic astronomical objects, e.g. coalescenceof neutron star binaries, black holes, supernovae, rotating pulsars and pulsarglitches. Detection of the gravitational waves from these objects will opena new door of ‘gravitational wave astronomy’ . Gravitational wave will be aprobe to study the physics and astrophysics.To search these gravitational waves, large-scale laser interferometers willcompose a global network of detectors. Advanced LIGO and advanced Virgoare upgrading from currents detectors. One of LIGO detector is consideringto move Australia Site. IndIGO or Einstein Telescope are future plans.LCGT (Large-scale Cryogenic Gravitational wave Telescope) is nowconstructing in Japan with distinctive characters: cryogenic cooling mirrorand underground site. We will present a design and a construction status ofLCGT, and brief status of current gravitational wave detectors in the world.Network of these gravitational wave detectors will start in late 2016or 2017, and may discover the gravitational waves. For example, thesedetectors will reach its search range for coalescence of neutron star binaryis over 200 Mpc, and several or more events per year will be expected.Since most of gravitational wave events are from high-energy phenomenonof the astronomical objects, these might have counterpart evidences inelectromagnetic radiation (visible light, X/gamma ray), neutrino, high energyparticles or others. Thus, the mutual follow-up observations will give us moreinformation of these objects.
1. Introduction : Gravitational Waves
Gravitational waves are predicted by Einstein’s general relativistic theory in1916. With the perturbation of space-time metric in Einsteins’s equation, awave equation is derived as ∇ − c ∂ ∂ t ! h µν = 0 (1)where, h µν respects the metric perturbation away from Minkowski metric as g µν = η µν + h µν . (2) N.Kanda
This equation suggest that small distortion of space-time h µν will be able topropagate as wave, which is called as “gravitational wave” .The gravitational wave will emitted from a changing of mass quadrupolemoment, just like as a non-spherical motion of mass distribution. The lowestorder of a gravitational wave is quadrupole radiation. With transverse-tracelessgauge, choosing z axis as a propagation, the wave can be represented the linearcombination of two polarization : h + = a − , h × = b . (3)It is a transverse wave, and it propagate with light speed. A gravitational wavewill interact with masses. When it incident, a tidal force will be induced on freefalling masses. The h + component will induce the distortion along x - and y -axisdifferentially, and h × will induce same but rotating 45 degree.Unit of gravitational wave amplitude is dimensionless metric. It meansthat space-time distortion relativity. The gravitational interaction is veryweak comparing with other fundamental inter, and also the gravitational waveamplitude is extremely small as h µν = 2 GRc ¨ I µν (4), where I µν is a quadrupole moment of mass distribution. For example, two 100kg masses connected with 1m beam, rotating 1000 cycles per second will emit2kHz gravitational wave of amplitude only ∼ − at a distance of 150km whereis wavelength. Since the gravitational wave is weak, we expect sources consists of huge massmotions - astronomical objects. Also the sources must have large acceleration tomake a large derivative of quadrupole motion. Typical sources of gravitationalwaves are coalescence of compact star (neutron star, black hole) binaries, stellar-core collapse of supernovae. These are occasionally gravitational wave sources.On the other hand, rotating pulsars or binaries might be a sources of continuousgravitational waves.Neutron star binary is a most promising gravitational wave sources.PSR1913+16 is a binary pulsar is known as that their Kepler orbit periodchanging is well consistent with a transfer of energy and momentum from binarysystem by gravitational wave radiation[1]. There are some observations of suchbinaries[2]. A Binary system will loss the energy emitting gravitational waves,will shrink its orbit, and become rotate faster. Finally, the binary coalesceand emit large gravitational wave. It is called as ‘the last three minutes’ [3].The amplitude h of gravitational wave neutron star binary from 200 Mpc awaywill be 10 − ∼ − in frequency band of 100Hz – 1kHz, and its frequencyspectral density will be h ( f ) ∼ − ∼ − [1 / √ Hz]. Gravitational waveformsof compact binary coalescence can be well predicted by post-newtonian [4]. The
CGT and gravitational wave detectors Figure 1.
Schematic view of laser interferometric gravitational wave detectorfrequency and amplitude development along the time ate determined by themasses of stars. Thus, once we measure the waveform, it guess the absoluteamplitude of gravitational wave from the source. Comparing observed amplitude,we can estimate the luminosity distance of sources only by gravitational wavemeasurement. In this mean, compact binary coalescence are called as ‘standardcandle (siren)’ . The rate of coalescence of neutron star binary is estimated as118 +174 − events/Myr/Galaxy [5]. Even this expectation contains large statisticalerror and dependency of some models, it is encouraging us to try to detect thegravitational waves from compact star coalescence.On the other hand, the weakness, i.e. small coupling constant of gravitationalwave make possible that its come from an inside the star. Electromagneticradiations are mostly emitted at the surface of stars. Neutrino may come frominside as a core of supernovae. Gravitational wave come from mass motionitself inside the stars, and pass through the materials. This fact suggest thatgravitational wave will bring many information of deep inside of high-energeticastronomical object. In the case of black hole, only a gravitational wave isradiation from themselves. We expect a new window of ‘gravitational waveastronomy’ will be opened with current constructing/upgrading gravitationalwave detectors. Gravitational wave induce the tidal force between free masses. Laserinterferometric gravitational wave detectors are Michelson interferometer thatconsists of suspended mirrors, beam splitter and laser as light source. Mirrorsand beamsplitter are suspended as pendulum that is a mechanical low pass filterwhich make mirror as a free mass. Laser light is divided to two perpendicularpaths, round trip from mirrors and re-combine at the beam splitter. We canmeasure the metric amplitude of gravitational wave by small change of intensityof the combined light. To enhance a gravitational wave signal, long base-line ofthe Michelson beam path and Fabry-Perot cavity are employed. Figure 1 showsthe schematic view of the detector.
N.Kanda
2. LCGT and Other Gravitational Wave Detectors
LCGT ( L large-scale C ryogenic G ravitational wave T elescop ) is a 3 km base-line length laser interferoemeteric detector at the Kamioka-mine, Gifu-prefecture,Japan[8]. As its name shows, LCGT consists of cryogenic mirrors to reduce thethermal motion noise of mirrors. The site of the LCGT is underground forstable environment with low seismic noises magnitude comparing with surfaceof the ground. LCGT is planning to start its observational operation in 2017. Asensitivity of gravitational wave detector is characterized by an strain equivalentnoise spectrum. LCGT’s target sensitivity which just corresponding to the strainequivalent noise level is h ∼ f actor × − [1 / √ Hz] around 100 Hz as same toother current upgrading gravitational wave detectors as shown in figure 2 withadvanced LIGO, advanced Virgo and ET[14][15][16][17].
There are some gravitational wave detector projects. LIGO[9] (LaserInterferometer Gravitational-Wave Observatory) is a US project with twodislocated detector site at west and east side of north American continent.Virgo[10] is a european (mainly from Italy and France) project at Pisa, Italy.These detectors achieved its ‘initial’ operation already, and now are upgradingas each sensitivity reach as 200 ∼
300 Mpc range for neutron star binarydetection. Comparing with initial detectors, these are called as to ‘second’generation detectors, including LCGT. LIGO-Australia[11] is a project thatone set of LIGO instruments will move to western Australia. IndIGo[12] isan organization of the Indian Initiative in Gravitational-wave Observations. ET(Einstein Telescope)[13] is a future plan of gravitational wave detector in Europe,which target more one order better sensitivity than second generation detectors. -24 -23 -22 -21 -20 S t r a i n E qu i v a l en t N o i s e s pe c t r u m [ / ! H z ] LCGT (varRSE Detuned) LCGT (varRSE Broadband) advanced LIGO(ZERO DET, High P) advanced LIGO(NS-NS) advanced Virgo Einstein Telescope ET_B ET_C
Figure 2.
Target sensitivity limits of current constructing/upgrading/planninggravitational wave detectors. Design values of each detectors are available inreferences[14][15][16][17].
CGT and gravitational wave detectors How far astronomical objects can be detected by the gravitational wave detection? The detection range is depend on the gravitational waveform. Here, wediscussed about the typical cases: compact binary coalescence and black holequasi-normal mode oscillation.In case of compact binary coalescence, a gravitational waveform can bepredicted with post-newtonian approximation[4]. Using the frequency spectraof gravitational wave and noise power spectral density, the detection rangefor optimal incident direction and arrangement of compact binaries. Figure3 displays the detection range as the function of star masses, in case of evenmass binary. LCGT’s detection range for 1 . ⊙ binary is about 280 Mpc inoptimal case with signal-to-noise ratio 8. Assuming galactic merger rate 118events/Galaxy in average and known density of galaxies, LCGT is expected todetect about 10 events per year.For case of black hole quasi-normal mode, we estimate the signal-to-noiseratio with assumption that 3% of mass will change as a radiation[6] and Kerrparameter as 0.9 in this figure. M p c M p c G p c G p c G p c Lu m i no c i t y D i s t an c e mass of one star [M solar ](BH mass = 2M) M y r G y r G y r G y r Loo k B a ck T i m e C o s m o l og i c a l R ed s h i ft : z . M s o l a r ( T y p i c a l N eu t r on S t a r) LCGT detection range (VRSE-D) for CBC | for BH QNM SNR=3 | SNR=3 SNR=8 | SNR=8 SNR=100 | SNR=100
Figure 3.
Detection range for LCGT for optimal direction and arrangement ofGW source. x -axis is mass of one star of binary, or half of black hole total mass.Thick solid and thick dashed lines are corresponding to signal-to-noise ratio 8,that is believed as enough signature to claim the detection.
3. Global Network of GW detectors
As we explained previous section, there are some gravitational wave detectorsin the world, and these are dislocated. This is important strategy to determinethe gravitational wave incident direction and polarization. Global network ofthe gravitational wave detector is necessary to determine the source direction,to improve whole sky coverage, and extract more information from gravitationalwave sources.Target frequency of the gravitational wave from typical astronomical objects,e.g. compact star coalescence, stellar-core collapse etc. are frequency bandof a few 10 Hz to several kHz. Since the wavelength λ of 1kHz gravitationalwave is 300 km that is longer than visible or infrared light, X or gamma-rays, N.Kanda
Figure 4.
Antenna pattern of single detector and combined detectors.each ground-based gravitational wave detectors can be treated as a point like.We should employ multi-detectors which dislocated longer distance D as 1000km to determine the direction against the diffraction limit order of ∼ λ/D . Theworld wide network of gravitational wave detectors can estimate source directionroughly in degree or sub-degree[7].On the other hand, there is a merit sky coverage with several detectors. Aone laser interferometric gravitational wave detector is sensitive for gravitationalwave from zenith (and opposite) direction. There is four dead area thatcorresponding the between interferometer baselines. It is called an antennapattern of the detector. Figure 4 shows (a) single detector’s antenna patternand (b) quadratic sum combined antenna pattern of LCGT, LIGO and Virgo,assuming that all detectors has same sensitivity. Figures are promotional tothe survey volume in the universe for non-polarized gravitational wave sources.Average survey range by combined detector is ∼ .
4. Eye and Ear : GW and Counterpart/Follow-up Observations
Since the gravitational wave is not measured at Summer 2011 yet, we would liketo discuss about the prospect of gravitational wave astronomy instead of thesummary.As we displayed in previous section, a gravitational wave detector’s apertureis widely open, almost as a omnidirectional. However, its angular resoletion ispoor comparing with optical telescopes. This is a analogy of “eye and ear”; here,gravitational wave detectors are ears, and optical/radio/X/gamma ray telescopesare eyes. Let’s image there is a box that contains something inside. Eyes can seethe surface of the box and determine the exact direction of the box, but cannotsee the inside. Ears cannot see the box, but suggest what is inside the box byhearing the sound when we shake the box. Same to this analogy, traditional toolsof astronomy and gravitational wave make possible to understand the structureand development of relativistic astronomical objects like as a compact binary,black hole, or supernovae. We hope to open the new window of the astronomywith gravitational waves and counterpart observations.
CGT and gravitational wave detectors
5. Acknowledgments
We would like to thank APRIM organization deeply to invite us the conference.The author’s work was also supported in part by a Monbu Kagakusho Grant-in-aid for Scientific Research of Japan (No. 23540346).