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Search for Gravitational Waves: Detection and Theory

This study explores the experimental search for gravitational waves, covering sources, detection principles, and the theory of GW detectors using resonant masses and interferometers. It delves into historical milestones, real data from detectors like LIGO and Virgo, and details of 1st-generation detectors. The potential sources of gravitational waves include compact object binaries, pulsars, and more, with detection based on monitoring distances between masses and laser interference techniques. Theoretical aspects focus on Newton's and Einstein's gravitational theories, including the prediction of gravitational waves and information transmission through gravitational radiation.

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Search for Gravitational Waves: Detection and Theory

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  1. Experimental search for Gravitational Waves Geppo Cagnoli cagnoli@fi.infn.it INFN - Firenze University of Glasgow Physik-Institut der Universität Zürich/ETH 28th June 2006

  2. The GR prediction Newton’s Theory “instantaneous action at a distance” Gmn= 8pTmn Einstein’s Theory information carried by gravitational radiation at the speed of light Physik-Institut der Universität Zürich / ETH

  3. Sources of Gravitational Waves Mass quadruplemoment Small amplitude approximation • Compact object binaries • Pulsars • Neutron Star internal dynamics • Non symmetrical supernovae • Cosmological gravitational waves Physik-Institut der Universität Zürich / ETH

  4. New potential sources January 05: A swarm of 10,000 or more black holes may be orbiting the Milky Way's supermassive black hole, according to new results from NASA's Chandra X-ray Observatory. This would represent the highest concentration of black holes anywhere in the Galaxy. Physik-Institut der Universität Zürich / ETH

  5. Detection Principles -1 Inertia Dimensions • In the reference frame of the lab (Fermi’s coordinates) the effect of GW is pure mechanical. The potential is: • 3 types of detectors • Resonators • Interferometers • RF cavities Physik-Institut der Universität Zürich / ETH

  6. Detection Principles -2 DL L DL/L < 10 -21 Expected from astronomical sources Effect of a sinusoidal gravitational wave going through the slideon the space-time frame and on a circular distribution of free masses Figure: M.Lorenzini Physik-Institut der Universität Zürich / ETH

  7. Detection Principles -3 Two detectors fully developed: Resonant Masses Interferometers Figure: S. Reid Physik-Institut der Universität Zürich / ETH

  8. Theory of GW Detectors - 1 V Read-out h x f Detectorinternalnoise Readoutinternalnoise Detector Physik-Institut der Universität Zürich / ETH

  9. First attempt of buildinga resonant detector Sensitivitypattern Joseph Weber(~1960) Resonant barsuspended in the middle Piezoelectrictransducers Physik-Institut der Universität Zürich / ETH

  10. The Band Width of a resonant detector Read-out noise Detector noise DetectorBW x/h Physik-Institut der Universität Zürich / ETH

  11. Resonant detectors today Bars mechanicalsignalenhancement Spheres GW bursts excite the resonances of the test masses Capacitive + SQUIDor optical readout Physik-Institut der Universität Zürich / ETH

  12. A capacitive Read-out systemof a resonant detector Cryogenic Switch Transducer Decoupling Charging Line Capacitor C d M M i Bar L L L s i C T SQUID Matching Capacitive Amplifier Transformer Resonant Transducer Physik-Institut der Universität Zürich / ETH

  13. Physik-Institut der Universität Zürich / ETH

  14. Interferometric detectors:the concept • Monitoring the distances between free-flying masses with laser interferometer • The background noise comes from the readout and from the internal motion of the masses Physik-Institut der Universität Zürich / ETH

  15. A bit of history… • Gertsenshtein M E and Pustovoit V I 1962 Sov. Phys.—JETP 16 433 • Moss G E, Miller L R and Forward R L 1971 Appl. Opt. 10 2495b • Weiss R 1972 Q. Prog. Rep. Res. Lab. Electron. 105 54 Physik-Institut der Universität Zürich / ETH

  16. The Band Width of an interferometric detector x = h · L / 2 for each end mirror Read-out noise Detector noise DetectorBW Physik-Institut der Universität Zürich / ETH

  17. Interferometers today - 1 Fabry – Perot cavities • End mirrors positioned in theDark Fringe condition: laser beam is frequency modulated, the sidebands are detected • Multiple bouncingphase accumulation:laser power increasesfrom 20W to 1kW • Power recycling: number ofphotons in the interferometerincreases • Signal recycling:just the side bands are reflectedback in the interferometerGEO600 is the onlydetector that uses thistechnique to enhance the detector response in a narrow band Pendulumsuspensions Beamsplitter Photodiode Laser Physik-Institut der Universität Zürich / ETH

  18. Interferometers today - 2 Fabry – Perot cavities Pendulumsuspensions Beamsplitter Photodiode Laser Physik-Institut der Universität Zürich / ETH

  19. Interferometers today - 3 Fabry – Perot cavities Pendulumsuspensions Beamsplitter Photodiode The optics and suspensions are in vacuum to minimize fluctuation of index of refraction Laser Physik-Institut der Universität Zürich / ETH

  20. Interferometers today - 4 3 km 600 m TAMA 4 & 2 km 300 m AIGO 4 km Physik-Institut der Universität Zürich / ETH

  21. Real data from LIGO Physik-Institut der Universität Zürich / ETH

  22. Real data from GEO600 10 -17 Displacement [m] 10 -18 10 -19 [Hz] 100 1000 Physik-Institut der Universität Zürich / ETH

  23. Real data from Virgo Physik-Institut der Universität Zürich / ETH

  24. Detectors of 1st Generation 1ST GENERATION IS CLOSE TO REACH THEDETECTION RANGE FOR NS-NS COALESCENCE AT THE DISTANCE OF THEVIRGO CLUSTER (17MPc) LIGO VIRGO 10 -19 • 1ST GENERATION • FOR INTERFEROMETERS • STEEL SUSPENSIONS (APART GEO600) • ROOM TEMPERATURE • FOR RESONATORS • Al or AlCu • 100mK < T < 4K 10 -20 AURIGA NAUTILUS MiniGRAIL GEO600 10 -21 NS-NS 14 Mpc BH-BH 67 Mpc 10 -22 10 -23 10 -24 10 -25 10 100 1k 10k 1 Frequency [Hz] h Pulsars [ Hz –1/2 ] Supernovae NSvibration BUT THEEVENT RATEIS TOO LOW !! 1 EVENT/3 YRS MOST OPTIMISTICCASE Physik-Institut der Universität Zürich / ETH

  25. Future Detectors of Gravitational Waves • DUAL • Nested hollow cylinder resonant detector • AURIGA collaboration • Construction planned starting on 2009 • Ad. LIGO, Ad. Virgo and GEO HF • 2nd generation interferometers • Virgo + GEO600 collaboration • Commissioning starts on 2009 • 3rd Generation Interferometer • Cryogenic and underground interferometer • Construction envisaged by 2014 Physik-Institut der Universität Zürich / ETH

  26. DUAL – the concept read-out the differential deformations of two nested resonators The outer resonator is driven above resonance The inner resonator is driven below resonance πPhase difference 5.0 kHz useful GW band Physik-Institut der Universität Zürich / ETH

  27. DUAL performance M. Bonaldi et al. Phys. Rev. D 68 102004 (2003) Mo Dual 16.4 ton height 3.0m 0.94m SiC Dual 62.2 ton height 3.0m 2.9m Antenna pattern: like 2 IFOs colocated and rotated by 45° Q/T=2x108 K-1 Physik-Institut der Universität Zürich / ETH

  28. Real data from Virgo READOUT THERMALNOISE EARTHRELATEDNOISE CONTROL RELATED NOISE Physik-Institut der Universität Zürich / ETH

  29. Readout noise – shot noise √Hz • A fundamental limit to phase measurement is due to the quantum nature of light • Phase measurements to a level of 10 -13 rad require about 1 MW of laser power in the optical cavities • But more power = more fluctuating radiation pressure P=1 MW  F=3 mN  dF=1.5 DN · Dj ≥ 1/2 fN Physik-Institut der Universität Zürich / ETH

  30. Readout noiseThe Standard Quantum Limit Quantum limit onphase measurement Radiation pressure noise Strain [ 1/√Hz ] SQL For a simple Michelson interferometer (GEO HF parameters) RomanSchnabelMPG-AEI Hannover 10-21 Quantum noise with increased laser power (x100) 10-23 1 100 Frequency [ Hz ] Physik-Institut der Universität Zürich / ETH

  31. Beyond the SQL: Squeezed Light • In one representation of the EM field the two orthogonal states are the Amplitude Quadrature X1 and the Phase Quadrature X2 RomanSchnabelMPG-AEI Hannover Physik-Institut der Universität Zürich / ETH

  32. Beyond the SQL: Squeezed Light • In one representation of the EM field the two orthogonal states are the Amplitude Quadrature X1 and the Phase Quadrature X2 RomanSchnabelMPG-AEI Hannover Physik-Institut der Universität Zürich / ETH

  33. Beyond the SQL: Squeezed Light Noise reduction by squeezed light - 6 dB in variance Strain [ 1/√Hz ] 10-21 RomanSchnabelMPG-AEI Hannover Quantum limit onphase measurement Radiation pressure noise SQL 10-22 1 100 Frequency [ Hz ] Physik-Institut der Universität Zürich / ETH

  34. Squeezed light demonstrations [Vahlbruch et al., Phys. Rev. Lett., submitted (2005)]. [Chelkowski et al., Phys. Rev. A 71, 013806 (2005)]. Physik-Institut der Universität Zürich / ETH

  35. Intermediate frequencies 10-19 THERMALNOISE Strain [ 1/√Hz ] 10-25 1 10 k Frequency [ Hz ] From the realm of Quantum to the realm of Statistical Physics Physik-Institut der Universität Zürich / ETH

  36. Thermal noise • Non isolated system shows uncorrelated fluctuations of volume and temperature • The equipartition principle states that each observable has a mean energy equal to kBT/2 • The observable • Optical readout: part of the mirror sensed by the laser • Capacitive readout: the average position of the capacitor plates Physik-Institut der Universität Zürich / ETH

  37. Thermal noise reduction strategy Noise Log [S xx (w) ] R.K.Patria Statistical Mechanics Pergamon Press Log f • Linear systems & thermal equilibrium • Each dynamic variable <E>= kT • Fluctuation-Dissipation theorem Lower T  Lower thermal noise Thermal noise for Damped HarmonicOscillator Lower dissipation  Lower thermal noise Physik-Institut der Universität Zürich / ETH

  38. The most severe limit for IFOs:thermal noise from the coatings 10-19 Strain [ 1/√Hz ] 10-25 1 10 k Frequency [ Hz ] • Alternate layers of transparent materials with different index of refraction • Impedance mismatch andinterference produce highcoefficient of reflectivity • Its structure is not compact as the substrateDeposition with DIBS • 10 mm of coating produces morethermal noise than 10 cm of substrate QUANTUM COATINGS EGO SUBSTRATES Physik-Institut der Universität Zürich / ETH

  39. Suspensions at room temperature • Best material:silica (SiO2) • Silicate bonding • Tested on GEO600 Physik-Institut der Universität Zürich / ETH

  40. Silicon for mirrors and suspensions at low T • Thermal expansion null at 124K and 18K  main source of thermal noise is ruled out • High thermal conductivity • Monocrystal ingots up to 45cm diameter • Possibility of monolithic suspensions • Diffractive as well as transmissive interferometry allowed 5000 k 2.5e-6 a Physik-Institut der Universität Zürich / ETH

  41. Earth related noise - 1 • Test masses have to behave like free flying objects, yet they have to be suspended against gravity • Seismic motion always present has to be filtered Physik-Institut der Universität Zürich / ETH

  42. Earth related noise - 2:Isolation short-circuit Newtonian noise SEISMIC NOISE The Newtonian noisewill be dominant below 10 Hz for cryogenic detectors Surface waves die exponentially with depth: GO UNDERGROUND! Figure: M.Lorenzini Physik-Institut der Universität Zürich / ETH

  43. Further considerations • Building the most perfect inertial reference system • A system subjected to the quantum problem of measurement • All the fundamental parameters of the detector have to be CONTROLLED without introducing a significant noise Physik-Institut der Universität Zürich / ETH

  44. Detector Generations LIGO VIRGO 10 -19 10 -20 AURIGA NAUTILUS MiniGRAIL GEO600 Ad VIRGO 10 -21 10 -22 Mo DUAL 10 -23 SiC DUAL 10 -24 3rd GENERATIONINTERFEROMETER 10 -25 10 100 1k 10k 1 Frequency [Hz] h [ Hz –1/2 ] Physik-Institut der Universität Zürich / ETH

  45. BH-BH coalescence range NS-NS coalescence range GRB050509B 1ST GENERATION 2ND GENERATION 3RD GENERATION INTERFEROMETER Physik-Institut der Universität Zürich / ETH

  46. Beyond Earth based detectors:LISA Audio band1 Hz – 10 kHz LISA Physik-Institut der Universität Zürich / ETH

  47. A collaborative ESA NASA mission • Cluster of 3 S/C in heliocentric orbit • Trailing the earth by 20° (50 Mio km) • Equilateral triangle with 5 Mio km arms • Inclined against ecliptic by 60° Physik-Institut der Universität Zürich / ETH

  48. The spacecraft • LISA needs a purely gravitational orbit • Test masses have to be shielded from solar wind • Capacitive sensing of the test masses • Feedback loop to propulsion • FEEP thrusters with micro-Newton thrust Physik-Institut der Universität Zürich / ETH

  49. The Payload Physik-Institut der Universität Zürich / ETH

  50. LISA technology demonstration Torsion pendulum Flight test LISA 10-12 10-13 10-14 10-15 Physik-Institut der Universität Zürich / ETH

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