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Gravitational Radiation Gravitational Radiation: 3. Gravitational-Wave Detection: Methods, Status and Plans Kip S. Thorne Lorentz Lectures, University of Leiden, September & October 2009 PDFs of lecture slides are available at http://www.cco.caltech.edu/~kip/LorentzLectures/ each Thursday night before the Friday lecture Frequency Bands and Detectors 10-5 CMB Pulsar LIGO/Virgo Aniso- Timing 10-10 LISA resonant-mass tropy Arrays BBO Einstein h 10-15 -20 10 ELF VLF LF HF 10-18-10-16 10-9 - 10-7 10-5-10-1 10 - 104 Hz 10-25 -8 +8 10-16 10 1 10 Frequency, Hz Some Sources in Our Four Bands <-"# 2-"# ####-"# !"# =>?# ⇐ 567&)8# ⇐ -.34# ⇐ $%&'()(*+,)&&# 5'7)8:@)A'(# 9:,:(;# BBO -./012.$/0# 9B%#?:;#?)(;#3:(;67)8:*C#D57)(EF#%8)GH##.(I)A'(# <J'AE#5BC&:E&#:(#2%8C#<)87C#K(:L%8&%M###5B)&%#*8)(&:A'(&N#E'&,:E# &*8:(;&N#O',):(#P)77&N#,%&'&E'Q:E#%JE:*)A'(&N##R#S# >)&&:L%#?!T&# 3,)77#?!T&#DX#*'# Stochastic GWs 36Q%8,)&&:L%# DUVV&6(&##*'#UV# YVVV#&6(&GN# Bruce Allen ,:77:'(#&6(&GN# 14:00 today, here ?!T&##D>#'(%# W%6*8'(#&*)8&# Z:77:'(#&6(&G" EMRIs >)&&:L%#?!1?!# ?!1?!N#W31?!N# W31W3#Z:()8:%&# ?:()8C#&*)8&# 36Q%8('L)%# 3'7:*'(#&*)8&S# ?'&'(#&*)8&S# W)F%O# &:(;67)8:A%&S# W)F%O# !" &:(;67)8:A%&S# 3 Ground-Based GW Detectors: High-Frequency Band (HF) 1Hz - 10,000 Hz GWs: Review GW z • The gravitational-wave field, hjk Symmetric, transverse, traceless (TT); two polarizations: +, x • + Polarization hGW = h (t z/c)=h (t z) y xx + − + − x hGW = h (t z) yy − + − Lines of force x¨ = h¨+x 1 ¨GW x¨j = hjk xk y¨ = h¨ y 2 − + • x Polarization GW GW hxy = hyx = h (t z) × − Gravitational-Wave Interferometer GW Field Beam Patterns + Polarization x Polarization Unpolarized International Network Network Required for: TAMA300 »Detection Tokyo Confidence LIGO Hanford, WA »Waveform GEO600 [LIGO] Extraction Hanover Germany »Direction by Triangulation VIRGO Pisa, Italy LIGO Livingston, LA !!! !! ! ! 8 LIGO: Laser Interferometer Gravitational Wave Observatory Collaboration of ~500 scientists at ~50 institutions in 8 nations [J. Marx, Director; D. Rietze, Spokesman] Hanford Washington !!! !! ! ! 9 LIGO USA, UK, Germany, Australia, India, Japan, Russia, Spain Livingston, Louisiana !!! !! ! ! 10 GEO600 [Germany/UK] Hannover, Germany Next-Generation Technology Directors: J Hough, Glasgow, K. Danzmann, Hannover !!! !! ! ! 11 VIRGO [France, Italy; ... NIKHEF] Pisa, Italy !!! !! ! ! 12 JAPAN: TAMA: in Tokyo CLIO Kamioka Mine Precursors to LCGT: Large Cryogenic Gravitational Telescope !!! !! ! ! 13 AIGO [Australia] - 5 km Arms Australian International Director: D. McClelland Gravitational Observatory Gin-Gin, West Australia 80 meter test facility !!! !! ! ! 14 Initial LIGOʼs Optical System • Arm cavities store light ~half GW period~100 round trips; build up phase shift ~ 100 k(h2L); k=2π/λlight • Power recycling cavity maximizes light power in arm cavities: 15kW 5 W Photodetector How characterize noise: Spectral Density, Sh(f) ∆L(t) ● h(t) = (interferometer’s strain) ≡ L ● Sh(f) = (spectral density of h, at frequency f) = (“noise power” in h(t) fluctuations, per unit bandwidth) Units: 1/Hz ● Sh(f)∆f = rms fluctuations of h(t) in bandwidth∆f ● fSh(f) = rms fluctuations of h(t) in bandwidth equal to frequency h (f) ≡ rms Initial-LIGO Noise Curves May 2007 Livingston, LA; Hanford, WA √Sh strain √Hz -22 hrms=3x10 frequency, Hz Fundamental Noise Sources Seismic noise May 2007 Livingston, LA; Hanford, WA √Sh strain √Hz Thermal noise Photon shot noise frequency, Hz Photon Shot Noise L = 4km Parm=15 kW 100 round trips • At GW frequency f = 100 Hz (optimal sensitivity) 18 - Parm=15 kW ⇒ Number of photons in arm cavity: N = 2x10 - Light in coherent state ⇒ variance is ΔN=√N ≃109 - Uncertainty Principle: ΔΦ ΔN ≥ 1 ⇒ rms phase fluctuations in arm cavity light: ΔΦ=10-9 - GW moves mirrors, produces phase shift on the arm cavity light Φ= 100 k 2hL ≃ 10-9 for h = 3×10-22 ; so lightʼs phase fluctuations -22 -23 correspond to hrms = 3×10 at f = 100 Hz; √Sh = 3×10 • At GW frequency f > 100 Hz - GW has less time to put phase shift onto light, so: √Sh ~ 1/f 19 Fundamental Noise Sources Seismic noise May 2007 Livingston, LA; Hanford, WA √Sh strain √Hz Thermal noise Photon shot noise -22 hrms=3x10 frequency, Hz Thermal Noise • rms thermal motions of atoms in mirror surface: 2 1/2 -11 7 13 ◊ amplitude ~ (kT/µωο ) ~ 10 meters ~ 10 ΔL; at ωο~10 Hz • Light beam averages over: ◊ ~50 cm2 (~109 surface atoms) ◊ ~0.01 sec (~1011 atomic vibrations) • Result: Light is sensitive almost solely to center-of-mass motion • So mirror behaves like a 40 kg “particle” • Residual motions: thermal noise Light Beam 21 Thermal Noise in Initial LIGO Interferometers • Thermal noise in suspension wires dominates Frictional force mirrorʼs center of mass motion near its eigenfrequency: - 2 Mx¨ + M x˙ + Mω2 = F (t) τ o 2π (1 Hz pendulum frequency) × Light 105 sec pendulum damping time Beam ∼ kT Fluctuating force F(t), together with damping, can produce x = - rms 2 Mωo only if SF = 8MkT/τ at f = ωo/2πf [fluctuation-dissipation theorem] - We are interested in the noise at f=10 to 100 Hz ; experiment shows that SF scales ~ ωo / 2π f so SF = 8MkT/τ (ωo/2πf) 2 - Since 2π f ≫ ωo ≫ 1/τ, amplitudes at frequency f are -(2πf ) Mx = F, 2 2 so spectral densities are Sx = SF / [(2πf ) M] Combining: 1/2 23 5/2 - 32kT ωo 2 10− 100Hz Sh = = × ML2(2πf)4τ 2πf √Hz f Fundamental Noise Sources Seismic noise May 2007 Livingston, LA; Hanford, WA √Sh strain √Hz Thermal noise Photon shot noise frequency, Hz Seismic Noise • Spring between masses 1 and 2; 2 rigidity m2 ωo so m x¨ = m ω2(x x ) 2 2 2 o 1 − 2 • If seismic noise is driving x1 x2 at frequency f = ω/2π, then x1 ω2x = ω2(x x ) − 2 o 1 − 2 ωo = 2π (10 Hz); GW frequencies are • 2 ω >> ωo so x 2 =( ω o / ω ) x 1 and 4 Sx2 ωo ω 10 Hz = • Four mass-spring sets with o ≃ , Sx1 ω plus pendulum with ωo ≃ 1 Hz 2 4 18 m 10Hz Ground motion at LIGO sites: Sx 10− • g Hz f 16 4 4Sx 4Sxg 10 Hz 1 Hz So: LIGO seismic strain noise is Sh = = • L2 L2 f f 22 12 1 10− 40 Hz Sh = × √Hz f Fundamental Noise Sources Seismic noise May 2007 Livingston, LA; Hanford, WA √Sh strain √Hz Thermal noise Photon shot noise frequency, Hz GW Searches: Data Analysis • If waveforms are known [e.g. 7 parameter BH/BH inspiral, merger, ringdown] and have many cycles: Matched Filter Method - Build discrete family of templates covering the parameter space (up to ~ 10,000 template shapes with unknown arrival times) - Cross correlate each template with interferometer output, for various times of arrival [using FFT to deal with all times of arrival simultaneously; Waveform in weighting integral with 1/Sh(f)] Theoretical Noisy data waveform - If waveform and template agree, cross correlation is big. Amplitude SNR h˜(f) 2 So a good measure df SNR = | | df of sensitivity is Sh(f) Sh(f) • If waveforms are not known, a variety of other data analysis methods are used. [e.g.: for stochastic background - Bruce Allenʼs lecture, 14:00 this afternoon] 2 Year Long “S5” Search: Examples of Results ! BH/BH Binaries with Mtot < 35Msun: <1/860 yrs in MWEG" !! GRB070201 (coincident with Andromeda) is not a NS/NS or NS/BH in Andromeda ! !! Targeted Pulsar Search ! »! Crab pulsar: < 7% of spindown energy goes to GWs" !! Stochastic Background: !< 7 x 10-6 in 41-178 Hz band (Bayesian 90% confidence)" From Initial Interferometers to Advanced • 1989: LIGO Proposed • 1995-2000: Construction; installation of initial interferometers • 2000-2005: Initial interferomters ommissioned • 2005-2007: “S5” gravitational-wave search • 2007-2010: Advanced interferometers procurement & preparation for installation. Initial interferometers enhanced; “S6” search now underway • 2011-2012: Advanced interferometers installation • 2012 - : Advanced interferometers commissioning From Initial Interferometers to Advanced Seismic Noise Steel wire Thermal Noise 11kg quartz Shot Noise ~10kW ACTIVE VIBRATION ISOLATION Seismic wall: 40 Hz10 Hz Initial Interferometers Fused silica ~1MW Drever, Meers, Strain Signal 40 kg sapphire Recycling Mirror Advanced Interferometers heater !!! !! ! ! Squeezed vacuum Caves 29 Two Paradigm Shifts on Fundamental Noises (largely from theory students in my group) Thermal Noise [Yuri Levin] Optical Noise & Quantum Noise [Carlton Caves, ..., Alessandra Buonanno and Yanbei Chen] !!! !! ! ! 30 Thermal Noise Paradigm Shift • Previous paradigm: sum over normal modes • Yuri Levin’s thought experiment (variant of fluctuation dissipation theorem) Applied Force • To compute spectral density of noise at frequency f=2πω: • CONSEQUENCES: • Apply an oscillating force Fo with frequency f and cross- • Previous paradigm is gives wrong sectional profile same as light answers if dissipation inhomogeneous beam • Classify noise by dissipation location & mechanism • Compute total rate of • Mirror coating dangerous! dissipation Wdiss = T dS/dt Huge effort has gone into 2 2 • Sx(ω) = (4kT/ω )(Wdiss/Fo ) exploring this and optimizing design 31 substratesubstrate Thermal Noises in Advanced LIGO 10-21 √Sh 10-22 strain √Hz 10-23 suspension fibers 10-24 mirror coatings substrate 10-25 !!!10 100!! !1000 ! 10,000 frequency, Hz 32 Optical and Quantum Noise Paradigm Shift 10-21 Rad’n Pressure noise ~ 1/√P Standard Quantum Limit [Braginsky, Caves] -22 » Like Heisenberg 10 microscope » SQL enforced by L 10-23 radiation pressure fluctuations -24 Shot noise ~ √P 10 L SQL 10-25 GW Field 10 100 1000 10,000 !!! !! ! ! 33 Optical and Quantum Noise Paradigm Shift 10-21 Standard Quantum Limit Change position & reflectivity of [Braginsky, Caves] SR mirror; move signal-gathering photons from ~100 Hz to ~600 Hz
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