LIGO-G1401365-v1 Koji Arai – LIGO Laboratory / Caltech Ph.D at Univ of Tokyo (1995-1999) Design & build of TAMA300 double-pendulum suspensions Interferometer length sensing for power recycled Fabry-Perot Michelson Interferometer Commissioning and science runs of TAMA300 interferometer (1999-2009) @LIGO Caltech (2009-) Output mode cleaner development eLIGO/aLIGO commissioning Mission: To convey technical knowledge necessary for building and operating the LIGO India detector, or similar interferometer, including prototypes by going through: the common technologies in laser interferometer GW detectors Detailed description / discussion about the interferometer sensing & control Lecture plan DAY1 General overview of laser interferometer GW detectors Interferometer configurations DAY2 Noises in GW detectors DAY3 Control system & its modeling DAY4 Interferometer length sensing and control Feedforward noise cancellation Quantum noise DAY5 Higher-order laser modes General Relativity Gravity = Spacetime curvature Gravitational Wave = Wave of spacetime curvature GW Generated by motion of massive objects Propagates with speed of light Cause quadrupole deformation of the spacetime Free mass GW What does the balls feel? The balls are free mass (= free falling) ...Geodesic lines GW Q. What happens if the balls are connected by bars Free mass Michelson-type interferometers are used Differential change of the arm path lengths =>change interference condition Mirror Beamsplitter Laser Mirror Interference Fringe p p iWL/ c b2( W a ( W) + p E0 1 )−= Re2iWL/ c e p Rec2iWL/ − cR 2 ✓ 2 Te2iWL/ 2w ! p 1 − T 1 − p E0 TeiWL/ cpRe 2w x ( W) b2(eW ) = c − pR a2( W2) + ◆ 2iWL/ 2iWL/ c p 1 − Re p 1 − Re2iWL/0c b2( W) = a2( W) + p E0 T c c 1 − Re2iWL/ c T 1 − Re2iWL/ ! p ✓ ◆ g + iW 2 2/ pT ! 2w0 x ( W) p E0 ◆ b2( W) = a2( W) + ✓ iW ✓ 2 2wc0 x ( W ! T g g− +iW g p 1 − 2/iW/ pT E2/ b2(g(at W+) iW = a2( W2) + ◆ low frequencies) 0 T1 − iW/ 2w0gx ( W) c g − iW T p b2( W) = a2( W) + E0 g − iW 1 − iW/ g c T e1 = ex cos qcos f + ey cos qsin f − ez cos q eyfcos qsin f − ez cos q e2e1= =−exexcos sinqcos f + fey+cos e1 = ex cos qcos f + ey cos qsin f − ez cos q e2 = − ex sin f + ey cos f e2 = − ex sin f + ey cos f e2 ⇥ ⇤ F+ = e⇥ e − e e : [e1e1 − e2e2] x x y y ⇤ ⇥ ⇤ F = e e − e e + x x y 1 −e2ee21e]2] F = e e − e e : [:e[1ee12e+ ⇥ x x y y y⇤ e1 ⇥ F⇥ = ex ex − ey ey : [e1e2 + e2e1] Antenna pattern Low-Frequency AntennaPattern z θ ! y q Frms = 2 F+2 + F⇥ x Rev. Mod. Phys. 86 (2014) 121-151 http://link.aps.org/doi/10.1103/RevModPhys.86.121 (http://arxiv.org/abs/1305.5188) The effect of GW is very small h ~ 10-23 => distance of 1m changes 10-23m Corresponds to: change by ~0.01 angstrom (or 1pm) for distance between the sun and the earth 1.5 x 1011 m changes by 1/100 of a H atom diameter! Mirror GW Detection = Length measurement The longer arms, the bigger the effect GW works as strain => dx = hGW x Larm Until cancellation of the signal happens in the arms Optimum arm length Mirror Mirror Larm = 75km (for fGW =1kHz) Laser Laser 4Larm = lGW (= c / fGW ) Photodetector Photodetector Mirror LIGO Observatories Hanford / Livingston 4km Still shorter than the optimum length => Use optical cavity to increase life time of the photons in the arm \ c.f. Virgo (FRA/ITA) 3km, KAGRA (JPN) 3km, GEO (GER/GBR) 600m “Still simplified” LIGO Interferometer 4km Fabry-Perot Cavity Vacuum Chamber / Beam tube 4km Fabry-Perot Cavity Mirror Suspension Beamsplitter Recycling Mirrors Laser Mode Cleaner L~16m Photodetector Digital Control System Vibration Isolation System Data Acquisition /Analysis System Mirror 3 fundamentals of the GW detector Mechanics Optics Electronics 3 fundamentals of the GW detector Mechanics Optics Electronics An IFO produces a continuous signal stream in the GW channel The detector is fixed on the ground => can not be directed to a specific angle GWs and noises are, in principle, indistinguishable => Anything we detect is GW Reduce noises! Obs. distance is inv-proportional to noise level x10 better => x10 farther => x1000 more galaxies Sensitivity (=noise level) of Enhanced LIGO Laser shot noise Laser radiation pressure noise thermal noise seismic noise Laser intensity /frequency noise h= 2x10-23 /rtHz electronics noise digitization noise angular control noise ...... aLIGO sensitivity Preliminary x= 4x10-20 m/rtHz h= 1x10-23 /rtHz Compact Binary Coalescence => Chirp signal NS-NS binaries Accurate waveforms predictable (Post Newtonian approximation) => Template banks & Matched Filter analysis (amplitude & phase information) BH-BH binaries Similar waveforms, but more difficult to predict because of earlier merging Mat]ched filtering analysis B. F. Schutz, “Gravitational wave astronomy”, 10-15 Spectral sensitivity (strain per root Hz) 10 2-1 6 0M Class. Quantum Grav. 16 (1999) A131. o BH at z =1 -16 f_ISCO = 1/(pi (6 M)^3/2) 10-17 10-18 LISA 10 6 M 10-19 o -10 M o BH 10-20 at z = 2 -1 1 Crab (1 yr) 0M GEO600 o BH at 2 10-21 binary confusion background 10-22 10-23 00 Mp 2-0 c .5M o BH at 2 2-N 0M Sa pc t 20 0M pc r) c 1 y Mp ( 0 1 X- at 2 o Sc ode NS f-mode at 20Mpc r-m (10-4Moc2 energy) Sc LIGO II 10 -24 Stochastic background, 2-detector sensitivity -- 10-25 10-6 10-5 10-4 10-3 10-2 10-1 Wgw =10-14 100 gravitational wave frequency (Hz) 101 LIGO I oX Wgw =10-10 102 103 -1 (1 d ay ) Wgw =10-6 104 Binary inspiral range Chirp waveform PSD : Dist ribut ion of inspiral horizon dist ance for t he four gravit at ional wave det ect ors H1, L1, H2 and V1 for all of S5 SR1. T his hist ogram includes each 2048-second analyzed segment from S5 and VSR1. T he dist ribut ions shown here ond t o t he 1.4 -1.4 solar mass inspiral horizon dist ance for t he LIGO det ect ors. For t he V irgo det ect or, we have plot t ed -1.0 solar mass inspiral horizon dist ance dist ribut ion, scaled by (2.8/ 2) 5/ 6 t o adjust for t he lower mass. ISCO freq (HF cut off freq) M is t he chirp mass of t he binary, D is t he dist ance t o t he binary and is a real funct ion of f , paramet rized e t ot al mass M . Set t ing h⇢i = 8 and insert ing t his waveform int o eqn. 3, we find t hat t he inspiral horizon ce is given by s Z ✓ ◆1/ 2 f h i gh 1 5⇡ f − 7/ 3 5/ 6 − 7/ 6 D= (GM ) ⇡ 4 df , (6) 8 24c3 Sn (f ) f l ow Horizon range (Integrated SNR of 8) D is expressed in Mpc. T he inspiral horizon dist ance is defined for opt imally locat ed and orient ed sources. uniform dist ribut ion of source sky locat ions and orient at ions, we divide t he inspiral horizon dist ance by 2.26 t o t he SenseMon range [9] report ed as a figure of merit in t he LIGO and Virgo cont rol rooms. iLIGO 15Mpc ract ice, it is convenient t o measure dist ances in Mpc and mass in M . It is useful t herefore t o specialize eqn. his unit syst em. Furt her, since we measure t he st rain h(t) at discret e t ime int ervals eLIGO ∆ t = 1/ f s ,20Mpc t he spect ral y is only known wit h a frequency resolut ion of ∆ f = f s / N , where N is t he number of dat a point s used t o aLIGO 50Mpc re Sn (f https://dcc.ligo.org/LIGO-T0900499/public ). By put t ing f = k∆ t int o eqn. 6 and grouping t erms by unit s, we arrive at t he expression In the control room we use D/(2.26) taking all sky average LIGO-Virgo only From LIGO-G1201135-v4 LIGO-Virgo plus LIGO-India From LIGO-G1201135-v4 Burst gravitational waves Supernovae, binary merger phase, etc Accurate waveforms unpredictable => Find signals with an “unusual” amplitude => Important to distinguish from non-stationary noises Continuous waves Pulsars Sinusoidal signal with some modulations => Longterm integration => Important to distinguish from line noises (Remark: power line freq. US 60Hz, India 50Hz) Stochastic gravitational wave background From early universe The waveforms are random => Correlation analysis of the detector network => The total GW flux can be estimated => Or, skymap of the flux is obtained from radiometric analysis In all cases, it is highly desirable to have the detectors to have comparable sensitivities GWs ~ ripples of the spacetime Not yet directly detected ~ the effect is so small (h<10-21) Michelson-type interferometers are used GW detection is a precise length (=displacement) measurement! GW effect is very small Basically, the larger, the better. LIGO has two largest interferometers in the world, and the third one will have very important role in GW astronomy IFO consists of many components Optics / Mechanics / Electronics and their combinations (e.g. Opto-Electronics) Noises and signals are, in principle, indistinguishable. Noise reduction is essential