A gravitational wave is a differential strain in spacetime. Equivalently, it is a differential tidal force that can be sensed by multiple test masses. Plus-polarization Cross-polarization 2
Any system with an accelerating quadrupole moment I μν : h μν = 2G d 2 I μν c 4 r dt 2 (r = distance from system to observer) Inspiral, merger, and ringdown of binary systems Core-collapse supernovae Non-axisymmetric pulsars
First aligo observing run: Sep 2015 to Jan 2016 Observed two binary black hole coalescences 35 Hz 250 Hz PRL 116, 061102 (2016) PRL 116, 241103 (2016) 4
Basic idea: Michelson interferometer Test masses Arms are made into Fabry Perot cavities 125 W laser source Power recycling increases the power in the arms Power recycling Signal recycling Signal recycling broadens the interferometer s sensitivity to GWs GW readout 5
ASD of strain [1/Hz 1/2 ] 10-22 O1 sensitivity (25 W) Expected sensitivity (125 W) Shot (125 W) Radiation pressure (125 W) Test mass thermal Suspension thermal 10-23 10-24 10 1 10 2 10 3 Frequency [Hz] 6
Test mass Test mass Test masses, laser source 7
Beamsplitter Test mass 8
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40 kg mirrors made from low-loss fused silica High-reflectivity (>99.995%) mirror coatings made with ion-beam-sputtered thin films Layers of SiO 2 and Ta 2 O 5 (a few µm total thickness) Fused silica substrate 10
Active seismic isolation Four cascaded pendula give 1/f 8 isolation against seismic noise in the GW band Top three stages use electromagnetic actuation Final stage uses electrostatic actuation 11
Fluctuation dissipation theorem: thermally-driven fluctuations are proportional to the system s losses: Mean-square displacement fluctuation x 2 T Q Temperature Mechanical Q-factor Thermal noise arises from: Test mass coatings Test mass substrates Suspension fibers How to reduce thermal noise? Use materials with high Q-factors Make the laser spot size large Exploit dissipation dilution Silica Q ~ 10 6 Tantala Q ~ 10 4 Suspension Q ~ 10 9 12
Injectionlocked amplifier (220 W) To vacuum system Seed crystal (2 W) Single-pass amplifier (35 W) 13
220 W injection-locked amplifier 35 W single-pass amplifier 2 W, 1064 nm seed NPRO main interferometer (from AOM) end test masses 24 MHz power recycling mirror input test masses (from AOM) 21 MHz (to test masses) 9.1 MHz 5 45.5 MHz signal recycling mirror gravitational wave readout pre-modecleaner fused-silica reference cavity input modecleaner output modecleaner 14
Laser power: 125 W of 1064 nm light into interferometer Laser noise: must contribute no more than one tenth of the total GW strain ASD Laser noise affects GW readout because of arm imbalances: Different input test mass reflectivties Different arm losses Beamsplitter not perfectly 50/50 Differential arm length offset 15
Freerunning frequency noise is 100 Hz/Hz 1/2 at 100 Hz (falls like 1/f). Need to suppress this by 8 orders of magnitude at 100 Hz: Adhikari et al., LIGO-T070236 16
Freerunning relative intensity noise is 10 5 /Hz 1/2 at 100 Hz (falls like 1/f). Need to suppress this by 2 orders of magnitude at 100 Hz: Adhikari et al., LIGO-T070236 17
Frequency stabilization: Pound Drever Hall locking using three length references: Tabletop fused silica reference cavity (20 cm) Suspended, in-vacuum ring cavity (16 m) Interferometer s common-mode arm length (4 km) Common-mode arm length acts like a 4-km-long cavity with a 1 Hz linewidth Intensity stabilization: dc locking using three intensity references: Tabletop bow-tie cavity (2.0 m) Suspended, in-vacuum ring cavity (16 m) [NEW!] Interferometer s common-mode arm intensity (4 km) 18
asd of frequency Hz/Hz 1/2 10 4 10 5 Interferometer shot and length noises Frequency actuator Modecleaner shot Modecleaner length NPRO, reference cav. Total expected 10 6 10 7 10 8 10 9 10 1 10 2 10 3 10 4 Frequency [Hz] 19
Interferometer optics must be actively controlled in order to maintain resonance: 5 length DOFs 20 angular DOFs In total, there are about 300 servo loops that keep the interferometer running. Lowest bandwidth is ~10 mhz (hydraulic compensation of ground tides) Highest bandwidth is ~1 MHz (laser noise eater) 20
aligo H1 freer unning DARM, 2015 12 02 5:30:00 Z ASD of displacement m/hz 1/2 10 17 10 18 Measured Quantum noise Dark noise Seismic+Newt onian Ther mal Actuator noise Ambient elect rostatic Gas noise LSC ASC I ntensity+frequency Jitter SRM PEEK (1/f 1/2 ) Total expected 10 19 10 20 10 21 10 1 10 2 10 3 Frequency [Hz] 21
Different coating materials, e.g. AlGaAs Squeezed light Nature 7, 962 (2011) Also: Heavier test masses (reduces radiation pressure noise) Longer suspension fibers (reduces suspension thermal noises) 22
Use silicon instead of silica Operate at 120 K (where thermal expansion coefficient of silicon is zero) Use 1.5 µm or 2 µm laser 23
Design with shot noise, radiation pressure noise, and thermal noise in mind Laser noise rejection is never perfect in an interferometer, so crush it with servo loops The common-mode arm length makes a great reference cavity Need better coatings, and possibly a different laser wavelength 24
2 W seed crystal 35 W amplifier 220 W amplifier Modecleaning cavity Modecleaning cavity Laser frequency stabilized to ~1 µhz/hz 1/2 at 100 Hz Laser amplitude stabilized to ~10 8 /Hz 1/2 at 100 Hz 25
a M 1 For an equal-mass binary, h 4π2 G c 4 r Ma2 f 0 2 GW frequency is f GW = 2f 0 M 2 For M ~ 30M, a ~ 100 km, f 0 ~ 100 Hz, and r ~ 500 Mpc, we expect strains of order 10 21 Orbital frequency f 0 26