Gravitational-wave Detection with Interferometers

1. Gravitational-wave Detection with Interferometers LIGO, LISA, and the like Nergis Mavalvala8.971 seminar @ MITSeptember 18, 2002

2. Interferometric Detectors Worldwide TAMA LIGO LISA VIRGO LIGO GEO

3. Global network of detectors GEO VIRGO LIGO TAMA AIGO LIGO LISA

4. Science goals: detection of gravitational waves • Tests of general relativity • Waves  direct evidence for time-dependent metric • Black hole signatures  test of strong field gravity • Polarization of the waves  spin of graviton • Propagation velocity  mass of graviton • Astrophysical processes • Inner dynamics of processes hidden from EM astronomy • Cores of supernovae • Dynamics of neutron stars  large scale nuclear matter • The earliest moments of the Big Bang  Planck epoch • Astrophysics…

5. GWs neutrinos photons now Astrophysical sources of GWs • Coalescing compact binaries • Classes of objects: NS-NS, NS-BH, BH-BH • Physics regimes: Inspiral, merger, ringdown • Other periodic sources • Spinning neutron stars  numerically hard problem • Burst events • Supernovae  asymmetric collapse • Stochastic background • Primordial Big Bang (t = 10-43 sec) • Continuum of sources • The Unexpected

6. Gravitational Waves • General relativity predicts transverse space-time distortions propagating at the speed of light • In TT gauge and weak field approximation, Einstein field equations  wave equation • Conservation laws • Conservation of energy  no monopole radiation • Conservation of momentum  no dipole radiation • Lowest moment of field  quadrupole (spin 2) • Radiated by aspherical astrophysical objects • Radiated by “dark” mass distributions  black holes, dark matter

7. Astrophysics with GWs vs. E&M • Very different information, mostly mutually exclusive • Difficult to predict GW sources based on E&M observations

8. Gravitational waves and GR • From special relativity, “flat” space-time interval is • From general relativity, curved space-time can be treated as perturbation of flat space-timewhere , • In the transverse traceless gauge Einstein’s equation  gives wave equation

9. Gravitational waves and GR • Time-dependent solution  • Two polarizations  • Interaction with matter

10. M M h ~10-21 Strength of GWs:e.g. Neutron Star Binary • Gravitational wave amplitude (strain) • For a binary neutron star pair R r

11. DL = h L GWs meet Interferometers • Laser interferometer • Suspend mirrors on pendulums  “free” mass • Optimal antenna length a L ~ l/4 ~ 105 meter

12. Practical Interferometer • For more practical lengths (L ~ 1 km) a “fold” interferometer to increase phase sensitivity • Df = 2 k DL  N (2 k DL); N ~ 100 • Na number of times the photons hit the mirror • Light storage devices a optical cavities • Dark fringe operation a lower shot noise • GW sensitivity P a increase power on beamsplitter • Power recycling • Most of the light is reflected back toward the laser  “recycle” light back into interferometer • Price to pay: multiple resonant cavities whose lengths must be controlled to ~ 10-8l

13. Power-recycled Interferometer Optical resonance: requires test masses to be held in position to 10-10-10-13meter“Locking the interferometer” end test mass Light bounces back and forth along arms ~100 times 30 kW Light is “recycled” ~50 times 300 W input test mass Laser + optical field conditioning signal 6Wsingle mode

14. 3 0 3 ( ± 0 1 k 0 m m s ) LIGO WA 4 km 2 km LA 4 km

15. Initial LIGO Sensitivity Goal • Strain sensitivity < 3x10-23 1/Hz1/2at 200 Hz • Displacement Noise • Seismic motion • Thermal Noise • Radiation Pressure • Sensing Noise • Photon Shot Noise • Residual Gas • Facilities limits much lower

16. Limiting Noise Sources:Seismic Noise • Motion of the earth few mm rms at low frequencies • Passive seismic isolation ‘stacks’ • amplify at mechanical resonances • but get f-2 isolation per stage above 10 Hz

17. FRICTION Limiting Noise Sources:Thermal Noise • Suspended mirror in equilibrium with 293 K heat bath akBT of energy per mode • Fluctuation-dissipation theorem: • Dissipative system will experience thermally driven fluctuations of its mechanical modes: Z(f) is impedance (loss) • Low mechanical loss (high Quality factor) • Suspension  no bends or ‘kinks’ in pendulum wire • Test mass  no material defects in fused silica

18. Limiting Noise Sources:Quantum Noise • Shot Noise • Uncertainty in number of photons detected a • Higher input power Pbsa need low optical losses • (Tunable) interferometer response  Tifo depends on light storage time of GW signal in the interferometer • Radiation Pressure Noise • Photons impart momentum to cavity mirrorsFluctuations in the number of photons a • Lower input power, Pbs  Optimal input power for a chosen (fixed) Tifo

20. Displacement Sensitivity(Science Run 1, Sept. 2002)

21. The next-generation detectorAdvanced LIGO (aka LIGO II) • Now being designed by the LIGO Scientific Collaboration • Goal: • Quantum-noise-limited interferometer • Factor of ten increase in sensitivity • Factor of 1000 in event rate. One day > entire2-year initial data run • Schedule: • Begin installation: 2006 • Begin data run: 2008

22. Quantum LIGO I LIGO II Test mass thermal Suspension thermal Seismic A Quantum Limited Interferometer • Facility limits • Gravity gradients • Residual gas • (scattered light) • Advanced LIGO • Seismic noise 4010 Hz • Thermal noise 1/15 • Optical noise 1/10 • Beyond Adv LIGO • Thermal noise: cooling of test masses • Quantum noise: quantum non-demolition

23. f i (l) r(l).e Power Recycling l Signal Recycling Optimizing the optical response: Signal Tuning Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM Reflects GW photons back into interferometer to accrue more phase

24. Thorne… Advance LIGO Sensitivity:Improved and Tunable

25. ~10 min 20 Mpc ~3 sec 300 Mpc Implications for source detection • NS-NS Inpiral • Optimized detector response • NS-BH Merger • NS can be tidally disrupted by BH • Frequency of onset of tidal disruption depends on its radius and equation of state a broadband detector • BH-BH binaries • Merger phase  non-linear dynamics of highly curved space time a broadband detector • Supernovae • Stellar core collapse  neutron star birth • If NS born with slow spin period (< 10 msec) hydrodynamic instabilities a GWs

26. Sco X-1 Signal strengths for 20 days of integration Source detection • Spinning neutron stars • Galactic pulsars: non-axisymmetry uncertain • Low mass X-ray binaries:If accretion spin-up balanced by GW spin-down, then X-ray luminosity  GW strengthDoes accretion induce non-axisymmetry? • Stochastic background • Can cross-correlate detectors (but antenna separation between WA, LA, Europe a dead band) • W(f ~ 100 Hz) = 3 x 10-9 (standard inflation  10-15) (primordial nucleosynthesis d 10-5) (exotic string theories  10-5) Thorne GW energy / closure energy

27. Thorne Detection of candidate sources

28. New Instrument, New Field,the Unexpected…