1. Gravitational-wave Detection with Interferometers
LIGO, LISA, and the like
Nergis Mavalvala IAP, 2003

2. Global network of gravitational wave interferometers
GEO
VIRGO
LIGO
TAMA
AIGO
LIGO
LISA

3. Newton’s gravity Universal gravitation
Three laws of motion and law of gravitation (centripetal force)
eccentric orbits of comets
cause of tides and variations
precession of the earth’s axis
perturbation of motion of the moon by gravity of the sun
Solved most problems of astronomy and terrestrial physics known then
Unified the work of Galileo, Copernicus and Kepler
Worried about instantaneous action at a distance (Aristotle)
How could objects influence other distant objects? Fg

4. Clocks tick more slowly
Einstein’s gravity
The Special Theory of Relativity (1905) said outrageous things about space and time
Relative to an observer traveling near the speed of light space and time are altered
The General Theory of Relativity and theory of Gravity (1916)
No absolute motion  only relative motion
Space and time not separate  four dimensional space-time
Gravity is not a force acting at a distance  warpage of space-time
Gravitational radiation (waves)
Distances stretched
and
Clocks tick more slowly

5. Gravitational Waves
GR 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

6. Astrophysics with GWs vs. E&M
Very different information, mostly mutually exclusive
Difficult to predict GW sources based on EM observations
E&M (photons) GW
Space as medium for field
Spacetime itself ripples
Accelerating charge
Accelerating aspherical mass
Absorbed, scattered, dispersed by matter
Very small interaction; matter is transparent
10 MHz and up
10 kHz and down
Light = not dark (but >95% of Universe is dark)
Radiated by dark mass distributions  black holes, dark matter

7. Gravitational waves measured?
Emission of gravitational radiation from PSR
due to loss of orbital energy
period sped up 14 sec from
measured to ~50 msec accuracy
deviation grows quadratically with time
Nobel prize in  Taylor and Hulse

8. 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 = sec)
Continuum of sources
The Unexpected
Coalescing compact binaries  chirp sources
NS-NS  far away; long periods; final inspiral gives GW chirp
NS-BH  tidal disruption of NS by BH; merger  GRB triggers
Inspiral  accurate predition with PPN proportional to (v/c)^11
Merger  nonlinear dynamics of highly curved spacetime
Ringdown  ringdown of modes of coalesced object
Periodic sources
Spinning NS  axisymmetry unknown
Galactic pulsars in SN remnant gases  non-axisymmetry unknown
LMXBs  mass accretion from companion
Is accretion spin-up balanced by GW spin-down?
Issues  axisymmetric distortion from radiation reaction force
Supernovae
Collapse  Dynamics not understood. If instability makes star into tumblong bar, then GWs
Core convection  detect via correlations with neutrinos
GWs
neutrinos
photons
now

9. Strength of GWs: e.g. Neutron Star Binary
Gravitational wave amplitude (strain)
For a binary neutron star pair M R
Quadrupole formalism is accurate to order of magnitude for most sources.
Involves computing wave generation and radiation reaction from Einstein eqn.
Weak internal gravity and stresses  nearly Newtonian source
Kepler’s third law of planetary motion: period^2 = 4*pi^2*radius^3/(G*Msun)
Distances  1 parsec = 3.26 l.y. = 3e18 cm
r ~ 10^23 m ~ 10 Mpc (center of Virgo cluster)
Distance of earth to center of galaxy ~ l.y. ~ 10 kpc
h ~10-21 r

10. GWs meet Interferometers
Laser interferometer
DL = h L
(h ~ 10-21)
Earth diameter
1011
107
104
100
10-2
10-10
10-5
10-18
10-15
Earth-Sun distance
USA E-W
Short person
Pea
Width of hair
Size of atom
Size of nucleus
LIGO measurement m
Delta_L = h * L
10^-16 m = 10^-21 * 10^5 m

11. Power-recycled Interferometer
Optical resonance: requires test masses to be held in position to meter
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
6W single mode

12. The Laser Interferometer Gravitational-wave Observatory
2 km
4 km 3 k m ( 1 s ) WA LA
4 km

13. Initial LIGO Sensitivity Goal
Strain sensitivity < 3x /Hz1/2 at 200 Hz
Displacement Noise
Seismic motion
Thermal Noise
Radiation Pressure
Sensing Noise
Photon Shot Noise
Residual Gas
Facilities limits much lower

14. 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

15. Limiting Noise Sources: Thermal Noise
Suspended mirror in equilibrium with 293 K heat bath a kBT 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
FRICTION

16. Limiting Noise Sources: Quantum Noise
Shot Noise
Uncertainty in number of photons detected a
Higher input power Pbs a 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 mirrors Fluctuations in the number of photons a
Lower input power, Pbs
 Optimal input power for a chosen (fixed) Tifo
Shot noise:
Laser light is Poisson distributed  sigma_N = sqrt(N)
dE dt >= hbar  d(N hbar omega) >= hbar  dN dphi >= 1
Radiation Pressure noise:
Pressure fluctuations are anti-correlated between cavities

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

19. The next-generation detector Advanced 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 > entire 2-year initial data run
Schedule:
Begin installation: 2007
Begin data run: 2009

20. 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
LIGO I
LIGO II
Seismic
Suspension thermal
Test mass thermal
Quantum

21. Optimizing optical response: Signal Tuning
Power
Recycling
Signal
r(l).e i f
(l) l
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

22. Advance LIGO Sensitivity: Improved and Tunable
Thorne…
SQL  Heisenberg microscope analog
If photon measures TM’s position too well, it’s own angular momentum will become uncertain.

23. Laser Interferometer Space Antenna (LISA)
Three spacecraft
triangular formation
separated by 5 million km
Constant solar illumination
Formation trails Earth by 20°
Approx. constant arm-lengths
1 AU = 1.5x108 km

24. LISA and LIGO

25. Science from gravitational wave detectors?
Test 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
Different view of the Universe
Predicted sources: compact binaries, SN, spinning NS
Inner dynamics of processes hidden from EM astronomy
Dynamics of neutron stars  large scale nuclear matter
The earliest moments of the Big Bang  Planck epoch
Precision measurements at and below the quantum limit set by Heisenberg on photons

26. New Instruments, New Field, the Unexpected…

27. Major research activities at the MIT LIGO Laboratory
Initial LIGO (now!)
Instrument science  lasers and optics, interferometry, optical metrology, optical resonant systems, photonics, control systems, low-noise electronics, vibration isolation systems, thermally induced dissipation, thermally adaptive optics
Data analysis and astrophysical searches  signals of known and unknown signatures buried in noise, astrophysical source signatures, computing challenges
Advance LIGO (beyond 2006)
Instrument development  design and prototyping of mechanical and optical subsystems (R&D and implementation)
Other things we work on
LISA (advisory role at present)
Quantum measurement  precision measurements at or below the quantum limit)