1. Gravitational-wave Detection with Interferometers
LIGO, LISA, and the like
Nergis Mavalvala MIT September 18, 2002

2. Interferometric Detectors Worldwide
TAMA
LIGO
LISA
LIGO
VIRGO
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. 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

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
E&M GW
Space as medium for field
Spacetime itself
Accelerating charge  incoherent superpositions of atoms, molecules
Accelerating aspherical mass  coherent motions of huge masses
Wavelength small compared to sources  images
Wavelength large compared to sources  no spatial resolution
Absorbed, scattered, dispersed by matter
Very small interaction; matter is transparent
10 MHz and up
10 kHz and down
Detectors have small solid angle acceptance
Detectors have large solid angle acceptance

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-time where ,
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. 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

11. GWs meet Interferometers
Laser interferometer
Suspend mirrors on pendulums  “free” mass
Optimal antenna length a L ~ l/4 ~ 105 meter
DL = h L
Delta_L = h * L
10^-16 m = 10^-21 * 10^5 m

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
N a 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 ~ 10-8 l
Arm cavity  increase strain-to-phase conversion (phi = N * dL)
Power recycling  improves shot noise limited phase sensitivity

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

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

15. 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

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. 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

18. 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

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

21. 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: 2006
Begin data run: 2008

22. 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

23. Optimizing the 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

24. 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.

25. 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
~10 min
~3 sec
20 Mpc
300 Mpc

26. Source detection Spinning neutron stars Stochastic background
Galactic pulsars: non-axisymmetry uncertain
Low mass X-ray binaries: If accretion spin-up balanced by GW spin- down, then X-ray luminosity  GW strength Does 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)
Signal strengths for
20 days of integration
Sco X-1
Thorne
GW energy / closure energy

27. Detection of candidate sources
Thorne

28. New Instrument, New Field, the Unexpected…