1. Gravitational-wave Detection with Interferometers
Present and Future
Nergis Mavalvala
October 09, 2002

2. Interferometric Detectors Worldwide
TAMA
LIGO
LISA
LIGO
VIRGO
GEO

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

4. Gravitational Waves
General relativity predicts transverse space-time distortions propagating at 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

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

12. 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

13. 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

14. 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

15. 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

16. Core Optics 25 cm diameter, 10 kg fused silica optics
Polished substrates
Micro-roughness  < 10 ppm scatter
Optical coatings
< 2 ppm scatter
< 1 ppm absorption
Metrology 
Surface uniformity ~1 nm rms

18. Displacement Sensitivity (Preliminary S1, Sept. 2002)

19. Evolution of strain sensitivity
Major improvements
Front-end electronics (ADC) noise  whiten signal
Laser frequency noise  common-mode servo
Output electronics (DAC) noise  whiten signal
Sensing electronics noise  increase light level

20. LIGO I Instrument Status: What works
All three interferometers locked for hours at a time in power-recycled configuration a Grec ~ 25 – 45
Lock acquisition is done using sys id methods a MTTL ~ 1 – 2 minute
Optical parameters consistent with lab metrology a mirror losses < 70 ppm
Mechanical (internal) modes of test masses excited a 104 < Q < 107
End-to-end simulation program
Data analysis pipelines and algorithms

21. LIGO I Instrument Status: What doesn’t (yet)
Large factor to be gained in strain sensitivity
Laser input power 1 – 5 W but all light power not detected (PD saturations) a alignment control system
Coupling to environment, e.g.
Earthquakes
Trains twice a day at Livingston
Anthropogenic noise
seismic pre-isolation system
Electronics improvements

22. The Task Ahead Engineering runs Science runs
Characterize and improve detector sensitivity and reliability
Exercise data analysis system end-to-end pipeline
Science runs
Upper limits (E7 and beyond)
Scientific searches (S1 was 08/23/02 to 09/07/02)
Coincidence with GEO and TAMA
Commissioning remaining subsystems
Factor of 100 (above 400 Hz) to (at 40 Hz) improvement needed to reach design sensitivity
LIGO II R&D already underway

23. 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

24. 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

25. How will we get there? Seismic noise Thermal noise Quantum noise
Active isolation system
Mirror suspended as fourth (!!) stage of quadruple pendulum
Thermal noise
Suspension: fused quartz; ribbons
Test mass: higher mechanical Q material, e.g. sapphire
Quantum noise
Input laser power: increase to ~200 W
Optimize interferometer response, Tifo: signal recycling

26. 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

27. 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.

28. 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

29. 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

30. Detection of candidate sources
Thorne

31. When gravitational waves are detected…
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…

32. New Instrument, New Field, the Unexpected…