1. Detection of Gravitational Waves with Interferometers
Giant detectors Precision measurement The search for the elusive waves
Nergis Mavalvala (on behalf of the LIGO Scientific Collaboration)

2. Global network of detectors
GEO
VIRGO
LIGO
TAMA
AIGO
LIGO
Detection confidence
Source polarization
Sky location
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?

4. Einstein’s gravity
The Special Theory of Relativity (1905) said revolutionary 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
Transverse distortions of the space-time itself  ripples of space-time curvature
Propagate at the speed of light
Push on freely floating objects  stretch and squeeze the space transverse to direction of propagation
Energy and momentum conservation require that the waves are quadrupolar  aspherical mass distribution

6. Astrophysics with GWs vs. E&M
Very different information, mostly mutually exclusive
Difficult to predict GW sources based on EM observations
E&M GW
Accelerating charge
Accelerating aspherical mass
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

7. Astrophysical sources of GWs
Periodic sources
Pulsars  Spinning neutron stars
Low mass Xray binaries
Coalescing compact binaries
Classes of objects: NS-NS, NS-BH, BH-BH
Physics regimes: Inspiral, merger, ringdown
Burst events
Supernovae with asymmetric collapse
GWs
neutrinos
photons
now
Stochastic background
Primordial Big Bang (t = sec)
Continuum of sources
The Unexpected

8. Astrophysical sources of GWs
Periodic sources
Pulsars  Spinning neutron stars
Low mass Xray binaries
Coalescing compact binaries
Classes of objects: NS-NS, NS-BH, BH-BH
Physics regimes: Inspiral, merger, ringdown
Burst events
Supernovae with asymmetric collapse
GWs
neutrinos
photons
now
Stochastic background
Primordial Big Bang (t = sec)
Continuum of sources
The Unexpected

9. Pulsar born from a supernova
PULSAR IS BORN: A supernova is associated with the death of a star about eight times as massive as the Sun or more. When such stars deplete their nuclear fuel, they no longer have the energy (in the form of radiation pressure outward) to support their mass. Their cores implode, forming either a neutron star (pulsar) or if there is enough mass, a black hole. The surface layers of the star blast outward, forming the colorful patterns typical of supernova remnants.
ACCRETION SPINS UP THE PULSAR: When a pulsar is created in a supernova explosion, it is born spinning, but slows down over millions of years. Yet if the pulsar -- a dense star with strong gravitational attraction -- is in a binary system, then it can pull in, or accrete, material from its companion star. This influx of material can eventually spin up the pulsar to the millisecond range, rotating hundreds of revolutions per second.
GWs LIMIT ACCRETION INDUCED SPIN UP: As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up.
Courtesy of NASA (D. Berry)

10. Astrophysical sources of GWs
Periodic sources
Pulsars  Spinning neutron stars
Low mass Xray binaries
Coalescing compact binaries
Classes of objects: NS-NS, NS-BH, BH-BH
Physics regimes: Inspiral, merger, ringdown
Burst events
Supernovae with asymmetric collapse
GWs
neutrinos
photons
now
Stochastic background
Primordial Big Bang (t = sec)
Continuum of sources
The Unexpected

11. Millisecond pulsar accretion
As the pulsar picks up speed through accretion, it becomes distorted from a perfect sphere due to subtle changes in the crust, depicted here by an equatorial bulge. Such slight distortion is enough to produce gravitational waves. Material flowing onto the pulsar surface from its companion star tends to quicken the spin, but loss of energy released as gravitational radiation tends to slow the spin due to the principle of conservation of energy. This competition may reach an equilibrium, setting a natural speed limit for millisecond pulsars beyond which they cannot be spun up.
Courtesy of NASA (D. Berry)

12. Astrophysical sources of GWs
Periodic sources
Pulsars  Spinning neutron stars
Low mass Xray binaries
Coalescing compact binaries
Classes of objects: NS-NS, NS-BH, BH-BH
Physics regimes: Inspiral, merger, ringdown
Burst events
Supernovae with asymmetric collapse
GWs
neutrinos
photons
now
Stochastic background
Primordial Big Bang (t = sec)
Continuum of sources
The Unexpected

13. Neutron Stars spiraling toward each other
This is a simulation of two inspiralling neutron stars using the Newtonian high resolution shock capturing code.  The green/blue portion is the density and the red/orange portion is the volumetric isolevels of the internal energy.
Courtesy of WUStL GR group

14. Gravitational waves -- the Evidence
Neutron Binary System – Hulse & Taylor
PSR Timing of pulsars
17 / sec
~ 8 hr
NS rotates on its axis 17 times/sec  pulse period is 59 msec. Reaches periastron (minimum separation of binary pair) every 7.75 hours.
Systematic variation in arrival time of pulses. Variation in arrival time had a 7.75 hour period  binary orbit with another star.
Pulsar clock slowed when traveling fastest and in strongest part of grav field (periastron).
Figure shows decrease in orbital period of 76 usec/year. Shift in periastron due to decay of orbit.
Neutron Binary System
separated by 106 miles
m1 = 1.4m; m2 = 1.36m; e = 0.617
Prediction from general relativity
spiral in by 3 mm/orbit
rate of change orbital period

15. Strength of GWs: e.g. Neutron Star Binary
Gravitational wave amplitude (strain)
For a binary neutron star pair M r 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

16. Effect of a GW on matter

17. Measurement and the real world
How to measure the gravitational-wave?
Measure the displacements of the mirrors of the interferometer by measuring the phase shifts of the light
What makes it hard?
GW amplitude is small
External forces also push the mirrors around
Laser light has fluctuations in its phase and amplitude

18. GW detector at a glance L ~ 4 km For h ~ 10–21 Seismic motion --
DL ~ m
Seismic motion --
ground motion due to natural and anthropogenic sources
Thermal noise --
vibrations due to finite temperature
Shot noise --
quantum fluctuations in the number of photons detected

19. LIGO: Laser Interferometer Gravitational-wave Observatory3 k m ( 1 s ) WA
4 km
2 km LA
4 km

21. 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

22. Limiting Noise Sources Seismic Noise
Motion of the earth is a few mm at low frequencies
Passive and active seismic isolation
Amplify mechanical resonances
Get isolation above a few Hz

23. 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:
Low mechanical loss (high Quality factor)
Suspension  no bends or ‘kinks’ in pendulum wire
Test mass  no material defects in fused silica
Z(f) is mechanical impedance (loss)
FRICTION

24. Limiting Noise Sources Optical Noise
Shot Noise
Uncertainty in number of photons detected
Higher circulating power Pbs a low optical losses
Frequency dependence a light (GW signal) storage time in the interferometer
Radiation Pressure Noise
Photons impart momentum to cavity mirrors
Fluctuations in the number of photons
Lower input power, Pbs
Frequency dependence a response of mass to forces
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
 Optimal input power depends on frequency

25. Gravitational-wave searches

26. Reaching LIGO’s Science Goals
Interferometer commissioning
Intersperse commissioning and data taking consistent with obtaining one year of integrated data at h = by end of 2006
Science runs and astrophysical searches
Science data collection and intense data mining interleaved with commissioning
S1 Aug 2002 – Sep duration: 2 weeks
S2 Feb 2003 – Apr duration: 8 weeks
S3 Oct 2003 – Jan duration: 10 weeks
S4 Feb 2005 – Mar duration: 4 weeks
S5 Nov 2005 – duration: 1 yr integrated
Advanced LIGO

27. Science runs and sensitivity
1st Science Run
Sept 02
(17 days) S2
2nd Science Run
Feb – Apr 03
(59 days) S3
3rd Science Run
Nov 03 – Jan 04
(70 days)
Strain (sqrt[Hz]-1)
LIGO Target Sensitivity S5
5th Science Run
Nov 05 onward
(1 year integrated) S4
4th Science Run
Feb – Mar 05
(30 days)
Frequency (Hz)

28. Science Run 5 (S5) begins Schedule
Started in November, 2005
Get 1 year of data at design sensitivity
Small enhancements over next 3 years
Typical sensitivity (in terms of inspiral distance)
H1 10 to 12 Mpc (33 to 39 million light years)
H2 5 Mpc (16 million light years)
L1 8 to 10 Mpc (26 to 33 million light years)
Sample duty cycle (12/13/05 to 12/26/05)
68% (L1), 83% (H1), 88% (H2) individual
58% triple coincidence
1 light year = 9.5e12 km
1 pc = 30.8e12 km
1 Mpc = 3.26e6 l.y.

29. Advanced LIGO

30. Why a better detector? Astrophysics
Factor 10 better amplitude sensitivity
(Reach)3 = rate
Factor 4 lower frequency bound
Hope for NSF funding in FY08
Infrastructure of initial LIGO but replace many detector components with new designs
Expect to be observing 1000x more galaxies by 2013
NS Binaries
Initial LIGO: ~15 Mpc
Adv LIGO: ~300 Mpc
BH Binaries
Initial LIGO: 10 Mo, 100 Mpc
Adv LIGO : 50 Mo, z=2
Stochastic background
Initial LIGO: ~3e-6
Adv LIGO ~3e-9

31. A Quantum Limited Interferometer
LIGO I
LIGO II
Seismic
Suspension thermal
Test mass thermal
Quantum

32. How will we get there? Seismic noise Thermal noise Optical noise
Active isolation system
Mirrors suspended as fourth (!!) stage of quadruple pendulums
Thermal noise
Suspension  fused quartz; ribbons
Test mass  higher mechanical Q material, e.g. sapphire; more massive (40 kg)
Optical noise
Input laser power  increase to ~200 W
Optimize interferometer response  signal recycling

33. Signal-recycled Interferometerℓ
Cavity forms compound output coupler with complex reflectivity. Peak response tuned by changing position of SRM
800 kW
125 W
Reflects GW photons back into interferometer to accrue more phase
Signal Recycling
signal

34. Advance LIGO Sensitivity: Improved and Tunable
broadband
detuned narrowband
SQL  Heisenberg microscope analog
If photon measures TM’s position too well, it’s own angular momentum will become uncertain.
thermal noise

35. Laser Interferometer Space Antenna
LISA
Laser Interferometer Space Antenna

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

37. LISA and LIGO

38. Astrophysical searches from early science data runs completed
In closing...
Astrophysical searches from early science data runs completed
The most sensitive search yet (S5) begun with plan to get 1 year of data at initial LIGO sensitivity
Advanced LIGO approved by the NSB
Construction funding expected (hoped?) to begin in FY2008
Joint searches with partner observatories in Europe and Japan

39. Ultimate success… New Instruments, New Field, the Unexpected…

40. The End