1. Detection of gravitational waves with interferometers
Nergis Mavalvala
(the LIGO Scientific Collaboration)
8.282, MIT, April 2007

2. Outline
What are gravitational waves (GWs)?
What sources emit them?
How strong is the emission?
How can we detect them?
What are we searching for?
The GW world in the future

3. Understanding gravity
Newton (16th century)
Universal law of gravitation
Worried about action at a distance
Einstein (20th century)
Gravity is a warpage of space-time
Matter tells spacetime how to curve  spacetime tells matter how to move

4. Gravitational waves (GWs)
Prediction of Einstein’s General Relativity
Ripples of the space-time fabric
Like tides  for objects that are free to move, GWs change lengths by fractional amounts
GWs stretch and squeeze the space transverse to direction of propagation
Emitted by accelerating massive objects

5. Astrophysics with GWs vs. Light
Very different information, mostly mutually exclusive
Difficult to predict GW sources based on EM observations
Light GW
Accelerating charge
Accelerating mass
Images
Waveforms
Absorbed, scattered, dispersed by matter
Very small interaction; matter is transparent
100 MHz and up
10 kHz and down

6. Astrophysical sources of GWs
Ingredients
Lots of mass (neutron stars, black holes)
Rapid acceleration (orbits, explosions, collisions)
Colliding compact stars
Merging binaries
Supernovae
The big bang
Earliest moments
The unexpected
GWs
neutrinos
photons
now

7. Black hole mergers Contours of GWs in x polarization
Yellow contours represent tidal forces
As we zoom out we see red contours of GW waves
Notice that x-pol has no emission on equatorial plane.
Contours of GWs in x polarization
Courtesy of J. Centrella, GSFC

8. 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)

9. 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)

10. Gravitational waves -- the Evidence
Hulse & Taylor’s Binary Neutron Star System
(discovered in 1974, Nobel prize in 1993)
PSR
Two neutron stars orbiting each other at c
Compact, dense, fast  relativistic system
Emit GWs and lose energy
Used time of arrival of radio pulses to measure change in orbital period due to GW emission
Change in orbital period
NS rotates on its axis 17 times/sec. 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.
Y-axis = change in orbital period relative to 1975 measurement
Define periastron as measure of orbital period
Exactly as predicted by GR for GW emission
Years

11. Strength of GWs: e.g. Binary Neutron Star
Gravitational wave amplitude (strain) for a binary neutron star pair M r R
h ~10-21
Quadrupole formalism is accurate to order of magnitude for most sources.
Involves computing wave generation and radiation reaction from Einstein eqn.
1 light year = 9.5e12 km
1 pc = 30.8e12 km
1 Mpc = 3.26e6 l.y.
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
Virgo cluster 15 Mpc or 50 million l.y.

12. In our galaxy (21 thousand light years away)
Strength of GWs
Hulse-Taylor binary pulsar at the end of its lifetime (100 million years from now)
In our galaxy (21 thousand light years away)
h ~ 10-18
In the Virgo cluster of galaxies (50 million light years away)
h ~ 10-21

13. Detecting GWs
GW from space

14. Gravitational Wave Interferometers
Laser
Photodetector
GW from space
Laser
Photodetector
Very small!
1000 times smaller than the nucleus of an atom

15. LIGO: Laser Interferometer Gravitational-wave Observatory3 k m ( 1 s )
MIT
4 km
2 km
NSF
Caltech LA
4 km

17. 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

18. Initial LIGO – Sept
Initial LIGO

19. An example of a GW search
Primordial Stochastic Background

20. Cosmological GW Background
385,600
10-22 sec
10+12 sec
Waves now in the LIGO band were produced sec after the Big Bang
WMAP 2003

21. Stochastic GW background
What’s our Universe made of?
Elements in the early Universe
10-5
10-6
Dark matter 23%
Initial LIGO (1 year data)
Atoms 4%
Speculative structures (cosmic strings)
10-8
Energy density in GWs
GWs ??
10-9
Advanced LIGO (1 year data)
Sensitivity scales at sqrt(BW*T_int) for Omega, or fourth-root(BW*T_int) for strain.
Dark energy 73%
10-13
Inflation

22. Gravitational-wave searches
Pulsars

23. Continuous Wave Sources
Single frequency (nearly) continuous GW radiation, e.g. neutron stars with
Spin precession at
Excited modes of oscillation, e.g. r-modes at
Non-axisymmetric distortion of shape at
Joint Bayesian parameter estimation of unknown pulsar parameters: GW amplitude h0, initial phase f0, polarisation angle y and inclination angle i, using data from all interferometers
Produce probability distribution functions for unknown parameters and marginalise over angles to set 95% upper limit on h0
Compare with spin-down limits
Assuming all energy lost as the pulsar spins-down is dissipated via GWs
Get limit on ellipticity of rotating star
(PSR J ) f = Hz, r = 0.25kpc

24. Enhanced LIGO Advanced LIGO LISA
Future detectors
Enhanced LIGO Advanced LIGO
LISA

25. Why a better detector? Astrophysics
Factor 10 better amplitude sensitivity
(Range)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

26. Initial LIGO – Sept
Initial LIGO

27. Enhanced LIGO
Enhanced LIGO (2008)

28. Advanced LIGO
Advanced LIGO (2011)

29. Parameter LIGO I Adv LIGO Equivalent strain noise, minimum
3x10-23/rtHz
2x10-24/rtHz
Neutron star binary inspiral range
15 Mpc
300 Mpc
Stochastic background (WGW)
3x10-6
1.5-5x10-9
Interferometer configuration
Power-recycled MI w/ FP arm cavities
LIGO I, plus signal recycling
Input laser power
6 W
125 W
Test masses
Fused silica, 11 kg
Fused Silica, 40 kg
Seismic wall frequency
40 Hz
10 Hz
Optical beam size
3.6/4.4 cm
6.0 cm
Test mass Q
Few million
200 million
Suspension fiber Q
Few thousand
~30 million

30. Laser Interferometer Space Antenna
LISA
Laser Interferometer Space Antenna

31. Laser Interferometer Space Antenna (LISA)
Three space craft
Triangular formation
Separated by 5 million km
Formation trails earth by 20º
Approx. constant length arms
Constant solar illumination
1 AU = 1.5x108 km

32. LISA and LIGO

33. Science from gravitational wave detectors?
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
Astrophysics
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 below the quantum noise limit

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

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

36. The End