1. Laser interferometric gravitational wave detectors
The search for the elusive wave
Nergis Mavalvala
(LIGO Scientific Collaboration)
University of Colorado, Oct. 2007

2. Outline Gravitational waves (GWs) Astrophysical sources of GWs
Detecting GWs
Ongoing searches
Future detectors
Bold claims!!!
Measure distance changes of m over kilometers
Hear trees falling the forest
Detect a mm bump on 10 km object 800 l.y. away
Measurement below the (naïve) quantum limit

3. Gravitational wave basics
Gravitational Waves prediction of general relativity “Ripples in spacetime fabric”
Stretch and squeeze the space transverse to direction of propagation
Strain
Emitted by aspherical accelerating masses
“What better way to get at the juicy stuff than to shine a laser at it” Eric Cornell (June 25, 2007, ICOLS)

4. 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

5. 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

6. 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)

7. 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)

8. 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

9. 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  59 msec period. 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

10. In our galaxy (21 thousand light years away, 8 kpc)
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, 8 kpc)
h ~ 10-18
In the Virgo cluster of galaxies (50 million light years away, 15 Mpc)
h ~ 10-21 M r R

11. Laser interferometers
Photodetector
GW from space
Laser
Photodetector

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

13. GW detector at a glance Seismic noise
Ground motion (natural and anthropogenic)
Vibration isolation
20 kW
Thermal noise
Vibrations due to finite temperature
Low mechanical dissipation
Shot noise
Operate on dark fringe
High circulating power
10 W

14. 10 kg Fused Silica 25 cm diameter 10 cm thick < lambda/5000
over beam diameter

15. Some (small) numbers
Sensitivity: m/√Hz at 150 Hz rad/√Hz at 150 Hz
Actuation range: ~100 µm (tides)
Stabilization of 4 km arms: m rms
Laser intensity noise (RIN): ≤10-8 /√Hz at 150 Hz
Frequency noise: ≤ 3×10-7 Hz/√Hz at 150 Hz
Angular Control: ≤ 10-8 rad rms
Angular Sensing: radians/√Hz at 40 Hz
Input beam jitter: ≤4×10-9 rad/√Hz at 150 Hz
Mechanical loss angle: suspension ≤ optical coatings ≤ substrate ≤10-6

16. Sensitivity limit Initial LIGO Seismic noise Suspension thermal
Viscously damped pendulum
Shot noise
Photon counting statistics
SQL:
h(f) = sqrt(8*hbar/M)/Omega/L
Standard Quantum Limit

17. Gravitational-wave searches
Instrument and data

18. 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)

19. How do we do it? Sensitivity…

20. How do we do it? Duty factor…
RMS motion in 1-3 Hz band
day
night
Livingston
Displacement (m)
Hanford
PRE-ISOLATOR REQUIREMENT
Time (GPS seconds)

21. Pre-isolator performance
Lock acquisition threshold
Factor of 10 reduction in the critical band
Rel. velocity b/w mirrors 4k apart

22. Science runs and Sensitivity

23. S5 duty cycle
GEO 600 ~ 95%

24. Astrophysical searches
Coalescence of binary compact objects (neutron stars, black holes, primordial BH)
Core collapse supernovae
Black hole normal mode oscillations
Neutron star rotational instabilities
Gamma ray bursts
Cosmic string cusps
Periodic emission from pulsars (esp. accretion driven)
Stochastic background (incoherent sum of many sources or very early universe)
Expect the unexpected!
Transient
Campanelli et al., Lazarus Project
GWs
neutrinos
photons
now
High duty cycle

25. Sampling of current GW searches
Stochastic Background

26. Cosmological GW Background
385,600
During inflation, tensor modes are produced from amplification of initial quantum fluctuations into classical perturbations. Density perturbations lead to GWs that carry unique and “clean” information about the early Universe.
10-22 sec
10+12 sec
Waves now in the LIGO band were produced sec after the Big Bang
WMAP 2003

27. Predictions and Limits
Atoms 4%
Dark energy 73%
Dark matter 23%
GWs ??
What’s our Universe made of?
LIGO S1: Ω0 < 44
PRD (2004)
LIGO S3: Ω0 < 8.4x10-4
PRL (2005) -2
Pulsar
Timing
CMB+galaxy+Ly-a adiabatic homogeneous
BB Nucleo-
synthesis -4
LIGO S4: Ω0 < 6.5x10-5
(W0) -6
S5 (expected) ~ 4x10-6 -8
Log
Cosmic strings
Adv. LIGO, 1 yr data
Expected Sensitivity
~ 1x10-9
CMB
-10
Pre-BB model
Accuracy of big-bang nucleosynthesis model constrains the energy density of the universe at the time of nucleosynthesis  total energy in GWs is constrained integral_f<1e-8 d(ln f) Omega_GW
Pulsar timing  Stochastic GWs would produce fluctuations in the regularity of msec pulsar signals; residual normalized timing errors are ~10e-14 over ~10 yrs observation
Stochastic GWs would produce CMBR temperature fluctuations (Sachs Wolfe effect),
Measured Delta_T constrains GW amplitude at very low frequencies
Kamionkowski et al. (astro-ph/ )
Use Lyman-alpha forest, galaxy surveys, and CMB data to constrain CGWBkgd, i.e. CMB and matter power spectrums. Assume either homogeneous initial conditions or adiabatic. Use neutrino degrees of freedom to constrain models.
Adiabatic blue solid  CMB, galaxy and Lyman-alpha data currently available (Kamionkowski)
Homogeneous blue dashed  CMB, galaxy and Lyman-alpha data currently available
Adiabatic CMBPol (cyan solid)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data
Homogeneous CMBPol (cyan dashed)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data
-12
Inflation
-14
Slow-roll
Cyclic model
EW or SUSY
Phase transition
-18
-16
-14
-12
-10 -8 -6 -4 -2 2 4 6 8 10
Log
(f [Hz])

28. Example of current GW searches
Isolated pulsars

29. 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

30. Example of current GW searches
Binary Inspirals

31. Search for Binary Inspirals
Number of galaxies
Distance (~50 Mly)
Initial LIGO
Sources
Binary neutron stars (~1 – 3 Msun)
Binary black holes (< 30 Msun)
Primordial black holes (< 1 Msun)
Search method
Look for “chirps”
Limit on rate at which NS are coalescing in galaxies like our own
BBH
BNS
Here shown is inspiral range – averaged over all sky
BNS inspiral horizon distance – two 1.4 Msun NS optimally oriented, SNR =8
For binary black hole searches the effective distance is for two 5 Msun BHs optimally oriented with SNR =8.
24 galaxies like our Milky Way S4

32. Coming soon… to an interferometer near you
Enhanced LIGO Advanced LIGO

33. Ultimate limits ? Seismic gravity gradient
When ambient seismic waves pass near and under an interferometric gravitational-wave detector, they induce density perturbations in the Earth, which in turn produce fluctuating gravitational forces on the interferometer’s test masses.
Human gravity gradient
The beginning and end of weight transfer from one foot to the other during walking produces the strongest human-made gravity-gradient noise in interferometric gravitational-wave detectors (e.g. LIGO). The beginning and end of weight transfer entail sharp changes (time scale τ∼20 msec) in the horizontal jerk (first time derivative of acceleration) of a person’s center of mass.

34. Initial LIGO – S5 (now) Input laser power ~ 6 W Initial LIGO
Circulating power ~ 20 kW
Mirror mass
10 kg
Initial LIGO
SQL

35. Enhanced LIGO (Fall 2007) Input laser power ~ 30 W
Circulating power ~ 100 kW
Mirror mass
10 kg
Enhanced LIGO

36. Advanced LIGO (2011) Input laser power > 100 W
Circulating power > 0.5 MW
Mirror mass
40 kg

37. Advanced LIGO improvements
Seismic noise
Active isolation system
Mirrors suspended as fourth (!!) stage of quadruple pendulums
Thermal noise
Suspension  fused silica; ribbons
Test mass  higher mechanical Q materials; more massive (40 kg)
Optical noise
Laser power  increase to ~200 W
Tunable frequency response  signal recycling

38. Astrophysics with Advanced LIGO
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

39. Sub-quantum interferometry Space observatory
Farther in the future
Sub-quantum interferometry Space observatory

40. Advanced LIGO Quantum noise limited
Shot noise
Quantum radiation pressure noise
Advanced LIGO

41. Some quantum states of light
Heisenberg Uncertainty Principle for EM field
Phasor diagram analogy
Stick  dc term
Ball  fluctuations
Common states
Coherent state
Vacuum state
Amplitude squeezed state
Phase squeezed state
X+ and X- associated with amplitude and phase
McKenzie

42. Quantum Noise in an Interferometer
First proposed … C.M. Caves, PR D (1981)
Proof-of-principle demonstration … M. Xiao et al., PRL (1987)
More realistic configurations demonstrated …
Power Recycled Michelson K. McKenzie et al., PRL (2002)
Power and Signal Recycled Michelson H. Vahlbruch et al., PRL (2005)
Suspended prototype Goda et al. (2007)
Laser X+ X- X+ X- X+ X- X+ X-

43. Squeezed Input Interferometer
Laser
GW Detector
SHG
Faraday isolator
The squeeze source drawn is an OPO squeezer, but it could be any other squeeze source, e.g. an optical parametric oscillator.
OPO
Homodyne Detector
Squeeze
Source
GW Signal

44. Sub-quantum-limited interferometer
Narrowband unsqueezed
Broadband unsqueezed
Broadband Squeezed X+ X-
Quantum correlations
Input squeezing

45. Squeezing measured… Goda et al., submitted to Opt. Lett. (2007)
Vahlbruch et al., PRL 97, (2007)

46. Squeezing injected @ the 40m prototype @ Caltech
Goda et al. (2007)

47. 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

48. LISA (mid to late 2010’s)

49. When the elusive wave is captured…
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

50. In closing...
Astrophysical searches from early science data runs completed
The most sensitive search yet (S5) completed Oct. 01  1 year of data at initial LIGO sensitivity
Joint searches with partner observatories
Planned enhancements that give 2x improvement in sensitivity underway
Advanced LIGO
Approved by the NSB in 2006
“Marked up” by US House and Senate this summer (still to go)
Construction funding expected to begin in FY2008
Promising prospects for direct GW detection in coming years (and GWB’s exit)

51. The End

52. Make some upgrades with limited invasiveness to give ~2x improvement
Enhanced LIGO
Make some upgrades with limited invasiveness to give ~2x improvement
Mechanical changes ruled out
Seismic isolation and suspension systems
Changes mainly related to optical readout

53. Seismic Noise
Initial LIGO
Advanced LIGO

54. 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

55. 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

56. Advanced LIGO Target Sensitivity
Initial LIGO
Log [Strain (1/rtHz)]
Advanced LIGO
Newtonian background
Quantum noise
Mirror substrate thermal
Mirror coating thermal
Seismic
Suspension thermal 10
100
1000
Frequency (Hz)
Frequency (Hz)