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) LANL January 2006

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

3. 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

4. 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

5. 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

6. 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

7. 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)

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. 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. 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. 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

12. 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

13. Effect of a GW on matter

14. 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

15. 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

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

18. 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

19. 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

20. 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

21. 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

22. Gravitational-wave searches

23. 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

24. 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)

25. 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.

26. New rate predictions from SHBs?
4 Short Hard gamma ray Bursts since May 2005
Detected by Swift and HETE-2, with rapid follow-up using Hubble, Chandra, and look-back at BATSE
Find that SHB progenitors are too old (>5 Gyr) to be supernova explosions (cause of long GRBs)
Remaining candidates for progenitors of SHBs: old double neutron star (DNS) or neutron star-black hole (NS-BH) coalescences
Predicted rates for Initial LIGO (S5) could be as high as
But great uncertainty in rate estimates
Progenitors are older (>5 Gyr) binaries
Observed galactic DNS not a representative sample for SHB progenitors
Merger rates of observed DNS dominated by short-lived (<100 Myr) systems while SHB progenitors >3 to 5 Gyr
Possible that there is a large undetected population of older DNS in the galaxy
Or NS-BH are progenitors of SHBs
Nakar, Gal-Yam, Fox, astro-ph/

27. Gravitational-wave searches
Pulsars

28. Continuous Wave Sources
Nearly-monochromatic 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
Signal frequency modulated by relative motion of detector and source
Amplitude modulated by the motion of the antenna pattern of the detector
Search for gravitational waves from a triaxial neutron star emitted at

29. Summary of pulsar searches
S1 Setting upper limits on the strength of periodic gravitational waves from PSR J using GEO600 and LIGO data
Phys. Rev. D 69 (2004)
S2  Limits on GW emission from 28 selected pulsars using LIGO data
Phys. Rev. Lett. 94 (2005) S1
Crab pulsar
Time-domain analysis of 28 known pulsars with 2 frot > 50 Hz completed for S2 data
Limit on strain amplitude h0 < 1e-24 to 1e-22
Stars  upper limits found using S2 data. Compare to...
Circles  spindown upper limits assuming all measured rotational energy loss due to GWs and assuming moment of inertia Izz = 1e45 gm-cm^2
Results on h0 can be interpreted as upper limit on equatorial ellipticity
Assume a rigid rotator with Izz ~ 1045 g cm2 and where all observed spindown is due to GW emission
Distance to pulsar is known
Limit on ellipticity epsilon < 1e-6 to 1e-1

30. Gravitational-wave Searches
Binary Inspirals

31. Sources Search method Search for Inspirals
Orbital-decaying neutron star binaries
Black hole binaries
MACHOs
Search method
Waveforms calculable
Use optimal matched filtering  correlate detector output with template waveform
Template inputs from population synthesis

32. Binary Neutron Star Inspiral (S2)
Upper limit on binary neutron star coalescence rate
Express the rate as a rate per Milky-Way Equivalent Galaxies (MWEG)
Express as the distance to which radiation from a 1.4 Msun pair would be detectable with a SNR of 5
Important to look out further, so more galaxies can contribute to population of NS
Theoretical prediction: R < 2 x 10-5 / yr /MWEG
BNS inspiral paper for S2: Phys.Rev. D72 (2005) We use 373 hours ($\approx$ 15 days) of data from the second science run of the LIGO gravitational-wave detectors to search for signals from binary neutron star coalescences within a maximum distance of about 1.5 Mpc, a volume of space which includes the Andromeda Galaxy and other galaxies of the Local Group of galaxies. This analysis requires a signal to be found in data from detectors at the two LIGO sites, according to a set of coincidence criteria. The background (accidental coincidence rate) is determined from the data and is used to judge the significance of event candidates. No inspiral gravitational wave events were identified in our search. Using a population model which includes the Local Group, we establish an upper limit of less than 47 inspiral events per year per Milky Way equivalent galaxy with 90% confidence for non-spinning binary neutron star systems with component masses between 1 and 3 $M_\odot$.
BBH search paper (gr-qc/ ) abstract:
We report on a search for gravitational waves from binary black hole inspirals in the data from the second science run of the LIGO interferometers. The search focused on binary systems with component masses between 3 and 20 solar masses. Optimally oriented binaries with distances up to 1 Mpc could be detected with efficiency of at least 90%. We found no events that could be identified as gravitational waves in the hours of data that we searched.
Phys.Rev. D72 (2005)

33. Gravitational-wave searches
Stochastic Background

34. Stochastic Background
Waves now in the LIGO band were produced sec after the Big Bang
WMAP 2003

35. Stochastic Background of GWs
Given an energy density spectrum Wgw(f ), there is a GW strain power spectrum
For standard inflation (rc depends on present day Hubble constant)
Search by cross-correlating output of two GW detectors: L1-H1, H1-H2, L1-ALLEGRO
The closer the detectors, the lower the frequencies that can be searched (due to overlap reduction function)
Omega_GW(f) = (1/rho_critical) d(rho_GW)/d(ln f)
Ratio of energy density in GWs to total energy density needed to close the universe
Rho_c depends on the present day Hubble expansion rate H0.
H100 = H0/(100 km/sec/Mpc) ~ 0.72

36. Cross-correlated instrumental noise found
LIGO results for 0h1002
LIGO run
0h1002
Comments
Frequency Range
Observation Time S1
PRD 69 (2004)
< 23  4.6
(H2-L1)
Cross-correlated instrumental noise found
40 to 314 Hz
64 hours
(08/02 – 09/02) S2
< 0.018
(H1-L1)
50 to 300 Hz
387 hours
(02/03 – 04/03) S3
PRL 95 (2005)
< 8 x 10-4
a = 0  inflationary or CS models
a = 1  rotating NS
a = 2  pre-BB cosmology
70 to 160 Hz (H1-L1)
200 hrs (H1-L1)
(10/03 – 01/04) S4
Analysis underway
447 hrs (H1-L1)
510 hrs (H1-H2)
(02/05 – 03/05)
Initial LIGO (1 yr) 0h1002 < 2 x 10-6
Advanced LIGO (1 yr) 0h1002 < 7 x 10-10
For S2: the positive error is larger in magnitude than the negative error owing to a bias we found in the SW and HW injection pt. Est, that lowered its value. This was later found to be caused by the fact that we were using the PSD of the same interval on which the CC statistic was being computed -> so we graduated to doing sliding PSDs.
For S3:
======
Phys.Rev.Lett. 95 (2005) The Laser Interferometer Gravitational Wave Observatory (LIGO) has performed a third science run with much improved sensitivities of all three interferometers. We present an analysis of approximately 200 hours of data acquired during this run, used to search for a stochastic background of gravitational radiation. We place upper bounds on the energy density stored as gravitational radiation for three different spectral power laws. For the flat spectrum, our limit of Omega_0<8.4e-4 in the Hz band is ~10^5 times lower than the previous result in this frequency range.

37. Limits on Wgw from astrophysical observations
LIGO S2 data
LIGO S3 data
, at design
sensitivity
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
H0 = 72 km/s/Mpc

38. Gravitational-wave Searches
Transient or “burst’ events

39. Brief transients: unmodelled waveforms Time-frequency search methods
GWs from burst sources
Brief transients: unmodelled waveforms
Time-frequency search methods
Upper limit on rate, and rate as a function of amplitude for specific shapes
Triggered searches
Use external triggers (GRBs, supernovae)
Untriggered searches
compact binary system coalescences…
(SN1987A Animation: NASA/CXC/D.Berry)

40. Gamma Ray Burst: GRB030329 Targeted search  NO detection
A supernova at z ~ 0.17 ~ 800 Mpc
Targeted search  NO detection
H1 and H2 operational during S2
Integration time (logarithmic steps)
Segment time
(from HETE)
The corrgram images show time vs. integration length (log scale). Color scale refers to degree of excess correlation, red being most correlated.
Both false alarm rate (fixes threshold event strength) and efficiency determined from injection of simulated waveforms in both data streams. Waveforms used include sine Gaussians, as well as example astrophysically motivated ones, such as Dimmelmeier-Mueller ones.
Upper left is a sine-Gaussian injection (250 Hz, Q~8.9) well above preset detection threshold, upper right is well below detection threshold.
Lower images are both for different epochs of noise. The color scales are different on all quadrants.
Event strength threshold for detection is 2, which gives false alarm rate of 5e-4 Hz with a 90% CL (determined from background data).
Circles are SIGNAL REGION – duration of GRB. Yielded only events well below the predetermined threshold event strength.
Diamonds are expected distribution based on BACKGROUND.
Squares are expected distribution from TIME-SHIFTs – unphysical time shifts between H1 and H2.
11% error from calibration uncertainties. Fixed false alarm rate allows upper limits to be set directly from simulation results.
hrss  6 x Hz-1/2
(waveform-dependent)
Phys. Rev. D 72 (2005)

41. Advanced LIGO

42. 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

43. Laser Interferometer Space Antenna
LISA
Laser Interferometer Space Antenna

44. 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

45. LISA and LIGO

46. 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

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

48. The End