1. The search for those elusive gravitational waves
LIGO-G R
The search for those elusive gravitational waves
Recent results from interferometric detectors
Nergis Mavalvala IAS, Oct. 2006
(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. 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. 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

7. Effect of a GW on matter

8. 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

9. 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

10. LIGO: Laser Interferometer Gravitational-wave Observatory3 k m ( 1 s )
MIT WA
4 km
2 km
Caltech 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. Gravitational-wave searches

14. 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)

15. Science Run 5 (S5) underway
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 12 to 14 Mpc (33 to 39 million light years)
H2 6 Mpc (16 million light years)
L to 14 Mpc (26 to 33 million light years)
Duty factor
60% (L1), 72% (H1), 79% (H2) individual
45% triple coincidence
1 light year = 9.5e12 km
1 pc = 30.8e12 km
1 Mpc = 3.26e6 l.y.

16. S5 Goal: one year of coincident data, at design sensitivity
S5 Run Sensitivity
S5 Goal: one year of coincident data, at design sensitivity

17. Gravitational-wave searches
Pulsars

18. 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

19. Known pulsar searches S1 Crab pulsar
S1 Setting upper limits on the strength of periodic GW from PSR J using time domain and frequency domain techniques
Phys. Rev. D 69 (2004)
S2  Limits on GW emission from 28 known pulsars in the time domain
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

20. Analysis method
Heterodyne time domain data using the known phase evolution of the pulsar to remove Doppler/spin-down effects
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
Set limits on the ellipticity of the pulsar and compare with limits from spin-down arguments  assuming all energy lost as the pulsar spins-down is dissipated via GWs
R. Jones: University of Glasgow

21. S3 and S4 76 known radio pulsars S5 Method 32 isolated
frequency (Hz) h0 S5
76 known radio pulsars
32 isolated
44 in binary systems
30 in globular clusters
Method
Accurate timing data coherently follow phases
Coherently combine data from all detectors
Method:
* Accurate timing data, provided by Jodrell Bank Observatory and the ATNF, to coherently follow their phases over the run
* Coherently combine the data from all detectors (including GEO600 for the two fastest pulsars)

22. S5 95% upper limits GW amplitude S5 Ellipticity Spindown
(PSR J ) f = Hz, r = 1.6kpc
Ellipticity
(PSR J ) f = Hz, r = 0.25kpc
Spindown
2.1 x above spindown limit for Crab pulsar f = 59.6 Hz, dist = 2.0 kpc S5
All values assume I = 10^38 kgm^2 and no error on distance.

23. Astrophysically interesting?
Upper limits for most of these pulsars are generally well above those permitted by spin-down constraints and neutron star eqns of state
Crab pulsar is nearing the spin-down upper limit
Some others within < 100 x
Provide the limits independent of the cluster dynamics for 29 globular cluster pulsars
Apparent spin-ups due to accelerations within the cluster
Cannot set spin-down limits
Most stringent ellipticity limits (4.0x10-7) are starting to approach the range of neutron star structures for some NPE models (B. Owen, PRL, 2005
Maximum globular cluster frequency derivative seen ~ 4.6x10-13Hz/s

24. Light reading tonight...
B. Abbott et al. (LIGO Scientific Collaboration):
S1: Setting upper limits on the strength of periodic gravitational waves from PSR J using the first science data from the GEO 600 and LIGO detectors Physical Review D 69, , (2004)
S2: Limits on gravitational wave emission from selected pulsars using LIGO data (LSC+M. Kramer and A. G. Lyne) Phys. Rev. Lett. 94, (2005)
S2: First all-sky upper limits from LIGO on the strength of periodic gravitational waves using the Hough transform Phys. Rev. D 72, (2005)
S3, S4, S5: in progress (S3 searched with

25. Gravitational-wave Searches
Binary Inspirals

26. Search for Inspirals Sources Search method
Binary neutron stars (~1 – 3 Msun)
Binary black holes (< 30 Msun)
Primordial black holes (< 1 Msun)
Search method
Waveforms calculable (depend on mass and spin), so use templates and optimal filtering
Templates generated by population synthesis
Horizon distance (inspiral range)
The distance to which an optimally oriented and located ( ) Msun NS binary is detectable with SNR = 8
For binary black hole searches the effective distance is for tow 5 Msun BHs optimally oriented with SNR =8.

27. S5 Inspiral Range

28. Analysis pipeline
Tune pipeline using background, playground (10% of data) and injections
Measure background by applying time slides before coincidence
Add simulated signals to detector data to evaluate analysis performance
Search for double or triple coincident “triggers”
Estimate false alarm probability of resulting candidates: detection?
Compare with expected efficiency of detection and surveyed galaxies: upper limit S5
Left: accidental coincidences and simulated signals
Middle:
Right: detection efficiency

29. Binary Neutron Stars S3 search S4 search 0.09 yr of data
signal-to-noise ratio squared
Rate < 47 per year per
Milky-Way-like galaxy;
0.04 yr data, 1.27 Milky-Ways
cumulative number of events
S3 search
0.09 yr of data
~3 Milky-Way like galaxies
S4 search
0.05 yr of data
~24 Milky-Way like galaxies
Phys. Rev. D. 72, (2005)

30. Binary Black Holes S3 search S4 search 0.09 yr of data
signal-to-noise ratio squared
Rate < 38 per year per
Milky-Way-like galaxy
Log( cum. # of events )
S3 search
0.09 yr of data
5 Milky-Way like galaxies for Msun
S4 search
0.05 yr of data
150 Milky-Way like galaxies for Msun
Phys. Rev. D. 73, (2006)
The upper limit is set by looking at the loudest event in the data. That sets the threshold. Then use injected simulated data to ask the question of how many galaxies can we reach at that threshold?
The rate upper limit is set by R = 2.303/(T_obs*N_galaxies). In this case

31. Primordial Black Holes
S3 search
0.09 yr of data
1 Milky-Way like halos for Msun
S4 search
0.05 yr of data
3 Milky-Way like halos for Msun
Rate < 63 per year per
Milky-Way-like halo
Total mass (Msun)
Rate / MW halo / yr
Phys. Rev. D. 72, (2005)

32. Light reading tonight...
B. Abbott et al. (LIGO Scientific Collaboration)
S1: Analysis of LIGO data for gravitational waves from binary neutron stars Phys. Rev. D 69, (2004)
S2: Search for gravitational waves from primordial black hole binary coalescences in the galactic halo Phys. Rev. D 72, (2005)
S2: Search for gravitational waves from galactic and extra-galactic binary neutron stars Phys. Rev. D 72, (2005)
S2: Search for gravitational waves from binary black hole inspirals in LIGO data Phys. Rev. D 73, (2006)
S2: Joint Search for Gravitational Waves from Inspiralling Neutron Star Binaries in LIGO and TAMA300 data (LIGO, TAMA collaborations) Phys. Rev. D, in press
S3: finished searched for BNS, BBH, PBBH: no detection
S4, S5: searches in progress

33. Gravitational-wave searches
Stochastic Background

34. Stochastic GW Backgrounds
Astrophysical backgrounds due to unresolved individual sources
E.g.: BH mergers, inspirals, supernovae
Cosmological background from Big Bang (analog of CMB)
WMAP 3-year data
GW spectrum due to
cosmological BH ringdowns
(Regimbau & Fotopoulos)

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

36. 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

37. Isotropic search procedure
Cross correlate two data streams x1 and x2
For isotropic search optimal statistic is
“Overlap Reduction Function”
(determined by network geometry)
Detector noise spectra
g(f)
frequency (Hz)

38. Test other Wa(f) a = 0  inflationary or CS models a = 1  rotating NS
Measured
(S3, S4)
Bayesian 90% upper limits
Expected
from S5
a = 0  inflationary or CS models
a = 1  rotating NS
a = 2  pre-BB cosmology

39. Predictions and Limits
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
LIGO S4: Ω0 < 6.5x10-5
(new) -4
(W0) -6
Initial LIGO, 1 yr data
Expected Sensitivity
~ 4x10-6 -8
Log
Cosmic strings
CMB
Adv. LIGO, 1 yr data
Expected Sensitivity
~ 1x10-9
-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])

40. Light reading tonight...
B. Abbott et al. (LIGO Scientific Collaboration):
S1: Analysis of first LIGO science data for stochastic gravitational waves Phys. Rev. D 69, (2004)
S3: Upper Limits on a Stochastic Background of Gravitational Waves Phys. Rev. Lett. 95, (2005)

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

42. 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)

43. Gravitational-Wave Bursts
Expected from catastrophic events involving solar-mass (1-100 Mo) compact objects
core-collapse supernovae
accreting/merging black holes
gamma-ray burst engines
other … ???
Sources typically not well understood, involving complicated (and interesting!) physics
Dynamical gravity with event horizons
Behavior of matter at supra-nuclear densities
Lack of signal models makes GWBs more difficult to detect
SN 1987 A

44. Burst Search Techniques
Two main types of burst searches:
Untriggered: Scan ~all data, looking for excess power indicative of a transient signal
Robust way to detect generic waveforms
Triggered: Scan small amount of data around time of astronomical event (e.g., GRB), by cross-correlating data from pairs of detectors
Exploits knowledge of time of and direction to astronomical event
Always:
Use techniques that make minimal assumptions about the signal
Be open to the unexpected!

45. Excess-Power Detection
Look for transient jump in power in some time-frequency region:
frequency ~ [60,2000] Hz (determined by noise curves of instruments)
duration ~ [1,100] ms (time scale associated with solar-mass COs)
Anderson et al. PRD (2001)
Many different implementations in LIGO:
Fourier modes, wavelets, Gaussian-modulated sinusoids
Multiple time-frequency resolutions
Provide redundancy & robustness
Also time-domain & optimal filter searches
Simulated binary inspiral signal in S5 data
Chatterji: Q Pipeline search for GWBs with LIGO

46. time, frequency coincidence
Schematic
Typically require coincident detection in all 3 LIGO interferometers:
frequency
detector 2
time
detector 3
detector 1
time, frequency coincidence
range of
time-freq
resolutions Hz 
candidate event
1/128 – 1/4 s 2

47. Upper Limits
No GWBs detected through S4. So, set limit on GWB rate vs. signal strength:
h = upper limit on event number
T = observation time
e(hrss) = efficiency vs strength
Progress:
Central
Frequency
Lower rate limits from longer observation times
Rate Limit (events/day)
Lower amplitude limits from lower detector noise

48. 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 predeterimined 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)

49. Procedure: GRBs
Cross correlate data between pairs of detectors around time of event
25 – 100 ms target signal duration
[-2,+1] min around GRB
Compute probability of largest measured CC using distribution of CCs from neighboring times (no GRB, with time shifts).
Improbably large CC equals candidate GWB
sample GRB
lightcurve
(BATSE)
trigger
time
detector 2
detector 1

50. most significant excess at 9th least probable event:
Statistical Tests
No loud signals seen.
Look also for weak cumulative effect from population of GRBs.
Use binomial test to compare to uniform distribution.
No significant deviation from expected distribution.
Max-likelihood test also used.
Mohanty, CQG 22 S1349 (2005)
54 GRB
tests
most significant excess
at 9th least probable event:
P≥ 9 (p9 ) = 0.102
Leonor / Sannibale, Session W11

51. Short Hard Bursts? 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/

52. Light reading tonight...
B. Abbott et al. (LIGO Scientific Collaboration):
S1: First upper limits from LIGO on gravitational wave bursts Phys. Rev. D 69, (2004)
S2: A Search for Gravitational Waves Associated with the Gamma Ray Burst GRB Using the LIGO Detectors Phys. Rev. D 72, (2005)
S2: Upper Limits on Gravitational Wave Bursts in LIGO's Second Science Run Phys. Rev. D 72, (2005)
S2: Upper Limits from the LIGO and TAMA Detectors on the Rate of Gravitational-Wave Bursts Phys. Rev. D 72, (2005)
S3: Search for gravitational wave bursts in LIGO's third science run Class. Quant. Grav. 23, S29-S39 (2006)

53. Advanced LIGO

54. 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

55. Laser Interferometer Space Antenna
LISA
Laser Interferometer Space Antenna

56. 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

57. LISA and LIGO

58. 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

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

60. The End