1. Direct Searches for Stochastic Gravitational Waves with LIGO: status and prospects
Albert Lazzarini
California Institute of Technology
On behalf of the LIGO Scientific Collaboration
The 11th International Symposium on
Particles, Strings and Cosmology
30 May 2005
Gyeongju, Korea
 Black Holes courtesy of NCSA

2. Outline of Presentation
Stochastic gravitational waves
Characterization of strain
Sources
LIGO Concept
Principle of operation
Sites, facilities
Sensitivity
Recent observational results
Prospects
LIGO Laboratory at Caltech

3. Stochastic gravitational wave background
GWs are the able to probe the very early universe
Analog from cosmic microwave background -- WMAP 2003
Detect by cross-correlating interferometer outputs in pairs
US-LIGO : Hanford, Livingston
Europe: GEO600, Virgo
Japan: TAMA
Good sensitivity requires:
GW > 2D (detector baseline)
f < 40 Hz for LIGO pair over 3000 km baseline
Initial LIGO limiting sensitivity (1 year search):  <10-6
The integral of [1/f•GW(f)] over all frequencies corresponds to the fractional energy density in gravitational waves in the Universe
LIGO Laboratory at Caltech

4. Cosmological Gravitational Waves

Terrestrial
LIGO Laboratory at Caltech

5. Characterization of a Stochastic Gravitational Wave Background
GW energy density given by time derivative of strain
Assuming SGWB is isotropic, stationary and Gaussian, the strength is fully specified by the energy density in GWs
f) in terms of a measurable strain power spectrum, Sgw(f):
Strain amplitude scale:
Allen & Romano, Phys.Rev. D59 (1999)
LIGO Laboratory at Caltech

6. Stochastic signals from cosmological processes
Inflation -- flat spectrum
Kolb & Turner, The Early Universe
Phase transitions -- peaked at phase transition energy scale
Kamionkowski, Kosowski & Turner, Phys.Rev. D49 (1994)
Apreda et al., Nucl.Phys. B631 (2002)
Cosmic strings -- gradually decreasing spectrum
Damour & Vilenkin , Phys.Rev. D71 (2005)
Pre big-bang cosmology
Buonanno, Maggiore & Ungarellli , Phys.Rev. D55 (1997)
LIGO Laboratory at Caltech

7. Stochastic signals from astrophysical processes
Incoherent superposition of many signals from various signal classes
Coalescing binaries
Supernovae
Pulsars
Low Mass X-Ray Binaries (LMXBs)
Newly born neutrons stars
Normal modes - R modes
Binary black holes
Gaussian -> non-Gaussian (“popcorn” noise) depending on rates
Drasco & Flannigan, Phys.Rev. D67 (2003),
Spectra follow from characteristics of individual sources
Maggiore, Phys.Rept. 331 (2000)
LIGO Laboratory at Caltech

8. The Cosmological Gravitational Wave “Landscape”
Armstrong et al., ApJ 599 (2003)
 Range of
Interferometers (Ground & Space-Based
Kolb & Turner, The Early Universe (1990)
Lommen, astro-ph/
n & Koranda, PRD 50 (1994)
LIGO Laboratory at Caltech

9. The LIGO Laboratory Sites
Interferometers are aligned along the great circle connecting the sites
Caltech
MIT
3002 km
(L/c = 10 ms)
Livingston, LA
Hanford, WA
LIGO Laboratory at Caltech

10. The LIGO Observatories
Livingston Observatory
Louisiana
One interferometer (4km)
GEODETIC DATA (WGS84)
h: m X arm: S °W
: N30°33’ ” Y arm: S °E
: W90°46’ ”
<- Livingston, LA

Hanford Observatory
Washington
Two interferometers (4 km and 2 km arms)
GEODETIC DATA (WGS84)
h: m X arm: N °W
: N46°27’ ” Y arm: S °W
: W119°24’ ”
Hanford, WA ->
LIGO Laboratory at Caltech

11. LIGO Laboratory at Caltech
Light makes
Nb bounces
h = L/L => / = 2 Nb hL/
Detector concept
The concept is to compare the time it takes light to travel in two orthogonal directions transverse to the gravitational waves.
The gravitational wave causes the time difference to vary by stretching one arm and compressing the other.
The interference pattern is measured (or the fringe is split) to one part in 1010, in order to obtain the required sensitivity.
LIGO Laboratory at Caltech

12. LIGO First Generation Detector Limiting noise floor
Interferometer sensitivity is limited by three fundamental noise sources
seismic noise at the lowest frequencies
thermal noise (Brownian motion of mirror materials, suspensions) at intermediate frequencies
shot noise at high frequencies
Many other noise sources lie beneath and must be controlled as the instrument is improved
LIGO Laboratory at Caltech

13. The LIGO is Approaching its Design Sensitivity
 factor 2X of design goal throughout LIGO band
LIGO Laboratory at Caltech

14. LIGO Laboratory at Caltech
Detection strategy
Spectrum:
Cross-correlation statistic:
Optimal filter (assume gw(f) = const):
Make many (N~ 104) repeated short (T = 60s) measurements to track instrumental variations:
LIGO Laboratory at Caltech

15. (f) - Overlap reduction factor
g(f)
LIGO Laboratory at Caltech

16. S2 H1-L1 results using previously outlined method
Distribution of  over S2 run
Scatter plot of normalized residuals vs. 

LIGO Laboratory at Caltech

17. S3 Expected Sensitivity: H1-L1
Estimated error of measurement (+3) plotted for the H1-L1 pair as a function of run time.
Preliminary
LIGO Laboratory at Caltech

18. Current and expected results on gw h1002
H-L
H1-H2
Freq range
Observation Time
S1 (upper limit)
PRD 69, , 2004
< 23 +/- 4.6
(H2-L1)
see instrumental noise Hz
64 hours
(08/23/02 – 09/09/02)
S2 (upper limit)
Preliminary
<
(H1-L1) Hz
387 hours
(02/14/03 – 04/14/03)
S3 (sensitivity)
Expected based on power spectra
~5 x 10-4
potentially ~10x lower than S3 H1-L1
~240 hours
(10/31/03 – 01/09/04)
Design sensitivities
LIGO I
~1x 10-6
~1.5x 10-7 Hz
1 year
LIGO Advanced
nominal tuning
low-freq tuning
~1.5x 10-9
~3.5x 10-10
~3x 10-10
~2.5x 10-10 Hz
10-50 Hz
LIGO Laboratory at Caltech

19. The Cosmological Gravitational Wave “Landscape”
LIGO Laboratory at Caltech

20. Frequency range for GW Astronomy
Audio band
Dynamic range of Gravitational Waves
Terrestrial and space detectors complementary probes
Provide ~8 orders of magnitude coverage
Space
Terrestrial
LIGO Laboratory at Caltech

21. Initial and Advanced LIGO
LIGO Laboratory at Caltech

22. The Cosmological Gravitational Wave “Landscape”
LIGO Laboratory at Caltech

23. Growing International Network of GW Interferometers
Operated as a phased array:
- Enhance detection confidence
- Localize sources
- Decompose the polarization of gravitational waves
- Precursor triggers from low frequency
LISA
GEO: 0.6km
On-line
VIRGO: 3km
LIGO-LHO: 2km, 4km
On-line
TAMA: 0.3km
On-line
LIGO-LLO: 4km
On-line
AIGO: (?)km
Proposed
LIGO Laboratory at Caltech

24. LIGO Laboratory at Caltech
Summary
The current best published IFO-IFO upper-limit is from S1: h2 < 23+/-4.6
S2 result: ( ) PRELIMINARY
The S3 data analysis is in progress. Expect: < few x 10-4
H1-H2 is the most sensitive pair, but it also suffers from cross-correlated instrumental noise.
Also working on:
Set limits for gw(f) ~ n(f/f0)n
Targeted searches (astrophysical foregrounds, spatially resolved map)
Expected sensitivities with one year of data from LLO-LHO:
Initial LIGO h2 < 2x10-6
Advanced LIGO h2 < 7x10-10
LIGO Laboratory at Caltech

25. LIGO Laboratory at Caltech
FINIS
LIGO Laboratory at Caltech

26. What is known about the stochastic gravitational wave background?2
Allen & Koranda, PhysRevD
Lommen, astro-ph/
Kolb & Turner, TheEarlyUniverseAddisonWesley1990
LIGO Laboratory at Caltech