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Probing the Universe for Gravitational Waves
Barry C. BarishCaltech
Los Angeles Astronomical Society8-Nov-04
"Colliding Black Holes"
Credit:National Center for Supercomputing Applications (NCSA)
LIGO-xxx
2
Gµν= 8πΤµν
General Relativitythe essential idea
Overthrew the 19th-century concepts of absolute space and time
Gravity is not a force, but a property of space & time» Spacetime = 3 spatial dimensions + time» Perception of space or time is relative
Concentrations of mass or energy distort (warp) spacetimeObjects follow the shortest path through
this warped spacetime; path is the same for all objects
3
A Conceptual Problem is solved !
Gµν= 8πΤµν
Newton’s Theory“instantaneous action
at a distance”
Einstein’s Theoryinformation carried
by gravitational radiation at the speed
of light
4
Universal GravitationSolved most known problems of astronomy and terrestrial physics»eccentric orbits of
comets»cause of tides and
their variations»the precession of the
earth’s axis»the perturbation of the
motion of the moon by gravity of the sun
5
But, what causes the mysterious force in Newtons theory ?
Although the equation explains nature very well, the underlying mechanism creating the force is not explained !
6
After several hundred years, a small crack in Newton’s theory …..
perihelion shifts forward an extra +43”/century
compared to Newton’s theory
7
A new prediction of Einstein’s theory …
Light from distant stars are bent as they graze the Sun. The exact amount is predicted by Einstein's theory.
8
Confirming Einstein ….
Observation made during the solar eclipse of 1919 by Sir Arthur Eddington, when the Sun was silhouetted against the Hyades star cluster
bending of light
A massive object shifts apparent position of a star
9
Einstein’s Cross
The bending of light raysgravitational lensing
Quasar image appears around the central glow formed by nearby galaxy. The Einstein Cross is only visible in southern hemisphere.
10
Einstein’s Theory of Gravitation
a necessary consequence of Special Relativity with its finite speed for information transfer
gravitational waves come from the acceleration of masses and propagate away from their sources as a space-time warpage at the speed of light gravitational radiation
binary inspiral of
compact objects
11
Einstein’s Theory of Gravitationgravitational waves
0)1( 2
2
22 =
∂∂
−∇ µνhtc
• Using Minkowski metric, the information about space-time curvature is contained in the metric as an added term, hµν. In the weak field limit, the equation can be described with linear equations. If the choice of gauge is the transverse traceless gauge the formulation becomes a familiar wave equation
)/()/( czthczthh x −+−= +µν
• The strain hµν takes the form of a plane wave propagating at the speed of light (c).
• Since gravity is spin 2, the waves have two components, but rotated by 450 instead of 900 from each other.
12
The evidence for gravitational waves
Neutron binary system•
• separation = 106 miles• m1 = 1.4m• m2 = 1.36m• e = 0.617
Hulse & Taylor
•
•
17 / sec
period ~ 8 hrPrediction
from general relativity
• spiral in by 3 mm/orbit• rate of change orbital
period
PSR 1913 + 16Timing of pulsars
13
“Indirect”detection
of gravitational
wavesPSR 1913+16
14
Detectionof
Gravitational Waves
Detectors in space
LISA
Gravitational Wave Astrophysical
Source
Terrestrial detectorsVirgo, LIGO, TAMA, GEO
AIGO
15
Frequency range for EM astronomy
Electromagnetic wavesover ~16 orders of magnitudeUltra Low Frequency radio waves to high energy gamma rays
16
Frequency range for GW Astronomy
Gravitational wavesover ~8 orders of magnitudeTerrestrial and space detectors
Audio band
Space Terrestrial
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International Network on Earth
LIGO
simultaneously detect signal
detection confidence
GEO VirgoTAMA
AIGOlocate the sourcesdecompose the polarization of gravitational waves
18
The effect …
Leonardo da Vinci’s Vitruvian man
Stretch and squash in perpendicular directions at the frequency of the gravitational
waves
19
Detecting a passing wave ….
Free masses
20
Detecting a passing wave ….
Interferometer
21
The challenge ….I have greatly exaggerated the effect!!
If the Vitruvian man was 4.5 light years high, he would grow by only a ‘hairs width’
InterferometerConcept
22
Interferometer ConceptLaser used to measure relative lengths of two orthogonal arms
As a wave passes, the arm lengths change in different ways….
…causing the interference
pattern to change at the photodiode
Arms in LIGO are 4km Measure difference in length to one part in 1021
or 10-18 meters
SuspendedMasses
23
How Small is 10-18 Meter?One meter ~ 40 inches
Human hair ~ 100 microns000,10÷
Wavelength of light ~ 1 micron100÷
Atomic diameter 10-10 m000,10÷
Nuclear diameter 10-15 m000,100÷
LIGO sensitivity 10-18 m000,1÷
24
Simultaneous DetectionLIGO
3002 km(L/c = 10 ms)
Hanford Observatory
Caltech
LivingstonObservatory
MIT
25
LIGO Livingston Observatory
26
LIGO Hanford Observatory
27
LIGO Facilitiesbeam tube enclosure
• minimal enclosure
• reinforced concrete
• no services
28
LIGObeam tube
LIGO beam tube under construction in January 1998
65 ft spiral welded sections
girth welded in portable clean room in the field
1.2 m diameter - 3mm stainless50 km of weld
29
Vacuum Chambersvibration isolation systems
» Reduce in-band seismic motion by 4 - 6 orders of magnitude
» Compensate for microseism at 0.15 Hz by a factor of ten
» Compensate (partially) for Earth tides
30
Seismic Isolationsprings and masses
ConstrainedLayer
damped spring
31
LIGOvacuum equipment
32
Seismic Isolationsuspension system
suspension assembly for a core optic
• support structure is welded tubular stainless steel
• suspension wire is 0.31 mm diameter steel music wire
• fundamental violin mode frequency of 340 Hz
33
LIGO Opticsfused silica
Surface uniformity < 1 nm rmsScatter < 50 ppmAbsorption < 2 ppmROC matched < 3%Internal mode Q’s > 2 x 106
Caltech data CSIRO data
34
Core Optics installation and
alignment
35
LIGO Commissioning and Science Timeline
Now
36
Lock Acquisition
37
Detecting Earthquakes
From electronic logbook2-Jan-02
An earthquake occurred, starting at UTC 17:38.
38
Detecting the Earth TidesSun and Moon
Eric MorgensonCaltech Sophomore
39
Tidal Compensation DataTidal evaluation 21-hour locked section of S1 data
Predicted tides
Residual signal on voice coils
Residual signal on laser
Feedforward
Feedback
40
Controlling angular degrees of freedom
41
Interferometer Noise Limits
Thermal (Brownian)
Noise
LASER
test mass (mirror)
Beamsplitter
Residual gas scattering
Wavelength & amplitude fluctuations
Seismic Noise
Quantum Noise
"Shot" noise
Radiation pressure
photodiode
42
What Limits LIGO Sensitivity?Seismic noise limits low frequencies
Thermal Noise limits middle frequencies
Quantum nature of light (Shot Noise) limits high frequencies
Technical issues -alignment, electronics, acoustics, etc limit us before we reach these design goals
43
LIGO Sensitivity EvolutionHanford 4km Interferometer
Dec 01
Nov 03
44
Science Runs
S2 ~ 0.9Mpc
S1 ~ 100 kpc
E8 ~ 5 kpc
NN Binary Inspiral Range
S3 ~ 3 Mpc
Design~ 18 Mpc
A Measure of Progress
Milky WayAndromedaVirgo Cluster
45
Best Performance to Date ….
Range ~ 6 Mpc
46
Astrophysical Sourcessignatures
Compact binary inspiral: “chirps”» NS-NS waveforms are well described» BH-BH need better waveforms » search technique: matched templates
Supernovae / GRBs: “bursts”» burst signals in coincidence with signals in
electromagnetic radiation » prompt alarm (~ one hour) with neutrino
detectors
Pulsars in our galaxy: “periodic”» search for observed neutron stars
(frequency, doppler shift)» all sky search (computing challenge)» r-modes
Cosmological Signal “stochastic background”
47
Compact binary collisions
» Neutron Star – Neutron Star
– waveforms are well described» Black Hole – Black Hole
– need better waveforms » Search: matched
templates
“chirps”
48
Template Bank
2110 templatesSecond-orderpost-Newtonian
Covers desiredregion of massparam spaceCalculatedbased on L1noise curveTemplatesplaced formax mismatchof δ = 0.03
49
Optimal Filtering
Transform data to frequency domain : Generate template in frequency domain : Correlate, weighting by power spectral density of noise:
)(~ fh)(~ fs
|)(|)(~)(~ *
fSfhfs
h
|)(| tzFind maxima of over arrival time and phaseCharacterize these by signal-to-noise ratio (SNR) and effective distance
dfefS
fhfstz tfi
h
π2
0
*
|)(|)(~)(~
4)( ∫∞
=
Then inverse Fourier transform gives you the filter output
at all times:
frequency domain
50
Matched Filtering
51
Loudest Surviving CandidateNot NS/NS inspiral event1 Sep 2002, 00:38:33 UTC S/N = 15.9, χ2/dof = 2.2 (m1,m2) = (1.3, 1.1) Msun
What caused this?Appears to be due to saturation of a photodiode
52
Sensitivity
Reach for S1 DataInspiral sensitivity Livingston: <D> = 176 kpcHanford: <D> = 36 kpcSensitive to inspirals in Milky Way, LMC & SMC
Star Population in our GalaxyPopulation includes Milky Way, LMC and SMCNeutron star masses in range 1-3 MsunLMC and SMC contribute ~12% of Milky Way
neutron binary inspirals
53
Results of Inspiral Search
Upper limit binary neutron starcoalescence rate
LIGO S1 DataR < 160 / yr / MWEG
Previous observational limits» Japanese TAMA R < 30,000 / yr / MWEG» Caltech 40m R < 4,000 / yr / MWEG
Theoretical prediction R < 2 x 10-5 / yr / MWEG
Detectable Range of S2 data will reach Andromeda!
54
Astrophysical Sourcessignatures
Compact binary inspiral: “chirps”» NS-NS waveforms are well described» BH-BH need better waveforms » search technique: matched templates
Supernovae / GRBs: “bursts”» burst signals in coincidence with signals in
electromagnetic radiation » prompt alarm (~ one hour) with neutrino
detectors
Pulsars in our galaxy: “periodic”» search for observed neutron stars
(frequency, doppler shift)» all sky search (computing challenge)» r-modes
Cosmological Signal “stochastic background”
55
Detection of Burst SourcesKnown sources -- Supernovae &
GRBs» Coincidence with observed electromagnetic observations.
» No close supernovae occurred during the first science run» Second science run – We are analyzing the recent very bright and close GRB030329NO RESULT YET
Unknown phenomena» Emission of short transients of gravitational radiation of unknown waveform (e.g. black hole mergers).
56
‘Unmodeled’ Burstssearch for waveforms from sources for which we cannot currently make an accurate prediction of the waveform shape.
GOAL
METHODS
Time-Frequency Plane Search‘TFCLUSTERS’
Pure Time-Domain Search‘SLOPE’
freq
uenc
y
time
‘Raw Data’ Time-domain high pass filter
0.125s
8Hz
57
Determination of EfficiencyEfficiency measured for ‘tfclusters’ algorithm
0 10time (ms)
ampl
itude
0
h
To measure ourefficiency, we mustpick a waveform.
1ms Gaussian burst
58
Burst Upper Limit from S11ms gaussian bursts
Result is derived using ‘TFCLUSTERS’ algorithm
Upper limit in straincompared to earlier (cryogenic bar) results:
• IGEC 2001 combined bar upper limit: < 2 events per day having h=1x10-20 per Hz of burst bandwidth. For a 1kHz bandwidth, limit is < 2 events/day at h=1x10-17
• Astone et al. (2002), report a 2.2 σ excess of one event per day at strain level of h ~ 2x10-18
90% confidence
59
Astrophysical Sourcessignatures
Compact binary inspiral: “chirps”» NS-NS waveforms are well described» BH-BH need better waveforms » search technique: matched templates
Supernovae / GRBs: “bursts”» burst signals in coincidence with signals in
electromagnetic radiation » prompt alarm (~ one hour) with neutrino
detectors
Pulsars in our galaxy: “periodic”» search for observed neutron stars
(frequency, doppler shift)» all sky search (computing challenge)» r-modes
Cosmological Signal “stochastic background”
60
Detection of Periodic Sources
Pulsars in our galaxy: “periodic”» search for observed neutron stars » all sky search (computing challenge)» r-modes
Frequency modulation of signal due to Earth’s motion relative to the Solar System Barycenter, intrinsic frequency changes.
Amplitude modulation due to the detector’s antenna pattern.
61
Directed searches
( ) OBSGWh0 /TfS4.11h =
NO DETECTION EXPECTED
at present sensitivities
PSR J1939+21341283.86 Hz
Limits of detectability for rotating NS with equatorial ellipticity ε = δI/Izz: 10-3 , 10-4 , 10-5 @ 8.5 kpc.
Crab Pulsar
62
Two Search Methods
Frequency domain
• Best suited for large parameter space searches
• Maximum likelihood detection method + Frequentist approach
Time domain
• Best suited to target known objects, even if phase evolution is complicated
Bayesian approach
First science run --- use both pipelines for the same search for cross-checking and validation
63
The Data time behavior
>< hS
days
>< hS
>< hS >< hS
days
days
days
64
The Data
hS
frequency behaviorhS
hShSHz
Hz
Hz
Hz
65
PSR J1939+2134
Injected signal in LLO: h = 2.83 x 10-22
MeasuredF statistic
Frequency domain• Fourier Transforms of time series
• Detection statistic: F , maximum likelihood ratio wrt unknown parameters
• use signal injections to measure F’s pdf
• use frequentist’s approach to derive upper limit
66
PSR J1939+2134
95%
h = 2.1 x 10-21
Injected signals in GEO:h=1.5, 2.0, 2.5, 3.0 x 10-21
Data
Time domain• time series is heterodyned
• noise is estimated
• Bayesian approach in parameter estimation: express result in terms of posterior pdf for parameters of interest
67
Results: Periodic Sources
No evidence of continuous wave emission from PSR J1939+2134.Summary of 95% upper limits on h:
IFO Frequentist FDS Bayesian TDS
GEO (1.94±0.12)x10-21 (2.1 ±0.1)x10-21
LLO (2.83±0.31)x10-22 (1.4 ±0.1)x10-22
LHO-2K (4.71±0.50)x10-22 (2.2 ±0.2)x10-22
LHO-4K (6.42±0.72)x10-22 (2.7 ±0.3)x10-22
• Best previous results for PSR J1939+2134: ho < 10-20
(Glasgow, Hough et al., 1983)
68
Upper limit on pulsar ellipticityJ1939+2134
R
επRfIh zz
20
4
2
0 cG8
=
moment of inertia tensor
gravitational ellipticity of pulsar
h0 < 3 10-22 ε < 3 10-4
(M=1.4Msun, r=10km, R=3.6kpc)
Assumes emission is due to deviation from axisymmetry:..
69
Multi-detector upper limitsS2 Data Run
• Performed joint coherent analysis for 28 pulsars using data from all IFOs.
• Most stringent UL is for pulsar J1629-6902 (~333 Hz) where 95% confident that h0 < 2.3x10-24.
• 95% upper limit for Crab pulsar (~ 60 Hz) is h0 < 5.1 x 10-23.
• 95% upper limit for J1939+2134 (~ 1284 Hz) is h0 < 1.3 x 10-23.
95% upper limits
70
Upper limits on ellipticityS2 upper limits
Spin-down based upper limitsEquatorial ellipticity:
zz
yyxx
III −
=ε
Pulsars J0030+0451 (230 pc), J2124-3358 (250 pc), and J1024-0719 (350 pc) are the nearest three pulsars in the set and their equatorial ellipticities are all constrained to less than 10-5.
71
Approaching spin-down upper limits
Ratio of S2 upper limits to spin-For Crab pulsar (B0531+21) we are still a factor of ~35 above the spin-down upper limit in S2.
Hope to reach spin-down based upper limit in S3!
Note that not all pulsars analysed are constrained due to spin-down rates; some actually appear to be spinning-up (associated with accelerations in globular cluster).
down based upper limits
72
Astrophysical Sourcessignatures
Compact binary inspiral: “chirps”» NS-NS waveforms are well described» BH-BH need better waveforms » search technique: matched templates
Supernovae / GRBs: “bursts”» burst signals in coincidence with signals in
electromagnetic radiation » prompt alarm (~ one hour) with neutrino
detectors
Pulsars in our galaxy: “periodic”» search for observed neutron stars
(frequency, doppler shift)» all sky search (computing challenge)» r-modes
Cosmological Signal “stochastic background”
73
Signals from the Early Universestochastic background
Cosmic Microwavebackground
WMAP 2003
74
Signals from the Early Universe
Strength specified by ratio of energy density in GWs to total energy density needed to close the universe:
Detect by cross-correlating output of two GW detectors:
First LIGO Science Data
Hanford - Livingston
d(lnf)dρ
ρ1(f)Ω GW
criticalGW =
75
Limits: Stochastic Search
61.0 hrs62.3 hrs
Tobs
ΩGW (40Hz - 314 Hz) < 23ΩGW (40Hz - 314 Hz) < 72.4
90% CL Upper Limit
LHO 2km-LLO 4kmLHO 4km-LLO 4km
Interferometer Pair
Non-negligible LHO 4km-2km (H1-H2) instrumental cross-
correlation; currently being investigated.
Previous best upper limits:
» Garching-Glasgow interferometers :
» EXPLORER-NAUTILUS (cryogenic bars): 60 (907Hz)ΩGW <
5GW 103(f)Ω ×<
76
Gravitational Waves from the Early Universe
E7
S1S2
LIGO
Adv LIGO
results
projected
77
Advanced LIGOimproved subsystems
Multiple Suspensions
Active Seismic Sapphire Optics
Higher Power Laser
78
Advanced LIGOCubic Law for “Window” on the Universe
Initial LIGO
Advanced LIGO
Improve amplitude sensitivity by a factor of 10x…
…number of sources goes up 1000x! Virgo cluster
Today
79
Advanced LIGO2007 +
Enhanced Systems• laser• suspension• seismic isolation• test mass
RateImprovement
~ 104
+narrow band
optical configuration
80
LIGOConstruction is complete & commissioning is well underway
New upper limits for neutron binary inspirals, a fast pulsar and stochastic backgrounds have been achieved from the first short science run
Sensitivity improvements are rapid -- second data run was 10x more sensitive and 4x duration and results are beginning to be reported ----- (e.g. improved pulsar searches)
Enhanced detectors will be installed in ~ 5 years, further increasing sensitivity
Direct detection should be achieved and gravitational-wave astronomy begun within the next decade !
81
Gravitational Wave Astronomy
LIGOwill provide a new way to view the dynamics of the
Universe