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Probing the Universe for Gravitational Waves
Barry C. BarishCaltech
UC Davis12-April-04
"Colliding Black Holes"
Credit:National Center for Supercomputing Applications (NCSA)
LIGO-G040224-00-M
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A Conceptual Problem is solved !
Newton’s Theory“instantaneous action
at a distance”
Einstein’s Theoryinformation carried
by gravitational radiation at the speed of light
G= 8
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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 radiationbinary inspiral
of compact objects
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Einstein’s Theory of Gravitationgravitational waves
0)1
(2
2
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htc
• Using Minkowski metric, the information about space-time curvature is contained in the metric as an added term, h. 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
• The strain h 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.
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The evidence for gravitational waves
Hulse & Taylor
17 / sec
Neutron binary system
•
• separation = 106 miles• m1 = 1.4m
• m2 = 1.36m
• e = 0.617
period ~ 8 hr
PSR 1913 + 16Timing of pulsars
Predictionfrom
general relativity • spiral in by 3 mm/orbit• rate of change orbital period
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“Indirect”detection
of gravitational
wavesPSR 1913+16
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Detectionof
Gravitational Waves
Detectors in space
LISA
Gravitational Wave
Astrophysical Source
Terrestrial detectorsVirgo, LIGO, TAMA, GEO
AIGO
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Frequency range for EM astronomy
Electromagnetic waves over ~16 orders of
magnitude Ultra Low Frequency radio
waves to high energy gamma rays
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Frequency range for GW Astronomy
Gravitational waves over ~8 orders of
magnitude Terrestrial 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
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The effect …
Stretch and squash in perpendicular directions at the frequency of the gravitational
waves
Leonardo da Vinci’s Vitruvian man
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Detecting a passing wave ….
Free masses
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Detecting a passing wave ….
Interferometer
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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
The challenge ….
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Interferometer Concept Laser 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
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How Small is 10-18 Meter?
Wavelength of light ~ 1 micron
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One meter ~ 40 inches
Human hair ~ 100 microns000,10
LIGO sensitivity 10-18 m000,1
Nuclear diameter 10-15 m
000,100
Atomic diameter 10-10 m000,10
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Simultaneous DetectionLIGO
3002 km
(L/c = 10 ms)
Hanford Observatory
Caltech
LivingstonObservatory
MIT
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LIGO Livingston Observatory
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LIGO Hanford Observatory
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LIGO Facilitiesbeam tube enclosure
• minimal enclosure
• reinforced concrete
• no services
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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
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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
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Seismic Isolation springs and masses
ConstrainedLayer
damped spring
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LIGOvacuum equipment
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Seismic Isolationsuspension system
• support structure is welded tubular stainless steel • suspension wire is 0.31 mm diameter steel music wire
• fundamental violin mode frequency of 340 Hz
suspension assembly for a core optic
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LIGO Opticsfused silica
Caltech data CSIRO data
Surface uniformity < 1 nm rms Scatter < 50 ppm Absorption < 2 ppm ROC matched < 3% Internal mode Q’s > 2 x 106
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Core Optics installation and
alignment
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LIGO Commissioning and Science Timeline
Now
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Lock Acquisition
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An earthquake occurred, starting at UTC 17:38.
From electronic logbook 2-Jan-02
Detecting Earthquakes
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Detecting the Earth Tides
Sun and Moon
Eric MorgensonCaltech Sophomore
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Tidal Compensation DataTidal evaluation 21-hour locked section of S1 data
Residual signal on voice coils
Predicted tides
Residual signal on laser
Feedforward
Feedback
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Controlling angular degrees of freedom
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Interferometer Noise Limits
Thermal (Brownian)
Noise
LASER
test mass (mirror)
Beamsplitter
Residual gas scattering
Wavelength & amplitude fluctuations photodiode
Seismic Noise
Quantum Noise
"Shot" noise
Radiation pressure
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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
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LIGO Sensitivity EvolutionHanford 4km Interferometer
Dec 01
Nov 03
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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
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Best Performance to Date ….
Range ~ 6 Mpc
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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”
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Compact binary collisions
» Neutron Star – Neutron Star
– waveforms are well described
» Black Hole – Black Hole – need better waveforms
» Search: matched templates
“chirps”
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Template Bank
Covers desiredregion of massparam space
Calculatedbased on L1noise curve
Templatesplaced formax mismatchof = 0.03
2110 templatesSecond-orderpost-Newtonian
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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
dfefSfhfs
tz tfi
h
2
0
*
|)(|)(
~)(~
4)(
Then inverse Fourier transform gives you the filter output
at all times:
frequency domain
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Matched Filtering
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Loudest Surviving Candidate Not NS/NS inspiral event 1 Sep 2002, 00:38:33 UTC S/N = 15.9, 2/dof = 2.2 (m1,m2) = (1.3, 1.1) Msun
What caused this? Appears to be due to
saturation of a photodiode
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Sensitivity
Reach for S1 Data Inspiral sensitivity
Livingston: <D> = 176 kpc
Hanford: <D> = 36 kpc
Sensitive to inspirals in Milky Way, LMC & SMC
Star Population in our Galaxy Population includes Milky Way, LMC and SMC Neutron star masses in range 1-3 Msun LMC and SMC contribute ~12% of Milky Way
neutron binary inspirals
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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!
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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”
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Detection of Burst Sources Known 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 GRB030329
NO RESULT YET
Unknown phenomena » Emission of short transients of gravitational radiation of unknown waveform (e.g. black hole mergers).
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‘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
uen
cy
time
‘Raw Data’ Time-domain high pass filter
0.125s
8Hz
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Determination of Efficiency
Efficiency measured for ‘tfclusters’ algorithm
0 10time (ms)
amp
litu
de
0
h
To measure ourefficiency, we mustpick a waveform.
1ms Gaussian burst
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Burst Upper Limit from S1
Upper limit in strain compared 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 excess of one event per day at strain level of h ~ 2x10-
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90% confidence
Result is derived using ‘TFCLUSTERS’ algorithm
1ms gaussian bursts
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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”
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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.
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Directed searches
OBSGWh0 /TfS4.11h
NO DETECTION EXPECTED
at present sensitivities
PSR J1939+2134
1283.86 Hz
Limits of detectability for rotating NS with equatorial ellipticity =I/Izz: 10-3 , 10-4 , 10-5 @ 8.5 kpc.
Crab Pulsar
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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
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The Data
hS
days
hS
hS hS
days
days
days
time behavior
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The Data
hS
hShS
hS
Hz
Hz
Hz
Hz
frequency behavior
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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
PSR J1939+2134
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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
PSR J1939+2134
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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 (1.940.12)x10-21 (2.1 0.1)x10-21
LLO (2.830.31)x10-22 (1.4 0.1)x10-22
LHO-2K (4.710.50)x10-22 (2.2 0.2)x10-22
LHO-4K (6.420.72)x10-22 (2.7 0.3)x10-22
• Best previous results for PSR J1939+2134: ho < 10-
20 (Glasgow, Hough et al., 1983)
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R
R
fIh zz
20
4
2
0 c
G8
moment of inertia tensor
gravitational ellipticity of pulsar
Assumes emission is due to deviation from axisymmetry:
Upper limit on pulsar ellipticity
h0 < 3 10-22 < 3 10-4
..
(M=1.4Msun, r=10km, R=3.6kpc)
J1939+2134
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Multi-detector upper limits
S2 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
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Upper limits on ellipticity
zz
yyxx
I
II
Equatorial ellipticity:
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.
S2 upper limits
Spin-down based upper limits
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Approaching spin-down upper limits
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).
Ratio of S2 upper limits to spin-down based upper limits
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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”
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Signals from the Early Universe
Cosmic Microwave
background
WMAP 2003
stochastic background
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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
ρ
1(f)Ω GW
criticalGW
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Limits: Stochastic Search
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
61.0 hrs
62.3 hrs
Tobs
GW (40Hz - 314 Hz) < 23
GW (40Hz - 314 Hz) < 72.4
90% CL Upper Limit
LHO 2km-LLO 4km
LHO 4km-LLO 4km
Interferometer Pair
5GW 103(f)Ω
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Gravitational Waves from the Early Universe
E7
S1
S2
LIGO
Adv LIGO
results
projected
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Advanced LIGOimproved subsystems
Active Seismic
Multiple Suspensions
Sapphire Optics
Higher Power Laser
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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
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Advanced LIGO
Enhanced Systems• laser• suspension• seismic isolation• test mass Rate
Improvement
~ 104
+narrow band
optical configuration
2007 +
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LIGO Construction 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 !
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Gravitational Wave Astronomy
LIGO will provide a new way to view the dynamics of the
Universe
