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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

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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

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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

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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

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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 !

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After several hundred years, a small crack in Newton’s theory …..

perihelion shifts forward an extra +43”/century

compared to Newton’s theory

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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.

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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

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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.

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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 radiation

binary inspiral of

compact objects

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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.

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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

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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 wavesover ~16 orders of magnitudeUltra Low Frequency radio waves to high energy gamma rays

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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

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The effect …

Leonardo da Vinci’s Vitruvian man

Stretch and squash in perpendicular directions at the frequency of the gravitational

waves

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Detecting a passing wave ….

Free masses

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Detecting a passing wave ….

Interferometer

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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

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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

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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÷

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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 Isolationsprings and masses

ConstrainedLayer

damped spring

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LIGOvacuum equipment

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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

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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

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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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Detecting Earthquakes

From electronic logbook2-Jan-02

An earthquake occurred, starting at UTC 17:38.

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Detecting the Earth TidesSun and Moon

Eric MorgensonCaltech Sophomore

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Tidal Compensation DataTidal evaluation 21-hour locked section of S1 data

Predicted tides

Residual signal on voice coils

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

Seismic Noise

Quantum Noise

"Shot" noise

Radiation pressure

photodiode

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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

2110 templatesSecond-orderpost-Newtonian

Covers desiredregion of massparam spaceCalculatedbased on L1noise curveTemplatesplaced formax mismatchof δ = 0.03

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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

dfefS

fhfstz tfi

h

π2

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 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

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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

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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 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).

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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

uenc

y

time

‘Raw Data’ Time-domain high pass filter

0.125s

8Hz

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Determination of EfficiencyEfficiency measured for ‘tfclusters’ algorithm

0 10time (ms)

ampl

itude

0

h

To measure ourefficiency, we mustpick a waveform.

1ms Gaussian burst

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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

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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+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

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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 time behavior

>< hS

days

>< hS

>< hS >< hS

days

days

days

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The Data

hS

frequency behaviorhS

hShSHz

Hz

Hz

Hz

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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

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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

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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 (1.94±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)

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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:..

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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

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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.

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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

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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 Universestochastic background

Cosmic Microwavebackground

WMAP 2003

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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

ρ1(f)Ω GW

criticalGW =

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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 ×<

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Gravitational Waves from the Early Universe

E7

S1S2

LIGO

Adv LIGO

results

projected

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Advanced LIGOimproved subsystems

Multiple Suspensions

Active Seismic 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 LIGO2007 +

Enhanced Systems• laser• suspension• seismic isolation• test mass

RateImprovement

~ 104

+narrow band

optical configuration

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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 !

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Gravitational Wave Astronomy

LIGOwill provide a new way to view the dynamics of the

Universe