Probing the Universe for Gravitational
Waves
"Colliding Black Holes"
Credit:
National Center for Supercomputing Applications (NCSA)
Barry C. Barish
Caltech
UC Davis
12-April-04
LIGO-G040224-00-M
1
A Conceptual Problem is solved !
Newton’s Theory
“instantaneous action
at a distance”
Gmn= 8pTmn
Einstein’s Theory
information carried
by gravitational
radiation at the speed
of light
2
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
3
Einstein’s Theory of Gravitation
gravitational waves
• Using Minkowski metric, the
information about space-time
curvature is contained in the metric as
an added term, hmn. 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
1 2
(  2 2 )hmn  0
c t
2
• The strain hmn 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.
hmn  h (t  z / c )  hx (t  z / c )
4
The evidence for
gravitational waves
Hulse & Taylor
•
• m1 = 1.4m
• m2 = 1.36m
• e = 0.617
17 / sec


Neutron binary system
• separation = 106 miles
period ~ 8 hr
PSR 1913 + 16
Timing of pulsars
Prediction
from
general relativity
• spiral in by 3 mm/orbit
• rate of change orbital
period
5
“Indirect”
detection
of
gravitational
waves
PSR 1913+16
6
Detection
of
Gravitational Waves
Gravitational Wave
Astrophysical
Source
Terrestrial detectors
Detectors
in space
Virgo, LIGO, TAMA, GEO
AIGO
LISA
7
Frequency range for EM astronomy
Electromagnetic waves
 over ~16 orders of
magnitude
 Ultra Low Frequency radio
waves to high energy
gamma rays
8
Frequency range for GW Astronomy
Audio band
Gravitational waves
 over ~8 orders of
magnitude
 Terrestrial and space
detectors
Space
Terrestrial
9
International Network on Earth
simultaneously detect signal
LIGO
GEO
decompose
detection
locatethe
the
confidence
polarization
sources
of
gravitational waves
Virgo
TAMA
AIGO
10
The effect …
Leonardo da Vinci’s Vitruvian man
Stretch and squash in
perpendicular directions at the
frequency of the gravitational
waves
11
Detecting a passing wave ….
Free masses
12
Detecting a passing wave ….
Interferometer
13
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’
Interferometer
Concept
14
Interferometer Concept
 Arms in LIGO are 4km
 Laser used to
measure relative  Measure difference in
lengths of two
length to one part in
orthogonal arms
1021 or 10-18 meters
…causing the
interference
pattern to change
at the photodiode
As a wave
Suspended
passes, the
Masses
arm
lengths
change in
different
ways….
15
How Small is 10-18 Meter?
One meter ~ 40 inches
 10,000
100
Human hair ~ 100 microns
Wavelength of light ~ 1 micron
 10,000
Atomic diameter 10-10 m
 100,000
Nuclear diameter 10-15 m
 1,000
LIGO sensitivity 10-18 m
16
Simultaneous Detection
LIGO
Hanford
Observatory
MIT
Caltech
Livingston
Observatory
17
LIGO Livingston Observatory
18
LIGO Hanford Observatory
19
LIGO Facilities
beam tube enclosure
• minimal enclosure
• reinforced concrete
• no services
20
LIGO
beam 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 stainless
50 km of weld
21
Vacuum Chambers
vibration 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
22
Seismic Isolation
springs and masses
Constrained
Layer
damped spring
23
LIGO
vacuum equipment
24
Seismic Isolation
suspension 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
25
LIGO Optics
fused silica
 Surface uniformity < 1 nm
rms
 Scatter < 50 ppm
 Absorption < 2 ppm
 ROC matched < 3%
 Internal mode Q’s > 2 x 106
Caltech data
CSIRO data
26
Core Optics
installation and alignment
27
LIGO Commissioning and
Science Timeline
Now
28
Lock Acquisition
29
Detecting Earthquakes
From electronic logbook
2-Jan-02
An earthquake occurred,
starting at UTC 17:38.
30
Detecting the Earth Tides
Sun and Moon
Eric Morgenson
Caltech Sophomore
31
Tidal Compensation Data
Tidal evaluation
21-hour locked
section of S1
data
Predicted tides
Feedforward
Feedback
Residual signal
on voice coils
Residual signal
on laser
32
Controlling angular degrees
of freedom
33
Interferometer Noise Limits
test mass (mirror)
Seismic Noise
Quantum Noise
Residual gas scattering
"Shot" noise
Radiation
pressure
LASER
Wavelength &
amplitude
fluctuations
Beam
splitter
photodiode
Thermal
(Brownian)
Noise
34
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
35
LIGO Sensitivity Evolution
Hanford 4km Interferometer
Dec 01
Nov 03
36
Science Runs
Milky
Way
Virgo
Andromeda
Cluster
A Measure of
Progress
NN Binary
Inspiral Range
E8 ~ 5 kpc
S1 ~ 100 kpc
S2 ~ 0.9Mpc
S3 ~ 3 Mpc
Design~ 18 Mpc
37
Best Performance to Date ….
Range ~ 6 Mpc
38
Astrophysical Sources
signatures

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”
39
Compact binary collisions
» Neutron Star – Neutron
Star
– waveforms are well described
» Black Hole – Black Hole
– need better waveforms
» Search: matched
templates
“chirps”
40
Template Bank
 Covers desired
region of mass
param space
 Calculated
based on L1
noise curve
 Templates
placed for
max mismatch
of  = 0.03
2110 templates
Second-order
post-Newtonian
41
Optimal Filtering
frequency domain
~
 Transform data to frequency domain : h ( f )
~
 Generate template in frequency domain : s ( f )
 Correlate, weighting by power spectral density of
noise:
~*
~
s( f ) h ( f )
S h (| f |)
Then inverse Fourier transform gives you the filter output
~*
~
s ( f ) h ( f ) 2p i f t
z (t )  4 
e
df
S h (| f |)
0

at all times:
Find maxima of | z (t ) | over arrival time and phase
Characterize these by signal-to-noise ratio (SNR) and
effective distance
42
Matched Filtering
43
Loudest Surviving Candidate
 Not NS/NS inspiral
event
 1 Sep 2002, 00:38:33
UTC
 S/N = 15.9, c2/dof = 2.2
 (m1,m2) = (1.3, 1.1)
Msun
What caused this?
 Appears to be due to
saturation of a photodiode
44
Sensitivity
neutron binary inspirals
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
Reach for S1 Data
 Inspiral sensitivity
Livingston: <D> = 176 kpc
Hanford:
<D> = 36 kpc
 Sensitive to inspirals in
Milky Way, LMC & SMC
45
Results of Inspiral Search
Upper limit
binary neutron star
coalescence rate
LIGO S1 Data
R < 160 / yr / MWEG
 Previous observational limits
» Japanese TAMA 
» Caltech 40m 
 Theoretical prediction
R < 30,000 / yr / MWEG
R < 4,000 / yr / MWEG
R < 2 x 10-5 / yr / MWEG
Detectable Range of S2 data will reach Andromeda!
46
Astrophysical Sources
signatures

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
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).
48
‘Unmodeled’ Bursts
GOAL search for waveforms from sources for which we
cannot currently make an accurate prediction of the
waveform shape.
METHODS
‘Raw Data’
Time-domain high pass filter
frequency
Time-Frequency Plane Search
‘TFCLUSTERS’
Pure Time-Domain Search
‘SLOPE’
8Hz
0.125s
time
49
Determination of Efficiency
Efficiency measured for ‘tfclusters’ algorithm
To measure our
efficiency, we must
pick a waveform.
amplitude
h
0
0
10
time (ms)
1ms Gaussian burst
50
Burst Upper Limit from S1
1ms gaussian bursts
Result is derived using ‘TFCLUSTERS’ algorithm
90% confidence
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 s excess of one
event per day at strain level
of h ~ 2x10-18
51
Astrophysical Sources
signatures

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”
52
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.
53
Directed searches
NO DETECTION
EXPECTED
at present
sensitivities
Crab Pulsar
h 0  11.4 Sh f GW /TOBS
Limits of detectability for
rotating NS with equatorial
ellipticity e = I/Izz: 10-3 , 10-4 ,
10-5 @ 8.5 kpc.
PSR
J1939+2134
1283.86 Hz
54
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
55
The Data
time behavior
 Sh 
 Sh 
days
days
 Sh 
 Sh 
days
days
56
The Data
frequency behavior
Sh
Sh
Hz
Sh
Hz
Sh
Hz
Hz
57
PSR J1939+2134
Frequency domain
• Fourier Transforms of
time series
Injected signal in LLO: h = 2.83 x 10-22
• Detection statistic: F ,
maximum likelihood ratio
wrt unknown parameters
• use signal injections to
measure F’s pdf
Measured
F statistic
• use frequentist’s approach
to derive upper limit
58
PSR J1939+2134
Data
Time domain
Injected signals in GEO:
h=1.5, 2.0, 2.5, 3.0 x 10-21
• time series is
heterodyned
• noise is estimated
• Bayesian approach in
parameter estimation:
express result in terms of
posterior pdf for
parameters of interest
95%
h = 2.1 x 10-21
59
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)
60
Upper limit on pulsar ellipticity
J1939+2134
moment of
inertia tensor
8p G I zz f 0
h0  4
e
c
R
2
2
gravitational
ellipticity of
pulsar
h0 < 3 10-22  e < 3 10-4
R
(M=1.4Msun, r=10km, R=3.6kpc)
Assumes emission is due to deviation from axisymmetry:
..
61
Multi-detector upper limits
S2 Data Run
95% upper limits
• 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.
62
Upper limits on ellipticity
S2 upper limits
Spin-down based upper limits
Equatorial ellipticity:
Ixx  Iyy
e
Izz
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.
63
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 spindown based upper limits
64
Astrophysical Sources
signatures

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”
65
Signals from the Early Universe
stochastic background
Cosmic
Microwave
background
WMAP 2003
66
Signals from the Early Universe
 Strength specified by ratio of energy density in GWs to
total energy density needed to close the universe:
ΩGW (f) 

1
ρcritical
dρGW
d(lnf)
Detect by cross-correlating output of two GW
detectors:
First LIGO Science Data
Hanford - Livingston
67
Limits: Stochastic Search
Interferometer
Pair
90% CL Upper Limit
Tobs
LHO 4km-LLO 4km
WGW (40Hz - 314 Hz) < 72.4
62.3 hrs
LHO 2km-LLO 4km
WGW (40Hz - 314 Hz) < 23
61.0 hrs
 Non-negligible LHO 4km-2km (H1-H2) instrumental crosscorrelation; currently being investigated.
 Previous best upper limits:
» Garching-Glasgow interferometers :
ΩGW (f)  3 10 5
» EXPLORER-NAUTILUS (cryogenic bars): ΩGW (907Hz)  60
68
Gravitational Waves
from the Early Universe
results
projected
E7
S1
S2
LIGO
Adv LIGO
69
Advanced LIGO
improved subsystems
Multiple Suspensions
Active Seismic
Sapphire Optics
Higher Power Laser
70
Advanced LIGO
Cubic Law for “Window” on the Universe
Improve amplitude
sensitivity by a
factor of 10x…
…number of
sources goes up
1000x!
Virgo cluster
Today Initial
LIGO
Advanced
LIGO
71
Advanced LIGO
2007 +
Enhanced Systems
• laser
• suspension
• seismic isolation
• test mass
Rate
Improvement
~ 104
+
narrow band
optical configuration
72
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 !
73
Gravitational Wave
Astronomy
LIGO
will provide a new
way to view the
dynamics of the
Universe
74