The ideal

1
The ideal
Robert Millikan
Nikola Tesla
2
The reality
3
The hallmarks of Big Science

• Collaborations of hundreds of physicists and
  engineers
• Universities, lab sites spread out geographically
• Many fields of knowledge incorporated
• Particle physics for experiment goals, data
  analysis
• Mechanical and vacuum engineering for detector
  construction
• Electrical engineering for readout devices,
  electronics boards
• Computer science for design of data acquisition
• Thats for a relatively straightfoward
  experiment!
• Communication is critical!
• Not one large problem, but thousands of little
  problems, and every result is important!

4
Gravitational Waves

• What is a gravitational wave?
• Where do they come from?
• What can we learn from them?
• How large are they?
• How can we detect them?

5
Warped space-time Einsteins General Relativity
(1916)

• A geometric theory of gravity
• gravitational acceleration depends only on the
  geometry of the space that the test mass
  occupies, not any properties of the test mass
  itself
• for gravity (as opposed to all other forces),
  motion (acceleration) depends only on location,
  not mass
• Imagine space as a stretched rubber sheet.
• A mass on the surface will cause a deformation.
• Another (test) mass dropped onto the sheet will
  roll toward that mass.
• Einstein theorized that smaller masses travel
  toward larger masses, not because they are
  "attracted" by a force that acts across a
  distance, but because the smaller objects travel
  through space that is
• warped by
• the larger object.

/
/
6
Dynamics of changing spacetime curvature
Newton instantaneous action at a distance
Einstein information carried by gravitational
radiation at the speed of light
7
Experimental Tests of GR
Einstein Cross The bending of light
rays gravitational lensing Quasar image appears
around the central glow formed by nearby galaxy.
Such gravitational lensing images are used to
detect a dark matter body as the central object
Mercurys orbit perihelion shifts forward twice
Newtons theory Mercury's elliptical path around
the Sun shifts slightly with each orbit such
that its closest point to the Sun (or
"perihelion") shifts forward with each pass.
bending of light As it passes in the vicinity of
massive objects First observed during the solar
eclipse of 1919 by Sir Arthur Eddington, when the
Sun was silhouetted against the Hyades star
cluster
8
Hulse-Taylor binary pulsar
Neutron Binary System PSR 1913 16 -- Timing of
pulsars

• Discovered in 1975, orbital parameters measured
  very precisely
• System should lose energy through gravitational
  radiation
• Stars get closer together
• Orbital period gets shorter

9
Hulse-Taylor binary prediction
emission of gravitational waves by compact binary
system

• Period speeds up 14 sec from 1975-94
• Measured to 50 msec accuracy
• Deviation grows quadratically with time
• Compact system negligible losses from friction,
  material flow
• Beautiful agreement with prediction!
• Nobel Prize, 1993

10
Nature of Gravitational Radiation

• General Relativity predicts
• transverse space-time distortions, freely
  propagating at speed of light
• expressed as a strain (?h ?L/L)
• Conservation laws
• conservation of energy ? no monopole
  radiation
• conservation of momentum ? no dipole radiation
• quadrupole wave (spin 2) ? two polarizations
• plus (?) and cross (?)

Contrast with EM dipole radiation
11
Not all motion creates gravitational waves!

• Spherically symmetric mass can be described by
  point mass at center
• Spherically symmetric motion will not produce
  gravitational waves
• Symmetric rotating pulsar
• Ideal supernova
• Source must be non-axi-symmetric

12
AstrophysicalSources of Gravitational Waves
Coalescing compact binaries (neutron stars, black
holes)
Non-axi-symmetric supernova collapse
Non-axi-symmetric pulsar (rotating, beaming
neutron star)
13
GWs from coalescing compact binaries (NS/NS,
BH/BH, NS/BH)
Chirp Signal
14
Supernova collapse sequence

• Within about 0.1 second, the core collapses and
  gravitational waves are emitted.
• After about 0.5 second, the collapsing envelope
  interacts with the outward shock. Neutrinos are
  emitted.
• Within 2 hours, the envelope of the star is
  explosively ejected. When the photons reach the
  surface of the star, it brightens by a factor of
  100 million.
• Over a period of months, the expanding remnant
  emits X-rays, visible light and radio waves in a
  decreasing fashion.

Gravitational waves
15
Gravitational Waves from Supernova collapse
Non axisymmetric collapse
burst signal
Rate 1/50 yr - our galaxy 3/yr - Virgo cluster
LIGO will be part of worldwide supernova watch
(?, n, GW)
16
GWs from dark matter
Experiments such as BOOMERanG tell us that the
universe is flat, implying that 95 of its mass
is undiscovered, i.e. dark matter.
Gravitational waves may give us a new window to
this part of the universe.
17
Gravitational waves from Big Bang
Cosmic microwave background
Gravitational waves probe the universe at the
earliest times after the Big Bang
18
Who knows what else we might see?
19
Strong-field

• Most tests of GR focus on small deviations from
  Newtonian dynamics
• Space-time curvature is a tiny effect everywhere
  except
• The universe in the early moments of the big bang
• Near/in the horizon of black holes
• This is where GR gets non-linear and interesting!
• We arent very close to any black holes
  (fortunately!), and cant see them with light

But we can search for (weak-field) gravitational
waves as a signal of their presence and dynamics
20
How far must we look?
1 parsec 1 parallax second 3.26 light
years 3.09 1016 m So the Virgo cluster is
about 6 1023 m away!
Virgo cluster
21
How big are gravitational waves?

• Amplitude of the gravitational wave (dimensional
  analysis)
• second derivative
• of mass quadrupole moment
• (non-spherical part of kinetic energy
• tumbling dumb-bell)
• G is a small number!
• Need huge mass, relativistic
• velocities, nearby.
• For a binary neutron star pair,
• 10m light-years away, solar masses
• moving at 15 of speed of light

km
22
Thats REALLY small!
L 1.5 1011 m
Sun
Earth
?L 10-10 m
h 10-21 is equivalent to the distance from the
Earth to the Sun changing by the width of an atom!
23
Can we generate gravitational waves?
Imagine if we put two 1-ton masses on the ends of
a 2-meter long bar, and spun the bar at 100 Hz
(!?!). If our detector is next to this setup
2m
103 kg
103 kg
M 103 kg R 1 m F 100 Hz r 1 m
10-36 !!
Terrestrial sources are TOO WEAK!
24
First AttemptResonant Bar Detectors
In 1966 Joseph Weber constructed the first
resonant-bar gravitational wave detector. By
1969 the detector had reached a strain
sensitivity of h 10-16. The detector consisted
of an aluminum bar suspended in a vacuum chamber.
A passing gravity wave would stretch or contract
the bar, generating heat that would cause the bar
to ring at its resonant frequency. Such a
detector has two problems, both related to the
fact that it can sense only one frequency

• Cannot determine shape of gravitational wave
• Noise looks exactly the same as signal

GW wave
Aluminum bar
25
Bar detector improvements
Despite a sensitivity of 10-16, Weber announced
in 1970 that he had observed identical signals in
two detectors 1000 km apart. This set off a
flurry of construction of resonant bar detectors,
including several improvements ? More
massive bars (gt 103 kg) ? Cryogenics for
reduced thermal noise ? Low noise, resonating
transducers None of these detectors, however,
have reached a sensitivity of 10-21, and none
have been able to reproduce Webers findings.
26
The Michelson-Morley experiment
27
Application of Michelson interferometer
The Michelson interferometers shape is perfectly
suited to the quadrupole nature of gravitational
radiation. In addition, Michelson and Morley
could measure 1/100th of a fringe with 1900s
technology. With high-power lasers and modern
photodiodes, we can do far better.
28
How sensitive is an interferometer?
Imagine a high-powered NdYAG laser (? 1.064
µm) in an interferometer with 5 km arms (longest
curvature of Earth will allow) ?L/L
(?laser)/(length of arms) (10-6 m)/(10 km)
10-10, not even close!
Michelson and Morley didnt build 11m arms,
though (thats a lot of mercury!). They folded
the light path several times with nearly parallel
mirrors. But we dont have room or money for
thousands of mirrors!
29
Folding the arms two methods
Delay line simpler, but requires large mirrors to
prevent crosstalk limited storage
time. Fabry-Perot more compact, storage time in
msec, but harder to control.
For one fringe, ?L/L (?laser)/(length of arms
folding) (10-6
m)/(10 km 1000) 10-13 With enough laser
power, measuring 10-8 of a fringe can be done!
30
The LIGO Interferometer
Next time we will talk about

• How do we build such a large interferometer?
• How do we measure one billionth of a fringe?
• How do we reduce noise?
• How do we analyze the data?
• How do we eliminate fake events?

31
Physics of LIGO

• The international network
• How it all works
• Control systems
• Measuring the fringe
• Noise reduction
• Data analysis
• Schedule

32
The LIGO Project

• LIGO Laser Interferometer Gravitational-Wave
  Observatory
• US project to build observatories for
  gravitational waves (GWs)
• to enable an initial detection, then an astronomy
  of GWs
• collaboration by MIT, Caltech other institutions
  participating
• (LIGO Scientific Collaboration, LSC)
• Funded by the US National Science Foundation
  (NSF)
• Observatory characteristics
• Two sites separated by 3000 km
• each site carries 4km vacuum system,
  infrastructure
• each site capable of multiple interferometers
  (IFOs)
• Evolution of interferometers in LIGO
• establishment of a network with other
  interferometers
• A facility for a variety of GW searches
• lifetime of gt20 years
• goal best technology, to achieve fundamental
  noise limits for terrestrial IFOs

33
LIGO Livingston Observatory
34
Welcome to Louisiana
pet alligator
collecting bullet holes
35
LIGO Hanford Observatory
36
Gliches at Hanford
a view from the bridge
LIGO as a car stop
desert on fire
LIGO as a fire break
37
International network
Simultaneously detect signal (within msec)
GEO
Virgo
LIGO
TAMA

• detection confidence
• locate the sources
• verify light speed propagation
• decompose the polarization of gravitational
  waves

AIGO
38
How does the LIGO interferometer work?

• 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.

39
Power recycling

• The interferometer is run as a null instrument
  the arm lengths are set such that no light is
  output
• When a gravitational wave passes, the arm lengths
  change and light exits the dark port
• More laser power more sensitivity, but the
  power is being wasted out the bright port!
• Add a power recycling mirror at the bright port,
  making a resonant compound cavity to dump the
  light back in

bright port
dark port (GW signal)
40
Suspended test masses

• To respond to the gravitational wave, test
  masses (mirrors) must be free falling
• The Earth is vibrating like mad at low
  frequencies (seismic, thermal, acoustic,
  electrical)
• cant simply bolt the masses to the table
• Mirrors suspended on a pendulum with f0 1 Hz
• fixed against gravity at low frequencies, but
• free to move at frequencies above 100 Hz

Free mass pendulum at
41
Two problems

• If we are operating at the dark fringe, we are
  at the base of a sine wave in power, and a large
  phase shift will cause a small change in the
  output light. How can we make our interferometer
  more sensitive?

intensity shift
phase shift

• The arm lengths have to be kept in resonance to a
  fraction of a micron, but the mirrors are
  swinging! How do we sense and control the
  lengths of the arm cavities?

42
Beat frequencies
cos (ab) (cos a)(cos b) (sin a)(sin b) cos
(?1-?2)t cos (?1t) cos (?2t) sin (?1t) sin
(?2t) cos (?1?2)t cos (?1t) cos (?2t) sin
(?1t) sin (?2t) Thus cos (?1t) cos (?2t) ½ cos
(?1-?2)t cos (?1?2)t
The product of two sine waves equals the sum of
two waves at the beat frequencies (half the
average and difference). We can take advantage of
this property by modulating our laser light.
43
Cavity control

• Pound-Drever (reflection) locking used to control
  lengths of all the optical cavities in LIGO
• Phase modulate incoming laser light, producing
  RF sidebands
• Carrier is resonant in cavity, sidebands are not
• Beats between carrier and sidebands provide
  error signal for cavity length

44
Demodulation
Modulated light A cos (?t) B cos (? ?m)t
B cos (? ?m)t Power A2 AB cos (?mt)
B2 cos (2?mt)
If we multiply the power by our modulation
frequency in an electronic mixer and average over
several cycles, only the AB cos (?mt) term
will remain. But this term is linear in A! We
now have a correction signal for our length
controls, and a linearly-sensitive signal for GWs
in the arms. This is called heterodyning, and is
used frequently in radio applications.
45
Length sensing and control

• Each optic has five OSEMs (magnet and coil
  assemblies), four on the back, one on the side

• The magnet occludes light from the LED, giving
  position
• Current through the coil creates a magnetic
  field, allowing mirror control

46
Predicted LIGO sensitivity

• Sensitivity expressed as a function of frequency
• Optimal sensitivity from 100-300 Hz
• Too high for most stochastic sources
• Corresponds to last 1/100th of a second of
  inspiral
• Many pulsars rotate in the hundreds of Hz

47
Residual gas in beam tube

• Air in the beam tubes can cause four different
  sources of noise
• refractive index fluctuations in gas cause
  variations in optical path, phase noise
• residual gas scatters light out of, then back
  into, beam phase noise
• Residual gas pressure fluctuations buffet
  mirror displacement noise
• Contamination low-loss optics can not tolerate
  surface dirt High
  circulating powers of 10-50 kW burns dirt onto
  optic surface

• requirement for vacuum in 4 km tubes (1 atm
  760 torr)
• H2 at 10-6 torr initial, 10-9 torr ultimate
• H2O at 10-7 torr initial, 10-10 ultimate
• Hydro-, flourocarbons lt 10-10 torr

48
LIGO cleaning/baking
The initial beam tube and all in-vacuum
components must be baked to release all absorbed
gasses. The vacuum system is so clean that it
can maintain a pressure of 10-7 torr with pumps
off!
49
LIGO vacuum equipment
A series of oil-based, molecular vane, and ionic
pumps bring the total pressure down to 10-9
torr. 4 diameter gate valves close off the test
mass chambers during in-vacuum installation, so
that the baked-out arms never see air again.
50
Seismic displacement noise

• Motion of the earth
• wind, volcanic/seismic activity, ocean tides,
  humans
• requires roughly 109 attenuation at 100 Hz
• 300 micron tidal motion, microseismic peak at
  0.16 Hz
• Approaches to limiting seismic noise
• careful selection of isolated sites
• active control systems (only microseismic peak
  for now)
• simple damped harmonic oscillators in series
• one or more low-loss pendulums for final
  suspension

51
Seismic isolation stacks
52
Active isolation
Support Tube Installation
Stack Installation
Coarse ActuationSystem
53
Thermal noise

• Thermal noise comes primarily from
• Vibration of the atoms in the test masses
• Violin modes of the suspension wire
• Cannot get rid of it!
• Thermal noise kT
• Vacuum conducts heat poorly
• Cannot cool mirrors without
  seismic short
• Vibration confined to
  normal modes

54
Fluctuation-dissipation theorem
The narrowness of the normal mode resonance
peak in frequency is described by the quality
factor, or Q value of the mode.
The larger the Q value, the less energy that
leaks into other frequencies in the form of
noise. This is called the fluctuation-dissipation
theorem. So we design our supports and mirrors
to have normal modes with high f and Q.
55
Pre-stabilized laser (PSL)
The laser is a large source of amplitude and
phase noise, so a great deal of effort goes into
stabilizing the beam in frequency and intensity.
56
Sources of high-frequency noise
Cavity pole Loss of sensitivity past the
frequency where more than ½ of a wavelength is
stored in the arm cavities.
Shot noise Random fluctuations of laser
intensity, scales as power-1/2
Sensitivity at high frequencies is dominated by
laser power.
57
Standard quantum limit
There is another noise source -- radiation
pressure fluctuations of the test mass position
due to momentum transfer from the incoming
photons. This scales as power1/2, the opposite of
shot noise! The point at which the two are equal
is called the standard quantum limit, and is
theoretically the sensitivity limit of our
interferometer.
For LIGO parameters, this limit is h 10-24 at
600 kW stored power. LIGO stored power will be
lt30 kW, so we are not there yet!
58
Environmental monitoring
The gravitational wave information is only one
channel of data. But we log thousands of
channels of environmental data as vetoes.

• Seismic sensors (seismometers, accelerometers,
  tiltmeters)
• Weather stations (temperature, humidity, wind
  speed and direction)
• Magnetometers
• Microphones
• Line voltage monitors
• Dust monitors
• Earthquake and lightning alarms

59
Environmental vetoes
This waterfall display shows power as a
function of time and frequency. Vertical streaks
shows a sudden burst of power similar streaks in
environmental channels allow us to veto the event.
60
Data acquisition
A typical data channel is sampled at 16 bits of
precision and 16 kHz. Thats 2 bytes x 16,000
32 KB for one channel! In all, LIGO generates
over 1 MB of data per second! Whole racks of
computers and electronics are dedicated to
processing, storing, and serving this data.
61
Matched filtering
Inspirals searches are conducted through matched
filtering. 687 different possible waveforms are
generated in software, and cross-correlated with
the data from all three interferometers. Matching
waveforms within 10 ms at all detectors are
stored in a database.
62
From Bulldozers to First Results
63
LIGO Sensitivity Livingston 4km Interferometer
May 01
First Science Run 17 days - Sept 02
Jan 03
Second Science Run 59 days - April 03
64
LIGO II?

• The need for LIGO II
• RD prototyping goals
• Better seismic isolation
• New mirror materials
• Different optical configuration
• LIGO III and beyond
• Cryogenics
• Beating the quantum limit
• Reflective interferometers
• Non-IFO experiments
• ALLEGRO
• LISA

65
LASTI tour
The LIGO Advanced System Test Interferometer is
an engineering prototype for new methods of
reducing the seismic wall.
66
Active control of SEI system
Coarse hydraulic actuators in air
Optical table
Sensors seismometers, relative-position sensors
Actuators EM non-contacting forcers
Two active stages cages, masses, springs, S/A
pairs. All DOF under active control.
67
Thermal lensing
Fused silica does not radiate heat well, and our
laser deposits a lot of heat! This causes uneven
heating of the mirror, whose optic properties
then become a function of position. This is bad
if the beam translates a bit across the face of
the test mass, we will see a phase shift. This
problem is called thermal lensing. How to solve
it?
68
Two solutions to thermal lensing
69
Advanced LIGO and beyond

• The need for LIGO II
• RD prototyping goals
• Better seismic isolation
• New mirror materials
• Different optical configuration
• LIGO III and beyond
• Cryogenics
• Beating the quantum limit
• Reflective interferometers
• Non-IFO experiments
• ALLEGRO
• LISA

70
The need for Advanced LIGOIncreased event rate

• X10 in sensitivity x1000 volume searched
• LIGO 0.3-3 inspirals/year
• Adv. LIGO 300-3000 inspirals/year
• Factor of ten improvement needed at all
  frequencies

71
The need for Advanced LIGODetection vs.
astronomy
If we are just sensitive enough for detection of
the gravitational wave, we will not have enough
resolution to study the shape of the wave. With
greater sensitivity, we can learn new astronomy
by drawing conclusions about general relativity
from the waveform.
72
Prototype IFOs

• 40 meter (Caltech)
• full engineering prototype for optical and
  control plant for LIGO II
• Thermal Noise Interferometer (TNI, Caltech)
• measure thermal noise in LIGO II test masses
• LIGO Advanced Systems Testbed IFO (LASTI, MIT)
• full-scale prototyping of LIGO II seismic
  isolation suspensions
• Engineering Test Facility (ETF, Stanford)
• advanced IFO configs (Sagnac)
• 10 meter IFO at Glasgow prototype optics and
  control of RSE
• TAMA 30 meter (Tokyo) Advanced technologies

• Two main goals of prototyping
• Thoroughly test and understand new interferometer
  technologies
• Minimize transition time to Advanced LIGO at main
  sites

73
Seismic Attenuation System (SAS)
The heart of the SAS tower is a cascading series
of mechanical filters with a resonance frequency
of as low as 60 mHz.
74
Thermal noise issues

• Thermal noise is poorly understood were not
  entirely sure that we are estimating it
  correctly.
• The magnets and wire standoffs attached to our
  test masses ruin the Q value like gum on a bell.
• Ultimately, we are limited by the Q of the
  material in the test masses. Is there something
  better out there?

75
Thermal Noise Interferometer (TNI)

• LIGO laser power, stabilization
• High finesse cavities (105!)
• Short arms for low loss, higher finesse
• Expose thermal noise curve
• Test new test mass materials

76
Thermal Noise Measurement in Japan
77
GEO multiple pendulum design
The GEO multiple pendulum moves the magnets and
wire standoffs to an intermediate piece of fused
silica. Silica ribbons are chemically bonded to
the two masses, leaving the Q of the lower mass
unaffected.
Fused silica fibers
78
Sapphire mirrors
Sapphire offers a factor of ten better Q, as well
as better thermal conductivity than fused
silica. Research is currently devoted to growing,
machining, polishing, and testing.
79
Arm cavity parameters and LIGO sensitivity
As rITM is increased, Garm is increased, fpol-arm
is decreased.
fpol-arm
We wish to control Garm and fpol-arm
independently to optimize shot noise curve
80
The signal recycling mirror
We add a signal recycling mirror (SM) at the
asymmetric output port. This forms a compound
mirror with the input test masses (ITMs). We can
set this compound cavity to be resonant for the
beats between the carrier frequency and our
expected signal frequency.
81
Tuning the signal response
By adjusting the value of (fcarrfsig), we can
resonantly extract the signal at certain
frequencies, giving us a dip in sensitivity
rCC
rITM
RSE
tuned (narrow band)
RSE
SR
SR
82
Using DR to optimize sensitivity
Now we can independently tune hDC and fpolarm to
optimize sensitivity (eg, hug the thermal noise
curve)
83
The Caltech 40m Prototype
The 40m is a controls and engineering prototype
for signal recycling, and a testbed for Advanced
LIGO innovations.
84
Advanced LIGO control scheme
Adding an extra cavity length to control requires
a second modulation frequency and much more
complicated combinations of signals.
85
AdvLIGO predicted noise curves
Estimated beginning of installation 2006
86
LIGO III -- Cryogenics
The Large-scale Cryogenic Gravitational-wave
Telescope (LGCT) in Japan will link test masses
to a liquid helium tank through sapphire fibers
and metal springs.
87
The polarization Sagnac IFO

• All reflective optics to minimize thermal
  distortions
• Common path for interfering beams
• Grating beam splitter (double-pass, to null
  dispersion)
• Delay line arms
• Heroic efforts to minimize noise due to scattered
  light
• Polarization allows the light to exit the IFO at
  the symmetric port of the beam splitter
• Many clever tricks to ensure robust control, low
  noise

88
Defeating the quantum limit the speed meter
Theorists are exploring ways to defeat the
standard quantum limit of sensitivity. One method
involves measuring the velocity of the test
masses rather than position, such as with this
apparatus. The sloshing of information is
analogous to two pendula coupled by a weak
spring. The tricky problem how to control the
lengths if you do not know the positions?
Laser
High refl.
89
ALLEGRO
90
The Laser Interferometer Space AntennaLISA
The center of the triangle formation will be in
the ecliptic plane 1 AU from the Sun and 20
degrees behind the Earth.
Three spacecraft in orbit about the sun,
with 5 million km baseline
91
LISA orbit
The orbit of the triangle of spacecraft tumbles
as it orbits the sun, to be sensitive to all
directions in the sky, and to even out the
thermal load (from the sun) on the three
spacecraft.
92
LISA Spacecraft
93
Sensitivity bandwidth
Storage time L/c 5 x 106 m ? 3 x 108 m/s
0.017 s Thus the peak sensitivity for LISA
will be on the order of 10-2 Hz, completely
separate from the LIGO band. There are so many
sources here that we expect LISA to be confusion
limited, and most theoretical effort is going
toward disentangling signals.
94
BIG science!

• 180 collaborators in LIGO alone!
• Other interferometers
• GEO, VIRGO, TAMA, AIGO
• Future interferometry RD
• 40m, SAS, TNI, Sagnac, LCGT, speed meter,
  Glasgow, Gingin
• Other types of detectors
• Bar detectors, LISA, who knows what else?
• Necessary fields
• Relativity, mechanical engineering, vacuum
  engineering, optics, statistical mechanics,
  solid-state physics, material science, quantum
  mechanics, electrical engineering, computer
  science
• No lack of things to do! Interested?

95
http//www.ligo.caltech.edu