1. LIGO e la Sfida delle Inafferrabili Onde Gravitazionali
Laura Cadonati
Massachusetts Institute of Technology
LIGO Scientific Collaboration
Trento, 21 Febbraio 2007
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2. Newton’s Law of Universal Gravitation (1686)
Mechanics [F=ma] and the Universal law of gravitation [centripetal acceleration a=GM/d2] explained various puzzles of the time:
Why things fall
Orbit of planets and comets
Tides
Perturbation of the moon’s motion due to the gravitational attraction of the sun
BUT:
The gravitational field is static
The attraction between two masses
is instantaneous action at a distance
what mechanism produces the mysterious force of attraction in Newton’s theory?
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3. Einstein’s Vision: General Relativity (1916)
Gravity is not a force,
but a property of space-time
Smaller masses travel toward larger masses, not because "attracted" by a mysterious force, but because they travel through space that is warped by the larger object.
"Mass tells space-time how to curve,
and space-time tells mass how to move.“
John Archibald Wheeler
Einstein’s Equations:
When matter moves, or changes its configuration, its gravitational field changes. This change propagates outward as
a ripple in the curvature of space-time: a gravitational wave.
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4. Newton’s Universal Gravitation
action at a distance
Einstein’s General Relativity
information is carried by a gravitational wave traveling at the speed of light
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5. A New Probe into the Universe
Radio
x-ray
Gravitational Waves will give us a different, non electromagnetic view of the universe, and open a new spectrum for observation.
This will be complementary information, as different from what we know as hearing is from seeing.
CMB
g-ray IR
GRBs
EXPECT THE UNEXPECTED!
Gravitational Waves carry information from the bulk motion of matter.
With them we can learn the physics of black holes, spinning neutron stars, colliding massive bodies, and gain further insights in the early universe.
GW sky??
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6. Astrophysics with E&M vs Gravitational WavesGW
Accelerating charge
Accelerating aspherical mass
Wavelength small compared to sources  images
Wavelength large compared to sources  no spatial resolution
Absorbed, scattered, dispersed by matter
Very small interaction; matter is transparent
Frequency > 10 MHz and up
Frequency < 10 kHz
Dipole Radiation, 2 polarizations
(up-down and left-right)
Quadrupole Radiation, 2 polarizations
(plus and cross)
There are some important differences between light or radio waves and gravitational waves.
Light waves move through space and time as oscillations of electric and magnetic fields. The fields have directions that are perpendicular to the direction of the wave’s motion. A light wave coming toward an observer has fields that oscillate to the left and right, or up and down, or a mix of the two directions. This direction of oscillation of the fields, or polarization, determines how the wave interacts with matter.
An electric charge placed at various points along the wave shown above will be forced either to the left and right or up and down depending on the polarization of the wave. The wave’s electric field causes electrons in an antenna to move back and forth along the antenna when it is aligned with the polarization of the wave. This generates an electrical signal which a radio can use to produce sound.
Just as light waves have two polarizations, horizontal and vertical, gravitational waves also have two polarizations. These are vertical-horizontal, like an addition symbol "+," and at 45 degrees to these directions, like an "x."
A small mass placed at various points along the gravitational wave shown above will be stretched along one axis and squeezed along the perpendicular axis, then one-half cycle later the reverse occurs and the axis that was squeezing now stretches while the stretching axis squeezes.
plus
cross
Very different information, mostly mutually exclusive
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7. of the Existence of GWs:
We have Indirect Proof
of the Existence of GWs:
Pulsar System PSR (R.A. Hulse, J.H. Taylor Jr, 1975)
A 17/sec pulsar (neutron star in rapid rotation, emanating periodic pulses of electromagnetic radiation) orbits around a neutron star with period = 8 hours
Only 7kpc away
General Relativity prediction:
the orbital radius diminishes 3mm/orbit;
a collision is expected in 300 million years
Source:
The rotation period diminished 14 sec in ; energy loss
Optimum agreement with the predictions of general relativity: the energy is carried away by gravitational waves!
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8. …But They are Hard to Find: Space-Time is Stiff!
Einstein’s equations are similar to equations of elasticity: T = (c4/8πG)h
T = stress tensor, G = Curvature tensor
c4/8πG ~ 1042N is the space-time “stiffness” (energy density/unit curvature)
The wave can carry huge energy with miniscule amplitude:
h ~ (G/c4) (E/r)
For colliding 1.4M neutron stars in the Virgo Cluster: M r R
I =quadrupole mass distribution of source
M  1030 kg
R  20 km
F  400 Hz
r  1023 m
h ~10-21
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9. When a GW Passes Through Us…
…we “stretch and squash” in perpendicular directions at the frequency of the GW:
Time
Leonardo da Vinci’s
Vitruvian man
The effect is greatly exaggerated!!
If the Vitruvian man were 4.5 light years tall with feet on hearth and head touching the nearest star, he would grow by only a ‘hairs width’
To directly measure gravitational waves, we need an instrument able to measure tiny relative changes in length, or strain h=DL/L
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10. Suspended Mirrors as Free Masses
Interferometers:
Suspended Mirrors as Free Masses
Initial LIGO goal: measure difference in length to one part in 1021, or m
strain
h = DL/L
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11. Giant “Ears” Listen to the Vibrations of the Universe
Beam patterns:
F+,Fx : [-1, 1] F = F(t; a, d) Fx
average F+
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12. The LIGO Observatory Hanford (WA) 4 km + 2 km interferometers
Livingston (LA)
4 km interferometer
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13. Hanford, Washington
4 km
2 km
4 km
2 km
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14. Livingston, Louisiana
4 km
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15. The LIGO Scientific Collaboration
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16. An International Quest: Ground-Based Detectors
AURIGA
INFN Legnaro, Italy
1 Bar detector
ALLEGRO
Baton Rouge LA
Nautilus, Italy
1 Bar detector
Explorer, CERN
1 Bar detector
Interferometers
And Resonant Bars
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17. Initial LIGO Sensitivity Limits
Seismic Noise
test mass (mirror)
Thermal (Brownian) Noise
Residual gas scattering
Beam
splitter
LASER
Wavelength & amplitude fluctuations
Radiation pressure
photodiode
Quantum Noise
"Shot" noise
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18. Mitigation of Noise Sources
Photon Shot Noise:
10W Nd-YAG laser
Fabry Perot Cavities
Power Recycling
Thermal noise:
Use low loss materials
Work away from resonances
Thin suspension wires
Seismic noise:
Passive Isolation Stacks
Pendulum suspension
All under vacuum
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19. Interferometry Anti-Symmetric Strain Readout Ly ~ Lx ~ 4 km 14 kWRM BS
ITMX
ITMY
ETMY
ETMX
Reflected
Port
Anti-Symmetric
Pickoff Ly Lx lx
Input
Beam ly
Ly ~ Lx ~ 4 km
ly ~ lx ~ 9 m
Strain
Readout
(AS_Q)
∝ (Ly-Lx)
14 kW
6 W
250 W
Fabry-Perot cavities: light makes ~ 100 bounces
Power recicling: another factor 40 in power
~0.2 W
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20. Vacuum for a Clear Light Path
LIGO beam tube (1998)
1.2 m diameter - 3mm stainless steel
50 km of weld
Corner Station
20, torr; earth’s largest high vacuum system
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21. Suspended Mirrors 10 kg Fused Silica, 25 cm diameter and 10 cm thick
0.3mm steel wire
Local sensors/actuators for damping and control forces
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22. Passive Seismic Isolation System
Tubular coil springs with internal constrained-layer damping, layered with reaction masses
Isolation stack in chamber
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23. Active Seismic Pre-Isolation for a Special Livingston Problem: Logging
RMS motion in 1-3 Hz band
The Livingston Observatory is located in a pine forest popular with pulp wood cutters
Spiky noise (e.g. falling trees) in 1-3 Hz band creates dynamic range problem for arm cavity control
10-6
night
day
Livingston
10-7
Displacement (m)
Hanford
10-8
The installation of HEPI (Hydraulic External Pre-Isolator), for active feed-forward isolation (Advanced LIGO technology) has sensibly improved the stability of Livingston: can lock in day time!
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24. Despite some obstacles along the way…
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25. …LIGO meets its experimental challenges
the design sensitivity predicted in the 1995 LIGO Science Requirements Document was reached in 2005
S2: Feb.- Apr. 2003
59 days BNS reach ~ 1Mpc
S3: Oct. ‘03 - Jan. ‘04
70 days BNS reach ~ 3Mpc
Science Requirement. document (1995)
S1: Aug. - Sep. 2002
17 days BNS reach ~100kpc
S4: Feb. - Mar. 2005
30 days BNS reach ~ 15Mpc
S5: Nov 2005 – Current
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26. LIGO Hanford control room
Science Run 5
S5: started Nov 2005 and ongoing
Goal: 1 year of coincident live-time
LIGO Hanford control room
31 Mar 2006 – S5
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27. Science with LIGO: Sources Lurking in the Dark
Binary systems
Neutron star – Neutron star
Black hole – Neutron star
Black hole – Black hole
“Burst” Sources
Supernovae
Gamma ray bursts
Residual Gravitational Radiation
from the Big Bang
Cosmic Strings
Periodic Sources
Rotating pulsars
?????
BANG!
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28. Binary Neutron Stars: a Measure of Performance
The inspiral waveform for BNS is known analytically from post-Newtonian approximations.
We can translate strain amplitude into (effective) distance.
1 parsec = 3.26 ly
10 Mpc = 33 Mly
S5 BBH horizon distance peaks at 25+25, 130 Mpc => range ~ 50 Mpc ~150 Mly
Range: distance of a M binary, averaged over orientation/polarization
Predicted rate for S5: 1/3year (most optimistic), 1/30years (most likely)
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29. Astrophysical Sources: Binary Inspirals
S5 binary neutron star horizon
Credits: John Rowe Animation
Colliding black hole movie downloaded from the NASA web site:
This visualization shows what Einstein envisioned. Researchers crunched Einstein's theory of general relativity on the Columbia supercomputer at the NASA Ames Research Center to create a three-dimensional simulation of merging black holes. This was the largest astrophysical calculation ever performed on a NASA supercomputer. The simulation provides the foundation to explore the universe in an entirely new way, through the detection of gravitational waves. (7.4 Mb - no audio). Credit:Henze, NASA
R. Powell
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S5 binary black hole horizon
Simulation of gravitational waves produced by colliding black holes. Credit:Henze, NASA

30. Astrophysical Sources: Bursts?
Uncertainty of waveforms complicates the detection  minimal assumptions, open to the unexpected
For sine-gaussians:
E_GW is proportional to r^2*f^2*hrss^2
S5 sensitivity:
~0.1M from 20MPc at 153 Hz
Swift/
HETE-2/
IPN/
INTEGRAL
RXTE/RHESSI
LIGO-LHO
LIGO-LLO
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31. Astrophysical Sources: Stochastic Background
Cosmological background: Big Bang and early universe
Astrophysical background: unresolved bursts
NASA, WMAP
cosmic GW background
CMB (10+12 s)
S5 sensitivity:
Cosmic GW background limits expected to be near GW~10-5
below the BBN limit!
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32. Landscape (W0) Log(WGW) Log (f [Hz]) -2 Pulsar Timing-2
Pulsar
Timing
LIGO S4: Ω0 < 6.5x10-5
(newest)
BB Nucleo-
synthesis -4
Cosmic strings
(W0) -6
Initial LIGO, 1 yr data
Expected Sensitivity
Log(WGW) -8
Log
CMB
Adv. LIGO, 1 yr data
Expected Sensitivity
~ 1x10-9
-10
Pre-BB model
Accuracy of big-bang nucleosynthesis model constrains the energy density of the universe at the time of nucleosynthesis  total energy in GWs is constrained integral_f<1e-8 d(ln f) Omega_GW
Pulsar timing  Stochastic GWs would produce fluctuations in the regularity of msec pulsar signals; residual normalized timing errors are ~10e-14 over ~10 yrs observation
Stochastic GWs would produce CMBR temperature fluctuations (Sachs Wolfe effect),
Measured Delta_T constrains GW amplitude at very low frequencies
Kamionkowski et al. (astro-ph/ )
Use Lyman-alpha forest, galaxy surveys, and CMB data to constrain CGWBkgd, i.e. CMB and matter power spectrums. Assume either homogeneous initial conditions or adiabatic. Use neutrino degrees of freedom to constrain models.
Adiabatic blue solid  CMB, galaxy and Lyman-alpha data currently available (Kamionkowski)
Homogeneous blue dashed  CMB, galaxy and Lyman-alpha data currently available
Adiabatic CMBPol (cyan solid)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data
Homogeneous CMBPol (cyan dashed)  CMB, galaxy and Lyman-alpha data when current CMB is replaced with expected CMBPol data
-12
Inflation
-14
Slow-roll
EW or SUSY
Phase transition
Cyclic model
-18
-16
-14
-12
-10 -8 -6 -4 -2 2 4 6 8 10
Log
(f [Hz])
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33. Continuous Waves Preliminary S5 expectations:
J. Creighton
M. Kramer
Preliminary
Wobbling neutron stars
Pulsars with mountains
Dana Berry/NASA
Credits:
A. image by Jolien Creighton; LIGO Lab Document G Z.
B. image by M. Kramer; Press Release PR0003, University of Manchester - Jodrell Bank Observatory, 2 August 2000.
C. image by Dana Berry/NASA; NASA News Release posted July 2, 2003 on Spaceflight Now.
Rotating stars produce GWs if they have asymmetries or if they wobble.
Accreting neutron stars: Neutron stars spin up when they accrete matter from a companion Observed neutron star spins “max out” at ~700 Hz. Gravitational waves are suspected to balance angular momentum from accreting matter
Wobbling neutron stars: The wobbling (or precession) causes the rotation axis of the pulsar to follow a circle-like motion in time (see yellow and green axes at different epochs). The motion is very much like the wobble of a top or gyroscope. As a result, we see the cone-like lighthouse beam of the radio pulsar under different angles, resulting in the observed changes in pulse shape and arrival times. (Image by M. Kramer)
Surface asymmetries in neutron stars: a “mountain”, mm high
Observed spindown can be used to set strong indirect upper limits on GWs.
GWs (or lack thereof) can be used to measure (or set up upper limits on) the ellipticities of the stars.
There are many known pulsars (rotating stars!) that produce GWs in the LIGO frequency band (40 Hz-2 kHz).
Targeted searches for 73 known (radio and x-ray) systems in S5: isolated pulsars, binary systems, pulsars in globular clusters…
There are likely to be many non-pulsar rotating stars producing GWs.
All-sky, unbiased searches; wide-area searches.
Search for a sine wave, modulated by Earth’s motion, and possibly spinning down: easy, but computationally expensive!
S5 expectations:
Best limits on known pulsars ellipticities at few x10-7
Beat spin-down limit on Crab pulsar
Hierarchical all-sky/all-frequency search
Accreting neutron stars
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34. The Einstein@home Project
Thur Nov :14 UTC
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35. How do we avoid fooling ourselves
How do we avoid fooling ourselves? Seeing a false signal or missing a real one
Require at least 2 independent signals:
e.g. coincidence between interferometers at 2 sites for inspiral and burst searches, external trigger for GRB or nearby supernova.
Apply known constraints:
Pulsar ephemeris, inspiral waveform, time difference between sites.
Use environmental monitors as vetos
Seismic/wind: seismometers, accelerometers, wind-monitors
Sonic/acoustic: microphones
Magnetic fields: magnetometers
Line voltage fluctuations: volt meters
Understand the detector response:
Hardware injections of pseudo signals (actually move mirrors with actuators)
Software signal injections
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36. LIGO timeline S5 S6 ~2 years 3.5 yrs4Q
‘05
‘06
‘07
‘08
‘10
‘09
Adv
LIGO
~2 years
Other interferometers in operation (GEO and/or Virgo)
3.5 yrs
The first science run of LIGO at design sensitivity is in progress
Hundreds of galaxies now in range for
1.4 M neutron star binary coalescences
Enhancement program
In 2009 ~8 times more galaxies in range
Advanced LIGO
Construction start expected in FY08
1000 times more galaxies in range
Expect ~1 signal/day - 1/week in ~2014
100 million light years
LIGO today
Advanced LIGO
~2014
Enhanced LIGO
~2009
The science from the first 3 hours of Advanced LIGO should be comparable to 1 year of initial LIGO
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37. Advanced LIGO: President Requests FY2008 Construction Start
Seismic ‘cutoff’ at 10 Hz
10-22
10-23
Quantum noise
(shot noise + radiation pressure) dominates at most frequencies
10-24
10 Hz
100 Hz
1 kHz
10 kHz
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38. Science Potential of Advanced LIGO
Binary neutron stars:
From ~20 Mpc to ~350 Mpc
From 1/30y(<1/3y) to 1/2d(<5/d)
Binary black holes:
From ~100Mpc to z=2
Known pulsars:
From e = 3x10-6 to 2x10-8
Stochastic background:
From ΩGW ~3x10-6 to ~3x10-9
Kip Thorne
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39. These are exciting times!
We are searching for GWs at unprecedented sensitivity.
Early implementation of Advanced LIGO techniques helped achieve goals:
HEPI for duty-cycle boost
Thermal compensation of mirrors for high-power operation
Detection is possible, but not assured for initial LIGO detector
We are getting ready for Advanced LIGO
Sensitivity/range will be increased by ~ 2 in 2009 and another factor of 10 in ~2014 with Advanced LIGO
Advanced LIGO will reach the low-frequency limit of detectors on Earth’s surface given by fluctuations in gravity at surface
Direct observation: Not If, but When
LIGO detectors and their siblings will open a new window to the Universe: what’s out there?
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