Gravitational Wave Detection

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Gravitational Wave Detection 1Gravity waves
and test masses

• Peter Saulson
• Syracuse University

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Plan for the week

• Overview
• How detectors work
• Precision of interferometric measurement
• Time series analysis, linear system
  characterization
• Seismic noise and vibration isolation
• Thermal noise
• Fabry-Perot cavities and their applications
• Servomechanisms
• LIGO
• LISA

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A set of freely-falling test particles
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Electromagnetic wave moves charged test bodies
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Gravity wave distorts set of test masses in
transverse directions
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Comparison table, EM vs GW
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Transmitters of gravitational waves solar mass
objects changing their quadrupole moments on msec
time scales
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Gravitational waveform lets you read out source
dynamics

• The evolution of the mass distribution can be
  read out from the gravitational waveform
• Coherent relativistic motion of large masses can
  be directly observed.

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Why not a Hertz experiment?

• Hertz set up transmitter, receiver on opposite
  sides of room.
• Two 1-ton masses, separated by 2 meters, spun at
  1 kHz, has
• kg m2s-2.
• At distance of 1 l 300 km,
• h 9 x10-39.
• Not very strong.

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Binary signal strength estimate
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Gravity wave detectors

• Need
• A set of test masses,
• Instrumentation sufficient to see tiny motions,
• Isolation from other causes of motions.
• Challenge
• Best astrophysical estimates predict fractional
  separation changes of only 1 part in 1021, or
  less.

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Resonant detector (or Weber bar)
A massive (aluminum) cylinder. Vibrating in its
gravest longitudinal mode, its two ends are like
two test masses connected by a spring.
Cooled by liquid He, rms sensitivity at/below
10-18.
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An alternative detection strategy

• Tidal character of wave argues for test masses as
  far apart as practicable. Perhaps masses hung as
  pendulums, kilometers apart.

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Sensing relative motions of distant free masses
Michelsoninterferometer
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A length-difference-to-brightnesstransducer
Wave from x arm.
Light exiting from beam splitter.
Wave from y arm.
As relative arm lengths change, interference
causes change in brightness at output.
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Laser Interferometer Gravitational Wave
Observatory
4-km Michelson interferometers, with mirrors on
pendulum suspensions, at Livingston LA and
Hanford WA. Site at Hanford WA has both 4-km and
2-km. Design sensitivity hrms 10-21.
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Other large interferometers

• TAMA (Japan), 300 m
• now operational
• GEO (Germany, Britain), 600 m
• coming into operation
• VIRGO (Italy, France) 3 km
• construction complete, commissioning has begun

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Gravity wave detection challenge and promise

• Challenges of gravity wave detection appear so
  great as to make success seem almost impossible.
• from Einstein on ...
• The challenges are real, but are being overcome.

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Einstein and tests of G.R.

• Classic tests
• Precession of Mercurys orbit already seen
• Deflection of starlight 1 arcsec, O.K.
• Gravitational redshift in a star 10-6, doable.
• Possible future test
• dragging of inertial frames, 42 marcsec/yr,
  Einstein considered possibly feasible in future
• Gravitational waves no comment!

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Why Einstein should have worried about g.w.
detection

• He knew about binary stars, but not about neutron
  stars or black holes.
• His paradigm of measuring instruments
• interferometer (xrms l /20, hrms10-9)
• galvanometer (qrms10-6 rad.)
• Gap between experimental sensitivity and any
  conceivable wave amplitude was huge!

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Gravitational wave detection is almost impossible

• What is required for LIGO to succeed
• interferometry with free masses,
• with strain sensitivity of 10-21 (or better!),
• equivalent to ultra-subnuclear position
  sensitivity,
• in the presence of much larger noise.

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Interferometry with free masses

• Whats impossible everything!
• Mirrors need to be very accurately aligned (so
  that beams overlap and interfere) and held very
  close to an operating point (so that output is a
  linear function of input.)
• Otherwise, interferometer is dead or swinging
  through fringes.
• Michelson bolted everything down.

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Strain sensitivity of 10-21

• Why it is impossible
• Natural tick mark on interferometric ruler is
  one wavelength.
• Michelson could read a fringe to l/20, yielding
  hrms of a few times 10-9.

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Ultra-subnuclear position sensitivity

• Why people thought it was impossible
• Mirrors made of atoms, 10-10 m.
• Mirror surfaces rough on atomic scale.
• Atoms jitter by large amounts.

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Large mechanical noise

• How large?
• Seismic xrms 1 mm.
• Thermal
• mirrors CM 3 x 10-12 m.
• mirrors surface 3 x 10-16 m.

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Finding small signals in large noise

• Why it is impossible
• Everyone knows you need a signal-to-noise ratio
  much larger than unity to detect a signal.

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Science Goals

• Physics
• Direct verification of the most relativistic
  prediction of general relativity
• Detailed tests of properties of grav waves
  speed, strength, polarization,
• Probe of strong-field gravity black holes
• Early universe physics
• Astronomy and astrophysics
• Abundance properties of supernovae, neutron
  star binaries, black holes
• Tests of gamma-ray burst models
• Neutron star equation of state
• A new window on the universe

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Freely-falling masses
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Distance measurement in relativity

• is done most straightforwardly by measuring
  the light travel time along a round-trip path
  from one point to another.
• Because the speed of light is the same for all
  observers.
• Examples
• light clock
• Einsteins train gedanken experiment

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The space-time interval in special relativity

• Special relativity says that the
  intervalbetween two events is invariant (and
  thus worth paying attention to.)
• In shorthand, we write it aswith the Minkowski
  metric given as

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Generalize a little

• General relativity says almost the same thing,
  except the metric can be different.
• The trick is to find a metric that
  describes a particular physical situation.
• The metric carries the information on the
  space-time curvature that, in GR, embodies
  gravitational effects.

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Gravitational waves

• Gravitational waves propagating through flat
  space are described by
• with a wave propagating in the z-direction
  described by
• Two parameters two polarizations

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Plus polarization
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Cross polarization
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Solving for variation in light travel time

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