Gravitational Waves Generating Phenomena and Detection

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Gravitational WavesGenerating Phenomena and
Detection

• Marino Maiorino

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Table of Contents

• Basics of Gravitational Waves (GW)
• GWs propagation
• GWs generation
• Low Frequency Astrophysical Phenomena
• High Frequency Astrophysical Phenomena
• Basics of Gravitational Waves Detection
• Resonating Bar Detectorss
• Long Base Interferometers
• VIRGO-EGO
• Data Processing
• Space-Based Interferometers (LISA)

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Basics of Gravitational Waves (GW)

• Special Relativity time is the 4th dimension
• Through Minkowski formalism (metric tensor)

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Basics of Gravitational Waves (GW)

• General Relativity space-time structure linked
  to matter presence through the gravitational
  field
• Gravity is not a force, it is rather a bending of
  space-time straight lines are defined by the
  trajectories of free-falling objects

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Basics of Gravitational Waves (GW)

• In General Relativity space-time is flat no more
  another metric tensor must be used. In the
  weak-field hypothesis, this can be written as
• With a special, transverse and null-trace gauge,
  one obtains
• which is the wave equation for a perturbation of
  the metric tensor which propagates with speed c!

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GWs Propagation

• As in electrodynamics, let us study GWs
  propagation in the approx. of a multipole series
  of a delayed potential (hyp. source dim. ltlt
  wavelength)
• Monopole term dm/dt 0 for an isolated system
• Dipole term
• constant because of momentum conservation of an
  isolated system
• Gravitational magnetic momentum
• no contribution because of angular momentum
  conservation of an isolated system

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GWs Propagation

• First non-null term of the series is the
  quadrupole term
• United with the transverse and null-trace gauge,
  this lets us see a GW as made up of two
  independent polarizations

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GWs Propagation
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GWs Generation

• Lets derive the irradiated power from the
  quadrupole term
• This corresponds to an estimation of space-time
  distortion
• (R distance from source second derivative of
  quadrupole computed at time t R/c)
• You get strong GWs close to a source with
  inconstant variations in quadrupole momentum!

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GWs Generation

• Lets try to generate GWs in a lab two masses,
  1 ton each, 2 m apart, 1 kHz rotation
• hlab 2.610-33 m 1/R!

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GWs Generation

• Lets study it better for a two-stars system
• Whence you get

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GWs Generation

• In one picture

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Low Frequency Astrophysical Phenomena

• Coalescing binaries
• Two stars revolve one around the other and get
  closer as they dissipate gravitational power.
• In these conditions, you get big values of h
  (10-16) at too low frequencies (1 pHz)!
• When the two stars unite, on the other hand, you
  get h 10-21 between 10 and 1000 Hz up to 40
  Mpc!
• Note our galaxy diameter is 50 kpc only.

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High Frequency Astrophysical Phenomena

• Supernovae (SN)
• Star explosion ? HUGE mass acceleration. From
  pulsars population we deduce that rotating SNs
  are common ? HUGE quadrupole momentum variation.
• h 10-23 _at_ 500 Hz _at_ 15 Mpc
• Pulsar (I)
• Supernova remnant spinning like the hell. A solar
  mass of 10 km rotating (sometimes) in ms!
• h 10-26 _at_ 100 Hz _at_ 10 kpc. Small, but
  integrable in time as it is periodic.

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High Frequency Astrophysical Phenomena

• Pulsar (II)
• Pulsar with fellow star. Two pulsars revolving
  one around the other at a 20 km distance, would
  generate
• h 10-21 _at_ 400 Hz _at_ 15 Mpc!
• Black Holes (BH)
• Even bigger masses. Theoretical estimations say
  that for a BH of 1 M? (solar mass) one could
  have
• h 10-20 _at_ 1 kHz _at_ 1Mpc

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Basics of GWs Detection

• How to measure distortions of 1/1021? Einstein
  himself doubted it could have EVER be done.
• Pioneering work of Joseph Weber (1960)
  resonating bar detectors.
• Problems small effects and plenty of noises.
• SN 1987A in LMC (Large Magellan Cloud) was
  detectable for these devices but
• ALL of them were shut off for maintenance!

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Basics of GWs Detection
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Resonating Bar Detectors

• Lets monitor the normal vibration modes of an
  aluminum cylinder (through piezoelectric
  sensors).
• Sharp resonance (like diapason), but sensitivity
  confined to a narrow bandwidth (a few Hz) around
  the resonance frequency.
• An incident GW is supposed to excite such
  vibration modes.
• Primary drawback sensitive to signals with
  frequency close to the bar mechanical ringing
  frequency (1 kHz). They respond to the signal at
  their own frequency.

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Long Base Interferometers

• Present strategy monitoring the length of the
  arms of a Michelson interferometer of suitable
  length.

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Long Base Interferometers

• An incoming GW will stretch one interferometer
  arm and will shrink the other one
• The typical GW distortion (10-21) could cause a
  change of one fringe in the interference pattern
  on an interferometer in infrared light ( 1 µm
  wavelength) with arms of 51011 km!
• On a 500 km instrument, the change would be of
  10-9 fringes!

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Long Base Interferometers

• Does this formula actually mean the longer, the
  better?
• A light beam will stay in the instrument for a
  time t 2L/c, so that the measured length
  variation will be only
• Optimum length makes maximum dL. Its value is
• GW interferometers are antennas they are tuned
  on search frequencies!

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Long Base Interferometers

• Frequency limits for a GW interferometer
  detector
• Minimum frequency (earthbound) 10 Hz because of
  the seismic noise
• Minimum frequency (space bound) much lower
• Maximum useful frequency a few kHz (maximum
  frequency for astrophysical sources
• Lengths range from 8 to 8000 km (earthbound).
• Choice is made based on the sources you want to
  detect and the noise sources.

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VIRGO-EGO

• Detection band is centred around 625 Hz (minimum
  noise contribution), which means an
  interferometer with arms of 120 km!

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VIRGO-EGO

• Cascina, near
• Pisa, Italy
• But 120 km is too much even Earth curvature
  would affect the instrument!

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VIRGO-EGO

• 120 km can be also made by folding 40 times a 3
  km path Fabry-Perot cavities
• Fabry-Perot cavities rely on the interference of
  multiple reflected beams .

Erif
Etr
t1
r1
t2
r2
d
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VIRGO-EGO

• Fabry-Perot cavities
• Reflected phase gives signal to lock the cavity!
• So, FPs have to be insensitive to ANY noise (even
  seismic)!

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VIRGO-EGO

• Superattenuator (SA)
• A pendulum is a mechanical low-pass filter of the
  second order for solicitations to its suspension
  point.
• A simple expr. for the Transfer
• Function of an n-stage pendulum is

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VIRGO-EGO

• The Superattenuator (SA)

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Data Processing

• VIRGO is an active instrument!
• Interferometer, polarizers and photodiodes
  (Detector)
• Electronics (Reaction Filter)
• Superattenuator coils (Actuators)

D
F
A
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Space-Based Interferometers

• LISA (Laser Interferometric Space Antenna)
• ESA-NASA, launch in 2010
• Frequencies 0.1 mHz 0.1 Hz
• Two arms make a Michelson interferometer third
  arm measures another interferometric observable.
• Laser light of 1 µm, 1 W.
• Only a single pass in the arms.
• Disturbances forces from the Sun (fluctuations
  in radiation pressure, solar wind).
• The proof masses are free-floating within,
  shielded by and not attached to the spacecraft.
  The spacecraft is in a feedback loop with
  precision thrust control to follow the proof
  masses (drag-free tech.)
• SNR 1000 or more _at_ z 1