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					The Gravity Wave Hunt

    LIGO and LISA

• According to Einstein’s theory of general relativity, the force of
  gravity is due to curvature of space-time itself. Such curvature is
  caused by the presence of mass in our universe.

• In a similar way as accelerating electric charges produce
  electromagnetic waves, massive objects accelerating in space-
  time produce gravitational waves. For gravitational waves, the
  massive objects must accelerate in a manner that is not
  spherically or cylindrically symmetric. When this occurs, ripples
  in space-time spread outward, just like ripples in a puddle.

• Gravitational radiation is the energy carried by these waves.

• The magnitude of most gravitational waves is incredibly small
• For instance, the gravitational waves produced by the earth
  orbiting the sun are on the order of  1 1.7 x1010 m
• Considering that objects of interest are located light years
  away (large r), the magnitude decreases to ≈10-26m for systems
  like that of the earth and the sun
• Systems of binary neutron stars, binary black holes, and
  supernovae (assumed to be asymmetric), should produce
  radiation of 1020 times greater than that of the earth/sun.
  However, these tend to be far away.
• The largest magnitude waves expected near earth should be on
  the order of 10-21m

• Although gravitational radiation has not yet been directly
  observed, it has been indirectly shown to exist through the
  Hulse-Taylor observations of the binary pulsar system PSR1913+16

• The system has been observed
  since its discovery in 1974,
  and the evolution of its orbit
  is in complete agreement with
  the loss of energy due to
  gravitational waves.

• Consider a perfectly flat region in space, with a few motionless
  particles lying in a plane. As a gravitational wave passes
  through, perpendicular to the plane, the particles will oscillate
  in a manner depicted by the diagrams.

                                            • The area enclosed by
                                              the test particles
                                              remains the same,
                                              and there is no
                                              motion along the
                                              direction of

• The most simple type of gravitational wave detector is called a
  Weber bar
                                              • Should a
• It consists of a                               gravitational wave
  solid piece of                                 pass through this
  metal, equipped                                bar, it is possible it
  with electronics                               would hit the bar at
  designed to                                    its resonance
  detect any                                     frequency,
  vibrations                                     effectively
                                                 amplifying the wave.
  Laser Interferometer Gravitational Wave

• A more sensitive apparatus designed to detect gravitational
  waves is the laser interferometer, involving separate masses placed
  several kilometers apart, acting as two ends of a bar.

• Several laser interferometers exist, but LIGO is probably the
  most prominent at this time

• LIGO is a joint project run by MIT and Caltech.
• There are three branches of LIGO, one in Livingston,
  Louisiana, and two near Richland, Washington.
                                           • The distance
                                             between the two
                                             sites is about 3000
                                             km, which is
                                             important because
                                             it allows for the
                                             use of
                                             triangulation to
                                             determine where
                                             the waves are
                                             coming from.
                           LIGO cont’d
• The basic setup of the three observatories consists of two
  vacuum tubes, 2 to 4 km in length. The two arms are at 90
  degree angles to each other.

• The primary interferometer is composed of mirrors suspended
  at each of the corners of the L, a laser emits a 10 watt beam,
  and hits a beam splitter at the vertex of the L.

• The two beam paths run
  down each arm of the L,
  and are kept out of
  resonance. so the light
  waves interfere destructively as
  they travel through the
  cavity, and no light hits the
• As was mentioned before, when a gravitational wave passes by,
  the space-time in the local area is altered.

• Depending on the polarization of the wave, and where it is
  coming from, this can result in the length of the cavities

• The change in length of the cavity will knock it out of
  resonance, and the light in the cavity will be out of phase with
  the incoming light.

• When a gravitational wave passes through the interferometer,
  the distances along the arms of the interferometer are changed,
  and the beams become less out of phase, and light will hit the
  photodiode, creating a current that can is recorded as a signal.
• Noise sources include seismic waves, cars and trains passing by
  the detector, falling logs and even waves crashing on the shore
  hundreds of miles away

• These all cause similar effects to real gravitational wave signals,
  and one of the pains of this type of setup is trying to reduce the
  motions of the mirrors due to noise.

• One other limitation on all detectors is shot noise, which occurs
  because the laser being used is composed of photons, and there
  are random fluctuations associated with the intensity of the
  beam (the number of photons arriving in a given time interval)
     Laser Interferometer Space Antenna

• LISA is a work in progress

• It will consist of three space-based satellites which will act as
  vertices of a triangular interferometer

• Due for launch in 2015, it should provide data for 5 years
• The main difference between LISA and ground-based
  interferometers is that LISA should observe gravitational waves
  in the 10-4 to 10-1 Hz bands, as opposed to ground-based
  interferometers which, when performing optimally, will
  observer in 101 to 103 Hz frequency bands

• LISA is thus designed to monitor binary stellar objects (such as
  neutron stars or black holes) over long periods as they orbit
  each other (on the order of months or years).

• LIGO (and other ground-based observatories) and LISA
  complement each other well as LISA can see long-duration
  radiation, possibly even predicting a short burst of radiation
  that could be recorded by LIGO
• LISA’s design presents many technical challenges
   – The three spacecraft are held in an equilateral, triangular
     formation, each separated by 5 million kilometres. Once
     stabilised, the separation between each will vary at most by
     10km, with 2mm/s variation in velocity
   – This is accomplished using precise, delicate booster control
• Each spacecraft contains a small, highly-polished test mass
   which is free-floating in gravity. The spacecraft tracks this mass
   with a precision of a few nanometres.
• The test masses are highly polished to also play a part in
   reflecting the laser where appropriate
• Just like LIGO, LISA employs laser interferometery to detect
   slight changes in distance between the satellites
•Each satellite acts as
the base of an
interferometer so the
system actually consists of
several interferometers.
The results of each system
can be combined using
linear algebra to provide
better precision
• The spacecraft will trail the earth in its solar orbit by about 20
  degrees, or about 50 million kilometres
• This distance allows for a minimization of radiation and orbit
  distortions at a minimum, while still retaining an acceptable
  communication rate
• At low frequencies, the resolution of LISA is dominated by
  temperature fluctuations.

• At optimal frequencies, the resolution is highest but is
  ultimately limited by an affect called shot noise

• At higher frequencies, the resolution is dominated by the
  antenna transfer noise, which is proportional to the frequency.
The detection of gravitational waves would be a
milestone in the history of physics, but is it likely to
happen soon? In 2004, it was estimated that the
chances of a definite detection by 2010 was 1 in 6,
using ground-based observations.

If all goes well with LISA, it will definitely be able to
detect gravitational waves, if they are as theorized.
However, it is not clear how well how well LISA will
be able to pick up individual signals as LISA does not
offer any directional observation tools
•   LISA mission overview - A. Hammesfahr
•   LISA technology-concept, status, prospects – Karsten Danzmann