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General Relativity

Results from Interferometer Gravitaional Wave Detectors

Gravitational wave detectors have now been operating for over 40 years, but none to data have positively detected a gravitational wave source. What do you do with a null result? You calculate an upper limit on some aspect of your unseen source. For the current generation of Michelson interferometer gravitational wave detectors, these upper limits are too high to be constraining on current theories.

The most recent results are those associated with the S2 data run of LIGO, with additional experimental data from TAMA. The best data to date is from the S3 data run of LIGO, combined with the data from GEO 660, but results from this data have not yet been releases.

Inspiraling Binaries

The signal of an inspiraling binary system is a short-lived burst of gravitational waves as the binary system comes together to form a single neutron star or black hole. The limit one finds from not observing a burst of gravitational radiation is a limit on the rate at which such mergers occur per unit surveyed volume. For the LIGO S2 data run, the sensitivity enabled the detectors to sample a volume of approximately a cubic megaparsec. For an optimally-oriented neutron star binary system with each star having 1.4 solar masses, the observational limit for a signal to noise ratio of 8 is 1.8Mpc for the 4km instrument at Livingston, 0.9Mpc for the 4km instrument at Hanford, and 0.6Mpc for the 2km instrument at Hanford. By way of orientation, the radius of the Milky Way galaxy is about 15kpc, the two Magellanic Clouds, which are two nearby irregular galaxies, are 50 and 60kpc away, and the Andromeda galaxy (M31), a nearby spiral galaxy similar in size to our own, is 0.73 Mpc away. The LIGO instruments are therefore sampling the inner part of the Local Group of galaxies.

The researchers with LIGO prefer to state the inspiral rate as the number of inspirals per year per “Milky Way Equivalent Galaxy,” (MWEG), which is to say as the number of mergers per year per unit of mass equal to the mass of the Milky Way galaxy. From 355 hours of S2 data from the two instruments at Hanford and the instrument at Livingston, LA, and using a 90% confidence level, the LIGO researchers give a conservative upper limit on this rate of less than 50 per year per MWEG.

Known Pulsars

Many pulsars with well-known spin characteristics exist within the Milky Way galaxy; if these spinning neutron stars deviate from axisymmetry, so that they have a quadrupole term in their moment of inertia, or if they wobble as they spin, they will emit gravitational radiation. Because the spin characteristics of many of these stars are well-known, one can conduct a search for gravitational waves from these pulsars by concentrating on signals with frequencies that are twice the spin frequency.

The expectation is that the known pulsars are emitting gravitational radiation at below the sensitivity of LIGO even at its design goal sensitivity. Still, it is worth while to look. Analysis of the L2 data for 28 known radio pulsars, including the Crab pulsar, places upper limits on the amplitude of the gravitational waves emitted by each star, and on the maximum ellipticity of each star. Currently the upper limit on the gravitational radiation from the Crab pulsar is 30 times greater than that derived from the measured spin-down of the star.1 The improved sensitivity of the S3 data run and of future data runs will lower this upper limit to the spin-down upper limit.

Gamma-ray Burst

The long gamma-ray bursts, those that last from 1 to 1000 seconds, are associated with the supernovae of massive stars. If during the core collapse of a massive star the core spins rapidly and non-axisymmetrically, then the core will produce gravitational waves that can escape through the outer layers of the star to observers on Earth. Because gamma-ray bursts are the first manifestations of a supernova, the gravitational waves should arrive at Earth close in time with the gamma-ray, and well ahead of the time when the supernova becomes optically bright.

During the collection of S2 data the gamma-ray burst GRB 030329 was observed by gamma-ray satellites. This gamma-ray burst has a cosmological redshift of z = 0.1685, making it a close gamma-ray burst. Compared to the inspiraling neutron stars, which, at its most gravitationally radiant, is what a core collapse will be like, this is an extremely distant: of order 800 times the distance sampled in the inspiral study. Not surprisingly, therefore, it did not appear in the S2 data. The upper limit on the wave amplitude associated with this gamma-ray bursts corresponds to an energy of 105 solar masses, which is orders of magnitude larger than the mass of the progenitor.

Another search was conducted corresponding to gamma-ray bursts with durations of less than a second. These gamma-ray bursts form a second class of gamma-ray burst; their origin is unknown. The search turned up no gravitational wave signal.

Stochastic Background Waves

The interest in stochastic background gravitational waves is spurred by research into the early universe. We have few diagnostics of the conditions in the early universe. The microwave background is the oldest direct diagnostic of the early universe, while the initial elemental composition that is inferred from stellar observations is the oldest indirect diagnostic. Gravitational waves from much earlier times than were responsible for the early elemental composition and the microwave background should be able to reach Earth without being absorbed, providing a new direct diagnostic of conditions in the early universe. Current L2 data places an upper limit on the gravitational wave energy density in units of closure density per unit log frequency ( d ρgwc d log f ) of 0.01(8+7-3) h-2100 over the 50 to 300Hz range, here h100 is the Hubble constant in units of 100km s-1 Mpc-1. This value is currently well above the expected values.

1 The rate at which a pulsar's rotation rate slows sets an upper limit on the energy it is losing to gravitational radiation. It is an upper limit rather than a measure, because pulsars lose most of their energy through electromagnetic dipole emission; pulsars have strong magnetic fields, and because the star spins, the rotating magnetic field produces electromagnetic radiation.

2 When all of the nuclear fuel is exhausted at the center of a star, so that the center of the star begins to cool, the center of the star begins to collapse because of the weight of the outer layers of the star. This leads to an event called core collapse, which liberates massive amounts of gravitational potential energy. This energy release causes the star to explode in an event known as a supernova.

3 The universe is expanding, so that the galaxies are moving away from us; this is seen observationally as a shift to lower frequencies of the emission lines of the stars. This cosmological redshift is parameterized by the equation νo = νs/( 1 + z), where νo is the observed frequency of the line and νs is the frequency of the line at the source.

4 The rate of expansion of the universe is expressed in terms of a parameter H called the Hubble constant. Its value is uncertain, with observations placing it in the range from 55 to 75km s-1 Mpc-1. Locally, the ratio of a galaxy's velocity away from us to its distance from us is equal to Hubble's constant.

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