Figure 1 shows two components of a gravitational wave versus time
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An example of gravitational waveforms and the information they carry.
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Each gravitational wave has two waveforms, dimensionless functions of time called h+(t) and hx(t).
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The specific waveforms shown here are from the last few minutes or seconds of the spiraling together of a compact binary system (one made of two black holes, two neutron stars, or a black hole and a neutron star).
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By monitoring these waveforms, LIGO can allow researchers to determine the binary's distance from Earth r, the masses of its two bodies or, equivalently, their total mass M and reduced mass m, and their orbital eccentricity e, and orbital inclination to the line of sight i.
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To allow the determination of the eccentricity e, LIGO will measure the shapes of the individual waveform oscillations; note the shape shown on the upper right.
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For the determination of i (when e = 0 for pedagogic simplicity), LIGO will measure the ratio of the amplitudes, h+ and hx see the formula in the lower right.
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The parameters r, m and M determine (i) the waveforms' absolute amplitudes as they sweep past a frequency f:
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hamp proportional to mu M^2/3 r^-1 f^2/3;
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and (ii) the number of cycles n=f^2 (df/dt)^-1 that the waveforms spend near frequency f:
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n**alpha (mu M^2/3 f^5/3)^-1 .
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From hamp and n, LIGO can be used to determine r and mu M^2/3.
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From mu M^2/3, and from late-time post-Newtonian facets of the waveform (not shown here)
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or the frequency at which the inspiral terminates or both,
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LIGO can be used to deduce the individual value of mu and M.
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The simple inspiral waves shown here are modified at late times by post-Newtonian
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and then fully relativistic effects and then are followed by much more complicated waveforms from the final collision or tidal disruption of the black holes or neutron stars.
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It is these final relativistic, collision, and disruption waveforms that will bring LIGO the most interesting information.
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Basic IMAGE version of Foils prepared 4 April 1996
