where and are ``beam-pattern'' factors, that depend on the direction of the source and on a polarization angle , and and are gravitational waveforms corresponding to the two polarizations of the gravitational wave (for a review, see [126]). In a source coordinate system in which the x - y plane is the plane of the sky and the z -direction points toward the detector, these two modes are given by
where represent transverse-traceless (TT) projections of the calculated waveform of Eq. (51), given by
where is a unit vector pointing toward the detector. The beam pattern factors depend on the orientation and nature of the detector. For a wave approaching along the laboratory z -direction, and for a mass whose location on the x - y plane makes an angle with the x axis, the beam pattern factors are given by and . For a resonant cylinder oriented along the laboratory z axis, and for source direction , they are given by , (the angle measures the relative orientation of the laboratory and source x -axes). For a laser interferometer with one arm along the laboratory x -axis, the other along the y -axis, and with defined as the differential displacement along the two arms, the beam pattern functions are and .
The waveforms and depend on the nature and evolution of the source. For example, for a binary system in a circular orbit, with an inclination i relative to the plane of the sky, and the x -axis oriented along the major axis of the projected orbit, the quadrupole approximation of Eq. (53) gives
where is the orbital phase.
The Confrontation between General Relativity and
Experiment
Clifford M. Will http://www.livingreviews.org/lrr-2001-4 © Max-Planck-Gesellschaft. ISSN 1433-8351 Problems/Comments to livrev@aei-potsdam.mpg.de |