Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

Phasing of GWF
Orbital phase = φ, ˙ φ = dφ/dt and ˙r = dr/dt = n · v, where
v = p ( ˙r cos φ − r ˙ φ sin φ) + (q cos i + N sin i) ( ˙r sin φ + r ˙ φ cos φ).
Must be supplemented by explicit expressions describing the
temporal evolution of the relative motion, i.e. describing the explicit
time dependences r(t), φ(t), ˙r(t), and ˙ φ(t).
Refer to as phasing, any explicit way to define the latter
time-dependences, because it is the crucial input needed beyond
the ‘amplitude’ expansions, given by to derive some ready to use
waveforms h+,×(t).
Structure for GW polarization amplitudes has only the relative
motion x, v, because one go to a suitable center-of-mass frame ..
Validity of a CM theorem .. O(c −7 ) ‘recoil’ of the center-of-mass is
expected to influence the waveform only at the O(c −8 ) level.
Time-dependent recoil of the latter rest frame will introduce both a
N · vCM/c Doppler shift of the phasing and a corresponding
modification of the amplitudes h+,×.
BRI-IHP06-I – p.99/??