(ed.). Gravitational waves (IOP, 2001)(422s).

The r-modes 73As we mentioned in chapter 4, since the frequency increases, the signal is said to‘chirp’.These results show that the chirp mass is the only mass associated with thebinary that can be deduced from observations of its gravitational radiation, at leastif only the Newtonian orbit is important. Moreover, if one can measure the fieldamplitude (e.g. h TTxx ) plus gw and ˙ gw , one can deduce from these the valueof Å and the distance r to the system! A chirping binary with a circular orbit,observed in gravitational waves, is a standard candle: one can infer its distancepurely from the gravitational-wave observations. To do this one needs the fullamplitude, not just its projection on a single detector, so one generally needs anetwork of detectors or a long-duration observation with a single detector to getenough information.It is very unusual in astronomy to have standard candles, and they are highlyprized. For example, one can, in principle, use this information to measureHubble’s constant [26].7.1.1 CorrectionsIn the calculation above we made several simplifying assumptions. For example,how good is the assumption that the orbit is circular? The Hulse–Taylor binaryis in a highly eccentric orbit, and this turns out to enhance its gravitational-waveluminosity by more than a factor of ten, since the elliptical orbit brings the twostars much nearer to one another for a period of time than a circular orbit with thesame period would do. So there are big corrections for this system.However, systems emitting at frequencies observable from ground-basedinterferometers are probably well approximated by circular orbits, because theyhave arrived at their very close separation by gravitational-wave-driven in-spiral.This process removes eccentricity from the orbit faster than it shrinks the orbitalradius, so by the time they are observed they have insignificant eccentricity.Another assumption is that the orbit is well described by Newtoniantheory. This is not a good assumption in most cases. Post-Newtonian orbitcorrections will be very important in observations. This is not because thestars eventually approach each other closely. It is because they spend a longtime at wide separations where the small post-Newtonian corrections accumulatesystematically, eventually changing the phase of the orbit by an observableamount. So it is very important for observations that we match signals witha template containing high-order post-Newtonian corrections, as described inBlanchet’s contribution. But even so, the information contained in the Newtonianpart of the radiation is still there, so all our conclusions above remain important.7.2 The r-modesWe consider rotating stars in Newtonian gravity and look at the effect that theemission of gravitational radiation has on their oscillations. One might expect