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

44 Astrophysics of gravitational-wave sourcesHowever, both kinds of mechanisms are difficult to model. The problem withgravitational collapse is that perfectly spherical motions do not emit gravitationalwaves, and it is still not possible to estimate in a reliable way the amountof asymmetry in gravitational collapse. Even modern computers are not ableto perform realistic simulations of gravitational collapse in three dimensions,including all the important nuclear reactions and neutrino- and photon-transport.Similarly, it is hard to model the r-mode instability because its evolution dependson nonlinear hydrodynamics and on poorly known physics, such as the coolingand viscosity of neutron stars.An alternative approach is to use general energy considerations. If, forexample, we assume that 1% of the available energy is converted into gravitationalradiation, then, from formulae we will derive in the next chapter, the amplitude hwould be large enough to be detected by the first ground-based interferometers(LIGO/GEO600/VIRGO) at the distance of Virgo Cluster (18 Mpc) if theemission centres at 300 Hz. Moreover, bar and spherical-mass detectors withan effective sensitivity of 10 −21 and the right resonant frequency could see thesesignals as well.The uncertainties in our predictions have a positive aspect: it is clear that ifwe can detect radiation from supernovae, we will learn much that we do not knowabout the end stages of stellar evolution and about neutron-star physics.4.1.2 Binary starsBinary systems have given us our best proof of the reliability of general relativityfor gravitational waves. The most famous example of such systems is thebinary pulsar PSR1916+16, discovered by Hulse and Taylor in 1974; they wereawarded the Nobel Prize for this discovery in 1993. From the observations ofthe modulation of the pulse period as the stars move in their orbits, one knowsmany important parameters of this system (orbital period, eccentricity, masses ofthe two stars, etc), and the data also show directly the decrease of the orbitalperiod due to the emission of gravitational radiation. The observed value is2.4 × 10 −12 s/s. Post-Newtonian theory allows one to predict this from the othermeasured parameters of the system, without any free parameters (see chapter 7);the prediction is 2.38 × 10 −12 , in agreement within the measurement errors.Unfortunately the radiation from the Hulse–Taylor system will be too weakand of too low a frequency to be detectable by LISA.4.1.3 Chirping binary systemsIf a binary gives off enough energy for its orbit to shrink by an observable amountduring an observation, it is said to chirp: as the orbit shrinks, the frequency andamplitude go up. LISA will see a few chirping binaries. If a binary systemis compact enough to radiate above 10 −3 Hz, it will always chirp within oneyear, provided its components have a mass above about 1M ⊙ . If they are above