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

48 Astrophysics of gravitational-wave sourcestotal energy loss. In most cases, this limit is rather weak, and stars would have tosustain strains in their crust of order 10 −3 or more. It is unlikely that crusts couldsustain this kind of strain, so the observational limits are probably significantoverestimates for most pulsars. However, millisecond pulsars have much slowerspindown rates, and it would be easier to account for the strain in their crusts,for example as a remnant Bildsten asymmetry. Such stars could, in principle, beradiating more energy in gravitational waves than electromagnetically.Observations of individual neutron stars would be rich with informationabout astrophysics and fundamental nuclear physics. So little is known aboutthe physics of these complex objects that the incentive to observe their radiationis great.However, making such observations presents challenges for data analysis,since the motion of the Earth puts a strong phase modulation on the signal, whichmeans that even if its rest-frame frequency is constant it cannot be found bysimple Fourier analysis. More sophisticated pattern-matching (matched-filtering)techniques are needed, which track and match the signal’s phase to within onecycle over the entire period of measurement. This is not difficult if the source’slocation and frequency are known, but the problem of doing a wide-area search forunknown objects is very challenging [21]. Moreover, if the physics of the sourceis poorly known, such as for LMXBs or r-mode spindown, the job of building anaccurate family of templates is a difficult one. These questions are the subject ofmuch research today, but they will need much more in the future.4.1.5 Random backgroundsThe big bang was the most violent event of all, and it may have created asignificant amount of gravitational radiation. Other events in the early universemay also have created radiation, and there may be backgrounds from morerecent epochs. We have seen earlier, for example, that compact binary systemsin the Galaxy will merge into a confusion-limited noise background in LISAobservations below about 1 mHz.Let us consider the r-modes as another important example. This process mayhave occurred in a good fraction of all neutron stars formed since the beginningof star formation. The sum of all of their r-mode radiation will be a stochasticbackground, with a spectrum that extends from a lower cut-off of about 200 Hz inthe rest frame of the emitter to an upper limit that depends on the initial angularvelocity of stars. If significant star formation started at, say, a redshift of five,then this background should extend down to about 25 Hz. If 10 −3 of the mass ofthe Galaxy is in neutron stars, and each of them radiates 10% of its mass in thisradiation, then the gravitational-wave background should have a density equal to10 −4 of the mean cosmological density of visible stars. Expressed as a fraction gw of the closure density of the universe, per logarithmic frequency interval, thisconverts to r-modesgw (25–1000 Hz) ≈ 10 −8 –10 −7 .