Binaries, ContinuedWe will now discuss various categories of binary sources and their properties. We will focuson compact objects: white dwarfs, neutron stars, and black holes.Double white dwarf systems (WD-WD) should be extraordinarily plentiful in the Milky Wayand other galaxies. In fact, they should be so common that they will provide a limiting noise forlow-frequency detectors such as LISA. We can understand this at a crude level as follows. Supposethat LISA, with its frequency range of ∼ 10−5− 10−1Hz, observes for three years (about 108s).Its frequency resolution is therefore 10−8Hz. It can observe both polarization modes, but if morethan two WD-WD sources are in the same frequency bin they can’t be distinguished, and in factthey act as unresolvable noise.If there are 108WD-WD binaries in our Milky Way, this implies that, assuming a maximumfrequency of ∼ 1 Hz, there is on average one binary per bin. However, the strong increase ofenergy loss to gravitational radiation as the orbit shrinks means that binaries spend most of theirtime at low frequencies. The net result is that low-frequency bins are buried in unresolvable WD-WD binaries, whereas at high frequencies there is on average less than one binary per 10−8Hzfrequency bin, meaning that it will be possible to identify them individually and model them outof the data stream. The frequency at which one can start to resolve individual WD-WD binarieshas been variously calculated to be in the 2-3 mHz range (see Farmer & Phinney 2003 for a recentdiscussion). In the ∼ 10−4− 10−3Hz range, it is expected that this background will be moreimportant than the LISA instrumental background for determining sensitivities. The extragalacticWD-WD background, although smaller in amplitude, involves so many sources that it will producean unresolvable background all the way up to ∼1 Hz, but at a level far below the current LISAbackground (see Farmer & Phinney 2003).What about neutron stars? There are fewer than ten double neutron star binaries (all in ornear our galaxy, of course), and about half of them will merge within a Hubble time (i.e., thecurrent age of the universe). In one of them, J0737, we observe both neutron stars as pulsars. It isinteresting to note that NS-NS mergers are the only high-frequency gravitational wave source knownto exist (see Figure 1 for a classic demonstration of gravitational waves taking away orbital energy).Other sources are extremely likely (e.g., NS-BH or BH-BH binaries) and many suggestions havebeen made for sources whose strength is uncertain (e.g., continuous or burst sources). Discovery ofany such source would yield important astrophysical information. However, when making the casefor ground-based gravitational wave detectors, it is necessary to estimate the rate of detection ofsources we can project with some confidence.This is typically done (e.g., see papers by Kalogera and colleagues) by using population synthe-sis codes (in which large populations of stars, including binaries, are evolved with certain assump-tions and the result is a simulated population of compact binaries). These results are calibratedstatistically by comparison with the observed population of NS-NS binaries that will merge in a– 2 –Fig. 1.— Predicted and inferred change in the orbital phase of the first binary pulsar. This figureshows the accuracy of the prediction of general relativity. Original figure from an unpublished workby Taylor and Weisberg.– 3 –Hubble time. One of the NS-NS binaries is in a globular cluster. There are ∼ 100 globulars aroundthe Milky Way galaxy, and in each there might be a few hundred neutron stars. Even if there arethen a hundred NS-NS binaries per cluster, and they all merge within a ∼ 1010yr Hubble time, thisgives a total rate of only ∼ 10−6yr−1per Milky Way Equivalent Galaxy (or MWEG, as it is knownin the business). The rates estimated from the binaries in the disk of our Galaxy are larger thanthis, hence only the disk binaries are usually included in such analyses. The best current estimatesare that the rate is about 10−5− 10−4per year per MWEG. At the high end there are tremendousuncertainties, because with the small number of sources a source that is dim (hence can only beseen nearby) and has a short time to merge (hence can only be seen for a short time) has a largestatistical weight. This is in fact the case for the double pulsar J0737. At the low rate end ofthe estimates, though, multiple sources contribute and the uncertainties are not as great. The netresult is that, with high confidence, one expects the next generation of ground-based instruments(such as Advanced LIGO) to see at least a few NS-NS mergers per year.Mergers of black holes with neutron stars have not received as much attention, but in mostbinary evolutionary models they are anticipated to be prominent sources for ground-based detectors.Although probably less common than NS-NS binaries (of course, none have been seen!), the highermass of the black hole implies a larger distance out to which the merger could be seen. It is possiblethat this could more than compensate for the smaller number density and make NS-BH mergersprominent sources at high frequencies.If such mergers do occur, what could they tell us? One hope has been that the tidal disruptionof the neutron star would show up in the gravitational wave train. If so, this would carry informationabout the radius of the neutron star. Combined with the mass, this would be informative aboutthe nature of the high-density matter in the core of the stars. The information would be easiest toextract if the disruption occurred outside the orbital radius of dynamical instability, because thestellar radius would be more easily determined over many orbits. It seems likely, however, thatdisruption will occur during the plunge part of the merger. It may therefore be difficult to extractinformation about neutron star radii from NS-BH mergers.The final category of compact object coalescences involves two black holes. The black holeswe know about are in the stellar-mass range (roughly 5 − 20 M¯), formed from the collapsed coresof massive stars, and in the supermassive range (∼ 106− 1010M¯) in the centers of galaxies. Thereis also growing but not conclusive evidence for intermediate-mass black holes in the 102− 105M¯range in some galaxies.BH-BH coalescences tell us different things depending on their mass and mass ratio. Mergersof