Many globular clusters lie off the plane of the galaxy and are relatively isolated systems with known positions. The angular resolution of LISA improves with signal strength. By focusing the search for gravitational radiation using known positions of suspected sources, it is possible to increase the signal-to-noise ratio for the detected signal. Thus, the angular resolution of LISA for globular cluster sources can be on the order of the angular size of the globular cluster itself at . Consequently, the orbital period distribution of a globular cluster’s population of relativistic binaries can be determined through observations in gravitational radiation. We will discuss the prospects for observing each class of relativistic binaries covered in this review.
White dwarf-white dwarf binaries that are formed from a common envelope phase will be briefly visible while the recently revealed hot core of the secondary cools. These objects are most likely the “non-flickerers” of Cool et al.  and Edmonds et al. . WD-WD binaries formed through exchange interactions may very well harbor white dwarfs which are too cool to be observed. In either case, hardening through dynamical interactions will become less likely as the orbit shrinks and the effective cross section of the binary becomes too small. These objects will then be effectively invisible in electromagnetic radiation until they are brought into contact and RLOF can begin. During this invisible phase, the orbital period is ground down through the emission of gravitational radiation until the orbital period is a few hundred seconds . With a frequency of 1 to 10 mHz, gravitational radiation from such a binary will be in the band of LISA . There are such systems predicted from encounter rates (see Table 4).
White dwarf-neutron star binaries that are expected to be progenitors of the millisecond pulsars must pass through a phase of gravitational radiation after the degenerate core of the donor star emerges from the common envelope phase and before the spin-up phase begins with the onset of mass transfer from the WD to the neutron star. The orbital period at the onset of RLOF will be on the order of 1 to 2 minutes and the gravitational wave signal will be received at LISA with a signal-to-noise of at a frequency of around for a globular cluster binary. Estimates of the number of such systems range from for semi-empirical methods (Section 5.3.4) to from encounter rates (Table 4).
Binaries with significant eccentricity will have a spectrum of harmonics of the orbital frequency, with the relative strength of the th harmonic for eccentricity given by .
Although the globular cluster population of NS-NS binaries is expected to be quite small (), they may have high eccentricities. The binary pulsar B2127+11Cis an example of a NS-NS binary in a globular cluster. In terms of the unknown angle of inclination , the companion mass to the pulsar is and its eccentricity is . These binaries may also be detectable by LISA. If the globular cluster systems of other galaxies follow similar evolution as the Milky Way population, these binaries may be potential sources for LIGO as gravitational radiation grinds them down to coalescence. With their high eccentricities and large chirp mass, black hole binaries will also be good potential sources for gravitational radiation from the galactic globular cluster system [17, 15].
The relatively close proximity of the galactic globular cluster system and the separations between individual globular clusters allows for the identification of gravitational radiation sources with their individual host clusters. Although the expected angular resolution of LISA is not small enough to allow for the identification of individual sources, knowledge of the positions of the clusters will allow for focused searches of the relativistic binary populations of the majority of the galactic globular clusters. Armed with a knowledge of the orbital periods of any detected binaries, concentrated searches in electromagnetic radiation can be successful in identifying relativistic binaries that may have otherwise been missed.