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. [26] and Edmonds et al. [41]. 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 [16]. With
a frequency of 1 to 10 mHz, gravitational radiation from such a
binary will be in the band of LISA [2]. 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 [120]
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
[98]. 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.