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6 Prospects of Gravitational Radiation

A very exciting prospect for the observation of relativistic binaries in globular clusters lies in the fact that they will be sources of gravitational radiation. There is a phase in the evolution of most relativistic binaries during which the orbital period is slowly shrinking due to the emission of gravitational radiation. If the binary is in a circularized orbit, the gravitational radiation will be peaked strongly in the second harmonic of the orbital period, so f = 2f gw orb. Gravitational radiation can be described by the dimensionless strain amplitude h0. Although the strength of the gravitational radiation varies with the orientation of the binary, an angle-averaged estimate of the signal strength is [23Jump To The Next Citation Point]

( )2 ∕3( ) ( )5∕3 h0 = 1.5 × 10− 21 ---fgw-- 1 kpc- ℳ--- . (41 ) 10 −3 Hz r M ⊙
At a typical globular cluster distance of r ∼ 10 kpc and typical chirp mass of ℳ ∼ 0.5M ⊙, a relativistic WD–WD or WD–NS binary with Porb = 400 s will have a gravitational wave amplitude of 10− 22. This value is within the range of the proposed space-based gravitational wave observatory LISA [23Jump To The Next Citation Point].

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 f > 1 mHz gw. 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.

WD–WD 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. [36] and Edmonds et al. [56]. 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 [19]. With a frequency of 1 to 10 mHz, gravitational radiation from such a binary will be in the band of LISA [23]. There are ∼ 175 such systems predicted from encounter rates (see Table 4).

WD–NS 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 white dwarf 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 50 – 100 at a frequency of around 20 mHz for a globular cluster binary. Estimates of the number of such systems range from 1 – 10 for semi-empirical methods (see Section 5.3.4) to ∼ 125 from encounter rates (see Table 4).

Binaries with significant eccentricity will have a spectrum of harmonics of the orbital frequency, with the relative strength of the nth harmonic for eccentricity e given by [176]

4{[ ]2 g(n,e) = n-- J (ne) − J (ne) + 2-J (ne) + J (ne ) − J (ne ) 32 n−2 n−1 n n n+1 n+2 2 2 4 2} +(1 − e )[Jn− 2(ne )− 2Jn(ne)+Jn+2 (ne )]+ ---2 [Jn(ne )] , (42 ) 3n
where Jn is the Bessel function. The higher harmonics of sufficiently eccentric binaries (e > 0.7) can be detected by LISA even though the fundamental orbital frequency is well below its sensitivity band of 1 – 100 mHz [21Jump To The Next Citation Point]. Dynamical interactions may produce an eccentric population of 30 – 140 white dwarf binaries that would be present in the LISA data after a 5 year observation [241].Update

Although the globular cluster population of NS–NS binaries is expected to be quite small (∼ 10), 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 i, the companion mass to the pulsar is M2 sin i ∼ 1M ⊙ and its eccentricity is e = 0.68 [144]. 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 [2021].

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.

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