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A&A 476, 121-135 (2007)
DOI: 10.1051/0004-6361:20077105
Orbital circularisation of white dwarfs and the formation of gravitational radiation sources in star clusters containing an intermediate mass black hole
P. B. Ivanov1, 2 and J. C. B. Papaloizou11 Department of Applied Mathematics and Theoretical Physics, CMS, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK
e-mail: pbi20@damtp.cam.ac.uk
2 Astro Space Center, P. N. Lebedev Physical Institute, Profsouyznaya St., 84/32 Moscow, Russia
(Received 15 January 2007 / Accepted 31 August 2007)
Abstract
Aims.We consider how tight binaries consisting of a super-massive black hole
of mass M = 103-104 
and a white dwarf in quasi-circular orbit
can be formed in a globular cluster.
We point out that
a major fraction of white dwarfs tidally captured by the black hole
may be destroyed by tidal inflation during ongoing
tidal circularisation, and therefore the formation
of tight binaries is inhibited. However some fraction
may survive
tidal circularisation through being spun up
to high rotation rates. Then the rates of energy loss through
gravitational wave emission induced by tidally excited pulsation
modes and dissipation through non linear effects may compete with the rate of increase of pulsation energy due to dynamic tides. The semi-major axes of these white dwarfs are decreased by tidal interaction below a "critical" value where dynamic tides decrease in effectiveness because pulsation modes retain phase coherence between successive pericentre passages.
Methods.We estimate the rate of formation of
such circularising
white dwarfs within a simple framework,
modelling them as n = 1.5 polytropes
and assuming that results obtained from the tidal theory
for slow rotators can be extrapolated to
fast rotators.
Results. We estimate the total capture rate
as ~ N ~ 2.5 
10-8
yr-1, where
M4 = M/104 and r0.1 is the radius of influence
of the black hole expressed in units 0.1 pc. We find that the formation rate of tight pairs is approximately 10 times smaller than the total capture rate, for typical parameters
of the problem. This result is used to estimate the probability of detection of gravitational waves coming from such tight binaries by LISA.
Conclusions. We conclude that LISA may detect
such binaries provided that the fraction of globular clusters
containing black holes in the mass range of interest
is substantial and that the dispersion velocity
of the cluster stars near the radius of influence of the black hole
exceeds ~20 km s-1.
Key words: black hole physics -- gravitational waves -- stellar dynamics -- white dwarfs -- galaxies: star clusters -- stars: oscillations
© ESO 2007