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(abbreviated) We consider how tight binaries consisting of a super-massiveblack hole of mass $M=10^{3}-10^{4}M_{\odot}$ and a white dwarf can be formedin a globular cluster. We point out that a major fraction of white dwarfstidally captured by the black hole may be destroyed by tidal inflation duringongoing circularisation, and the formation of tight binaries is inhibited.However, some stars may survive being spun up to high rotation rates. Then theenergy loss through gravitational wave emission induced by tidally excitedpulsation modes and dissipation through non linear effects may compete with theincrease of pulsation energy due to dynamic tides. The semi-major axes of thesestars can be decreased below a 'critical' value where dynamic tides are noteffective because pulsation modes retain phase coherence between successivepericentre passages. The rate of formation of such circularising stars isestimated assuming that they can be modelled as $n=1.5$ polytropes and thatresults of the tidal theory for slow rotators can be extrapolated to fastrotators. We estimate the total capture rate as $\sim \dot N\sim 2.5\cdot10^{-8}M_{4}^{1.3}r_{0.1}^{-2.1}yr^{-1}$, where $M_{4}=M/10^4M_{\odot}$ and$r_{0.1}$ is the radius of influence of the black hole in units $0.1pc$. Wefind that the formation rate of tight pairs is approximately 10 times smallerthan the total capture rate. It is used to estimate the probability ofdetection of gravitational waves coming from such tight binaries by LISA. Weconclude that LISA may detect such binaries provided that the fraction ofglobular clusters with black holes in the mass range of interest is substantialand that the dispersion velocity of the cluster stars near the radius ofinfluence of the black hole exceeds $\sim 20km/s$.

astronomy and astrophysics

Orbital circularisation of white dwarfs and the formation of  gravitational radiation sources in star clusters containing an intermediate  mass black hole