Observations have revealed that galaxies contain central supermassive
black holes and undergo merging. We therefore expect that binary black
hole coalescence is a realistic astrophysical event.  General
relativity predicts that a mass distribution with an accelerating
quadrupole moment will generate gravitational waves: perturbations in
space-time that propagate at the speed of light.  Gravitational wave
interferometers aim to detect the amplitude of this signal by
measuring the perturbation of isolated test masses.  The mass
distribution of coalescing binary black holes has a large quadrupole
acceleration and therefore the detection of these systems is one of
the main programs of the planned Laser Interferometer Space Antennae
(LISA).

The discovery of (black hole powered) quasars out to redshifts higher
than 6 indicates that supermassive black holes exist over a range of
epochs.  Given that the standard cosmological model predicts that
structures form hierarchically, the coalescence of supermassive black
holes may be a frequent event.  However, due to the lack of
understanding of the physical processes governing supermassive black
hole formation and binary black hole evolution, the rate at which such
events occur is uncertain.  We have estimated likely detection rates
for LISA as follows.

 We first performed a detailed signal to noise analysis for both the
inspiral and ringdown phases of binary coalescence using the
theoretical waveforms and the LISA noise curve.  These results allowed
us to construct accurate detection limits as a function of binary
redshift and mass.  We used an existing extended Press-Schechter
merger-rate code to estimate the rate of halo merging and calculated
the expected LISA detection rates for the observationally motivated
scenario in which black holes exist in all halos above a critical
mass.  We find that the expected number of counts decreases notably
with minimum black hole mass. However, guided by the mass of
black holes in the centre of local galaxy bulges ($\gtrsim 10^5
{\rm M}_{\odot}$) and assuming that binary black hole coalescence is
efficient, we expect of order 10 detectable events per year in each of
the ringdown and inspiral phases.  This work is the first to combine
accurate signal to noise calculations with a physically motivated
estimate of the event rate.