We calculate the gravitational wave signal from the growth of 10 million solar mass supermassive black holes (SMBH) from the remnants of Population III stars. The assembly of these lower mass black holes is particularly important because observing SMBHs in this mass range is one of the primary science goals for the Laser Interferometer Space Antenna (LISA), a planned NASA/ESA mission to detect gravitational waves. We use high resolution cosmological N-body simulations to track the merger history of the host dark matter halos, and model the growth of the SMBHs with a semi-analytic approach that combines dynamical friction, gas accretion, and feedback. We find that the most common source in the LISA band from our volume consists of mergers between intermediate mass black holes and SMBHs at redshifts less than 2. This type of high mass ratio merger has not been widely considered in the gravitational wave community; detection and characterization of this signal will likely require a different technique than is used for SMBH mergers or extreme mass ratio inspirals. We find that the event rate of this new LISA source depends on prescriptions for gas accretion onto the black hole as well as an accurate model of the dynamics on a galaxy scale; our best estimate yields about 40 sources with a signal-to-noise ratio greater than 30 occur within a volume like the Local Group during SMBH assembly -- extrapolated over the volume of the universe yields roughly 500 observed events over 10 years, although the accuracy of this rate is affected by cosmic variance.
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