Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals

In this paper, we explore the ability of future low-frequency gravitational wave detectors to measure the spin of stellar mass and intermediate mass black holes (IMBHs) that inspiral into spinning supermassive black holes (SMBHs). We describe a kludge waveform model based on the equations of motion derived by Saijo et al. [M. Saijo, K. Maeda, M. Shibata, and Y. Mino, Phys. Rev. D 58, 064005 (1998).] for spinning black hole (BH) binaries, augmented with spin-orbit and spin-spin couplings taken from perturbative and post-Newtonian (PN) calculations, and the associated conservative self-force corrections, derived by comparison to PN results. We model the inspiral phase using accurate fluxes, which include perturbative corrections for the spin of the inspiralling body, spin-spin couplings and higher-order fits to solutions of the Teukolsky equation. We present results of Monte Carlo simulations of parameter-estimation errors, computed using the Fisher Matrix formalism, and also of the model errors that arise when we omit conservative corrections from the waveform template. We present results for the inspirals of spinning BHs with masses mu = 10M(circle dot), 10(2)M(circle dot), 10(3)M(circle dot), 5 X 10(3)M(circle dot), into SMBHs of specific spin parameter q = 0.9, and mass M = 10(6)M(circle dot). The analysis shows that for intermediate-mass-ratio inspirals, e. g., a source 5 X 10(3)M(circle dot) + 10(6)M(circle dot) observed with a signal-to-noise ratio of 1000, observations made with LISA will be able to determine the inspiralling BH mass, the central SMBH mass, the SMBH spin magnitude, and the magnitude of the spin of the inspiralling BH to within fractional errors of similar to 10(-3), 10(-3), 10(-4), 10%, respectively. We also expect to determine the location of the source in the sky and the SMBH spin orientation to within similar to 10(-4) steradians. However, for extreme-mass-ratio inspirals, e. g., a 10M(circle dot) + 10(6)M(circle dot) system observed with signal-to-noise ratio of 30, LISA will not be able to determine the spin magnitude of the inspiralling object, although the measurement of the other waveform parameters is not significantly degraded by the presence of spin. We also show that the model errors which arise from ignoring conservative corrections become significant for mass-ratios above similar to 10(-4), but including these corrections up to second PN order may be sufficient to reduce these systematic errors to an acceptable level.