Importance of including small body spin effects in the modelling of intermediate mass-ratio inspirals. II. Accurate parameter extraction of strong sources using higher-order spin effects

Abstract

We improve the numerical kludge waveform model introduced in Huerta and Gair (2011) [E. A. Huerta and J. R. Gair, Phys. Rev. D 84, 064023 (2011).] in two ways. We extend the equations of motion for spinning black hole binaries derived by Saijo et al. [M. Saijo, K. Maeda, M. Shibata, and Y. Mino, Phys. Rev. D 58, 064005 (1998).] using spin-orbit and spin-spin couplings taken from perturbative and post-Newtonian (PN) calculations at the highest order available. We also include first-order conservative self-force corrections for spin-orbit and spin-spin couplings, which are derived by comparison to PN results. We generate the inspiral evolution using fluxes that include the most recent calculations of small body spin corrections, spin-spin, and spin-orbit couplings and higher-order fits to solutions of the Teukolsky equation. Using a simplified version of this model in [E. A. Huerta and J. R. Gair, Phys. Rev. D 84, 064023 (2011).], we found that small body spin effects could be measured through gravitational-wave observations from intermediate-mass-ratio inspirals (IMRIs) with mass ratio $\ensuremath{\eta}\ensuremath{\gtrsim}{10}^{\ensuremath{-}3}$, when both binary components are rapidly rotating. In this paper, we present results of Monte Carlo simulations of parameter-estimation errors to study in detail how the spin of the small/big body affects parameter measurement using a variety of mass and spin combinations for typical IMRI sources. We have found that for IMRI events involving a moderately rotating intermediate-mass black hole (IMBH) of mass ${10}^{4}{M}_{\ensuremath{\bigodot}}$ and a rapidly rotating central supermassive black hole (SMBH) of mass ${10}^{6}{M}_{\ensuremath{\bigodot}}$, gravitational wave observations made with LISA at a signal-to-noise ratio of 1000 should be able to determine the inspiralling IMBH mass, the central SMBH mass, the SMBH spin magnitude, and the IMBH spin magnitude to within fractional errors of $\ensuremath{\sim}{10}^{\ensuremath{-}3}$, ${10}^{\ensuremath{-}3}$, ${10}^{\ensuremath{-}4}$, and ${10}^{\ensuremath{-}1}$, respectively. LISA should also be able to determine the location of the source in the sky and the SMBH spin orientation to within $\ensuremath{\sim}{10}^{\ensuremath{-}4}$ steradians. Furthermore, we show that by including conservative corrections up to 2.5PN order, systematic errors no longer dominate over statistical errors. This shows that search templates that include small body spin effects in the equations of motion up to 2.5PN order should allow us to perform accurate parameter extraction for IMRIs with typical signal-to-noise ratio $\ensuremath{\sim}1000$.