LISA observations of rapidly spinning massive black hole binary systems

Binary systems of massive black holes will be detectable by the Laser Interferometer Space Antenna (LISA) throughout the entire Universe. Observations of gravitational waves from this class of sources will have important repercussions on our understanding of the behavior of gravity in the highly nonlinear relativistic regime, the distribution and interaction of massive black holes at high redshift, and the formation and evolution of cosmic structures. It is therefore important to address how accurately LISA can measure the source parameters and explore the implications for astronomy and cosmology. Present observations and theoretical models suggest that massive black holes could be spinning, possibly rapidly in some cases. In binary systems, the relativistic spin-orbit interaction causes the orbital plane to precess in space, producing a characteristic signature on the emitted gravitational waves. In this paper we investigate the effect of spins on the gravitational wave signal registered at the LISA output—we provide ready-to-use analytical expressions of the measured signal—and the implications for parameter estimation. We consider the inspiral phase of binary systems in circular orbit undergoing the so-called “simple precession” and we approximate the gravitational radiation at the restricted ${\mathrm{post}}^{1.5}$-Newtonian order. We show that the presence of spins changes dramatically the signature of the signal recorded by LISA. As a consequence, the mean square errors associated with the parameter measurements are significantly smaller than the ones obtained when the effect of spins is neglected. For a binary system of two ${10}^6{M}_{\odot }$ black holes, the angular resolution and the relative error on the luminosity distance improve by a factor of $\approx 3–10;$ the fractional errors on the chirp mass and the reduced mass decrease by a factor of $\sim 10$ and $\sim {10}^3,$ respectively.