Measuring coalescing massive binary black holes with gravitational waves: The impact of spin-induced precession

Abstract

The coalescence of massive black holes generates gravitational waves (GWs) that will be measurable by space-based detectors such as LISA to large redshifts. The spins of a binary's black holes have an important impact on its waveform. Specifically, geodetic and gravitomagnetic effects cause the spins to precess; this precession then modulates the waveform, adding periodic structure which encodes useful information about the binary's members. Following pioneering work by Vecchio, we examine the impact upon GW measurements of including these precession-induced modulations in the waveform model. We find that the additional periodicity due to spin precession breaks degeneracies among certain parameters, greatly improving the accuracy with which they may be measured. In particular, mass measurements are improved tremendously, by one to several orders of magnitude. Localization of the source on the sky is also improved, though not as much---low redshift systems can be localized to an ellipse which is roughly $10\ensuremath{-}\mathrm{\text{a few}}\ifmmode\times\else\texttimes\fi{}10\text{ }\text{ }\mathrm{arcminutes}$ in the long direction and a factor of 2 smaller in the short direction. Though not a drastic improvement relative to analyses which neglect spin precession, even modest gains in source localization will greatly facilitate searches for electromagnetic counterparts to GW events. Determination of distance to the source is likewise improved: We find that relative error in measured luminosity distance is commonly $\ensuremath{\sim}0.1%--0.4%$ at $z\ensuremath{\sim}1$. Finally, with the inclusion of precession, we find that the magnitude of the spins themselves can typically be determined for low redshift systems with an accuracy of about 0.1%--10%, depending on the spin value, allowing accurate surveys of mass and spin evolution over cosmic time.