Parameter estimation for heavy binary-black holes with networks of second-generation gravitational-wave detectors

Abstract

The era of gravitational-wave astronomy started with the discovery of the binary black hole coalescences (BBH) GW150914 and GW151226 by the LIGO instruments. These systems allowed for the first direct measurement of masses and spins of black holes. The component masses in each of the systems have been estimated with uncertainties of over 10%, with only weak constraints on the spin magnitude and orientation. In this paper we show how these uncertainties are typical for this type of source when using advanced detectors. Focusing, in particular, on heavy BBH of masses similar to GW150914, we find that typical uncertainties in the estimation of the source-frame component masses will be around 40%. We also find that for most events the magnitude of the component spins will be estimated poorly: for only 10% of the systems, the uncertainties in the spin magnitude of the primary (secondary) BH will be below 0.7 (0.8). Conversely, the effective inspiral spin along the angular momentum can be estimated more precisely than either spins, with uncertainties below 0.16 for 10% of the systems. We also quantify how often large or negligible primary spins can be excluded and how often the sign of the effective spin can be measured. We show how the angle between the spin and the orbital angular momentum can only seldom be measured with uncertainties below 60 °. We then investigate how the measurement of spin parameters depends on the inclination angle and the total mass of the source. We find that when precession is present, uncertainties are smaller for systems observed close to edge-on. Contrarily to what happens for low-mass, inspiral-dominated sources, for heavy BBH we find that large spins aligned with the orbital angular momentum can be measured with a small uncertainty. We also show how spin uncertainties increase with the total mass. Finally, considering a simple toy model, we show how detections can be combined to infer properties of the underlying population.