Toward inference of overlapping gravitational-wave signals

Merger rates of binary black holes, binary neutron stars, and neutron-star--black-hole binaries in the local Universe (i.e., redshift $z=0$), inferred from the Laser Interferometer Gravitational Wave Observatory and Virgo, are $16\ensuremath{-}130\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, $13\ensuremath{-}1900\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, and $7.4\ensuremath{-}320\text{ }\text{ }{\mathrm{Gpc}}^{\ensuremath{-}3}\text{ }{\mathrm{yr}}^{\ensuremath{-}1}$, respectively. These rates suggest that there is a significant chance that two or more of these signals will overlap with each other during their lifetime in the sensitivity band of future gravitational-wave detectors such as the Cosmic Explorer and Einstein Telescope. The detection pipelines provide the coalescence time of each signal with an accuracy $\mathcal{O}(10\text{ }\text{ }\mathrm{ms})$. We show that by using a prior on the coalescence time from a detection pipeline, it is possible to correctly infer the properties of these overlapping signals with the current data-analysis infrastructure. We study different configurations of two overlapping signals created by nonspinning binaries, varying their time and phase at coalescence, as well as their signal-to-noise ratios. We conclude that, for the scenarios considered in this work, parameter inference is robust provided that their coalescence times in the detector frame are more than $\ensuremath{\sim}1--2\text{ }\text{ }\mathrm{s}$. Signals whose coalescence epochs lie within $\ensuremath{\sim}0.5\text{ }\text{ }\mathrm{s}$ of each other suffer from significant biases in parameter inference, and new strategies and algorithms would be required to overcome such biases.