Early warning of precessing compact binary merger with third-generation gravitational-wave detectors

Rapid localization of gravitational-wave events is important for the success of the multi-messenger observations. The forthcoming improvements and constructions of gravitational-wave detectors will enable detecting and localizing compact-binary coalescence events even before mergers, which is called early warning. The performance of early warning can be improved by considering modulation of gravitational wave signal amplitude due to the Earth rotation and the precession of a binary orbital plane caused by the misaligned spins of compact objects. In this paper, for the first time we estimate localization precision in the early warning quantitatively, taking into account an orbital precession. We find that a neutron star-black hole binary at $z=0.1$ can typically be localized to $100\,\mathrm{deg}^2$ and $10\,\mathrm{deg^2}$ at the time of $12$ -- $15 \,\mathrm{minutes}$ and $50$ -- $300\,\mathrm{seconds}$ before merger, respectively, which cannot be achieved without the precession effect.