Eccentricity enables the earliest warning and localization of gravitational waves with ground-based detectors

The early and precise localization of gravitational waves (GWs) is pivotal in detecting their electromagnetic (EM) counterparts, especially for binary neutron stars (BNS) and neutron star-black hole binaries (NSBH). In this letter, we pioneer the exploration of utilizing the higher harmonic modes induced by the eccentricity of compact binaries to localize GWs with ground-based detectors even before the quadrupole baseline $\ell=2$ mode enters the detector band. Our theoretical analysis marks a first in proposing a strategy for gaining the earliest possible warning and maximizing preparation time for observing pre- and/or post-merger EM counterparts. We simulate three typical binaries from GWTC-3 with eccentricities ranging from 0.05 to 0.4. Our results reveal that the third-generation (3G) detectors (low frequency cut-off $f_0=5$ Hz) can accumulate sufficient signal-to-noise ratios through higher modes before the onset of the baseline $\ell=2$ mode entry into the band. Notably, relying solely on the higher modes, the 3G detector network ET+2CE achieves an average localization on the order of $1-10^2~\rm deg^2$ around 1-1.8 hours before the merger of a GW170817-like BNS, and $10-10^3~\rm deg^2$ approximately 18-30 minutes prior to the merger of a GW200115-like NSBH. A $100~\rm deg^2$ localization is attainable even 2-4 hours prior to a BNS merger. Moreover, in the near face-on orientations which are generally more favorable for EM counterpart detection, the localization can be further improved.