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 postmerger 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 cutoff $f_0=5\mathrm{Hz}$) 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 $\mathrm{ET}+2\mathrm{CE}$ achieves an average localization on the order of $1–{10}^2{\mathrm{deg}}^2$ around 1–1.8 hours before the merger of a GW170817-like BNS, and $10–{10}^3{\mathrm{deg}}^2$ approximately 18–30 minutes prior to the merger of a GW200115-like NSBH. A $100{\mathrm{deg}}^2$ 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.

• Received 25 October 2023
• Revised 11 January 2024
• Accepted 9 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.104041