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.

中文翻译：

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偏心率可以利用地面探测器对引力波进行最早的预警和定位

引力波（GW）的早期和精确定位对于探测其电磁（EM）对应物至关重要，特别是对于双中子星（BNS）和中子星-黑洞双星（NSBH）。在这封信中，我们率先探索利用致密双星偏心率引起的高次谐波模式，甚至在四极基线之前用地面探测器定位引力波$\ell =2$模式进入检测器波段。我们的理论分析首次提出了一种策略，以尽可能早地获得预警并最大限度地延长观察合并前和/或合并后新兴市场同行的准备时间。我们模拟了 GWTC-3 中三个典型的双星，其偏心率范围为 0.05 到 0.4。我们的结果表明，第三代 (3G) 探测器（低频截止$F_0=5\mathrm{赫兹}$）可以在基线出现之前通过更高的模式积累足够的信噪比$\ell =2$模式进入频段。值得注意的是，仅依靠更高的模式，3G 检测器网络$\mathrm{ET}+2\mathrm{CE}$实现平均本地化$1–{10}^2{度}^2$类似 GW170817 的 BNS 合并前大约 1-1.8 小时，并且$10–{10}^3{度}^2$在类似 GW200115 的 NSBH 合并之前大约 18-30 分钟。 A$100{度}^2$即使在 BNS 合并之前 2-4 小时也可以实现本地化。此外，在通常更有利于电磁对应物检测的近正面方向中，可以进一步改进定位。