Early Alert from Eccentric Binaries: Boosting Multi-Messenger Observations

Early warning of gravitational waves (GWs) from eccentric compact binaries is essential for multi-messenger astronomy. Eccentric binaries are important as their non-circular orbit signals a dynamical formation channel (e.g., dense stellar clusters), revealing the astrophysical origin of these systems. We investigate early warning prospects for eccentric binary neutron star (BNS) and neutron star-black hole (NSBH) mergers, whose oscillatory frequency evolution causes GW frequencies to recur. Generating eccentric waveform templates requires specifying initial conditions; we show that using the periastron frequency instead of the standard orbit-averaged frequency improves the signal-to-noise ratio (SNR) and sky localization. Further improvements result from including subdominant modes alongside the dominant $(2,2)$ mode. Exploring the parameter space $m_1 \in [1.4, 15] \, M_\odot$, $\chi_1 \in [0, 0.8]$, and $e \leq 0.4$ across O5, Voyager, and 3G detector configurations, we find substantial benefits. In the O5 configuration, eccentricity and subdominant modes reduce the sky localization area by $2-80 \%$ (for $e_5 = 0.1$ to $e_5 = 0.4$ at $1000$ square degrees), yielding up to $41$ seconds of additional early warning time. In the 3G scenario, eccentricity alone achieves an $80 \%$ sky area reduction ($e_{2.5} = 0.1$ to $e_{2.5} = 0.4$ at $100$ square degrees), with subdominant modes boosting the reduction up to $98 \%$ for NSBH systems.