Probing eccentric higher-order modes through an effective chirp-mass model

The three observational runs of advanced LIGO and Virgo detectors have detected $\ensuremath{\sim}90$ compact binary coalescence events with most of them being quasicircular compact binary merger events. Astrophysical models predict compact binary mergers with appreciable nonzero eccentricity if in dense stellar environments like globular clusters, active galactic nuclei discs. Gravitational wave searches from eccentric systems are either limited to very low eccentricities or rely on model-agnostic time-frequency-based searches. Typically, gravitational waves from eccentric systems with moderate eccentricities carry non-negligible energy in the eccentric higher-order modes. In this work, using the effective chirp mass model [N. Bose and A. Pai, Phys. Rev. D 104, 124021 (2021)] developed using EccentricTD waveform, we develop a phenomenological scaling relation for the eccentric higher-order mode time-frequency track. Further, we incorporate this additional information from the higher-order eccentric mode for nonspinning, stellar mass eccentric binaries to improve the constraint on eccentricity.