Effective chirp mass captures the inspiral frequency evolution of the non-spinning eccentric compact binary

Compact binary systems with black holes are the primary sources of interferometric advanced gravitational wave detectors. Astrophysical models suggest finite possibility of binary systems with appreciable non-zero eccentricity in the dense stellar environment like globular clusters and galactic nuclei. While most of the compact binary measurements have not shown appreciable eccentricity, constrains on the eccentricity have been placed on few detected events. With increasing sensitivity of the gravitational wave detectors, the eccentric binaries are plausible sources in the gravitational wave window. Nevertheless, the challenges in the waveform modelling for high values of eccentricity constrain both the search methodologies of eccentric system as well as parameter estimation of the eccentricity. Waveform independent approaches are being investigated. In this work, we demonstrate that a new effective chirp mass $\mathcal{M}_e$ parameter can be defined which governs the dynamics of the non-spinning eccentric compact binary system. We obtain the phenomenological model of the same for low to moderate eccentricity values. One direct implication is its application in the unmodelled searches and as an another implication, we demonstrate that this model can be used to constrain the eccentricity of the non-spinning eccentric binaries in the advanced detector era in the waveform model-independent way.