Eccentricity evolution of spinning binaries and its dependence on the equation of state of the components

We study the evolution of the eccentricity of an eccentric orbit with spinning components. We develop a prescription to express the evolving eccentricity in terms of reference eccentricity and frequency. For that purpose we considered the spins to be perpendicular to the orbital plane. Using this we found an analytical result for the contribution of spin in eccentricity evolution. As a result, we expressed orbital eccentricity in a series of reference eccentricity and gravitational wave frequency. The prescription developed here can easily be used to find arbitrarily higher-order contributions of reference eccentricity. With this we computed the eccentricity up to O(e₀⁵) O ( e 0 5 ) . This result can be used to construct the waveforms of spinning compact objects in an eccentric orbit. Since our expression depends on the spin induced quadrupole moments, we also study the impact of component properties on the eccentricity evolution through the quadrupole moment. We find for BNSs the evolution depends on the equation of state very mildly unless the NSs are subsolar mass. For subsolar mass NSs the deviations from BH case are comparatively larger and have equation of state dependence. For binary boson stars the deviations are comparatively larger across the mass values. We argue that it may affect our understanding of formation channels and their corresponding populations. We also argue that this can possibly be used as another tool to constrain exoticness of compact objects in a binary.