Systematic bias on the inspiral-merger-ringdown consistency test due to neglect of orbital eccentricity

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The inspiral-merger-ringdown (IMR) consistency test checks the consistency of the final mass and final spin of a binary black hole merger remnant, independently inferred via the inspiral and merger-ringdown parts of the waveform. As binaries are expected to be nearly circularized when entering the frequency band of ground-based detectors, tests of general relativity (GR) currently employ quasicircular waveforms. We quantify the effect of residual orbital eccentricity on the IMR consistency test. We find that eccentricity causes a significant systematic bias in the inferred final mass and spin of the remnant black hole at an orbital eccentricity (defined at $10$ Hz) of $e_0 \gtrsim 0.1$ in the LIGO band (for a total binary mass in the range $65$-$200 \,M_{\odot}$). For binary black holes observed by Cosmic Explorer (CE), the systematic bias becomes significant for $e_0 \gtrsim 0.015$ (for $200$-$600 \,M_{\odot}$ systems). This eccentricity-induced bias on the final mass and spin leads to an apparent inconsistency in the IMR consistency test, manifesting as a false violation of GR. Hence, eccentric corrections to waveform models are important for constructing a robust test of GR, especially for third-generation detectors. We also estimate the eccentric corrections to the relationship between the inspiral parameters and the final mass and final spin; they are shown to be quite small.