Eccentric, spinning, inspiral-merger-ringdown waveform model with higher modes for the detection and characterization of binary black holes

With the updated sensitivity of terrestrial gravitational-wave (GW) detectors in their fourth observing run, we expect a high rate of detection of binary black hole mergers. With this comes the hope that we will detect rarer classes of merger events. Compact binaries formed dynamically in dense stellar environments are likely to be detected with a residual eccentricity as they enter the sensitivity band of ground-based GW detectors. In this paper, we present a time-domain inspiral-merger-ringdowm (IMR) waveform model ESIGMAHM constructed within a framework we named ESIGMA for coalescing binaries of spinning black holes on moderately eccentric orbits [Phys. Rev. D 97, 024031 (2018).]. We now include the effect of black hole spins on the dynamics of eccentric binaries, as well as model sub-dominant waveform harmonics emitted by them. The inspiral evolution is described by a consistent combination of latest results from post-Newtonian theory, self-force, and black hole perturbation theory. We assume that these moderately eccentric binaries radiate away most of their orbital eccentricity before merger, and seamlessly connect the eccentric inspiral with a numerical relativity based surrogate waveform model NRSur7dq4 for mergers of spinning binaries on quasicircular orbits. We present two variants of ESIGMAHM: the inspiral-only version is named InspiralESIGMAHM, while the full IMR one is termed IMRESIGMAHM; or InspiralESIGMA and IMRESIGMA when only dominant modes are used. We validate ESIGMAHM against eccentric numerical relativity simulations, and also against contemporary effective-one-body and phenomenological models in the quasicircular limit. We find that ESIGMAHM achieves match values greater than 99% for quasicircular spin-aligned binaries with mass ratios up to 8, and above 97% for nonspinning and spinning eccentric systems with small or positively aligned spins. Using IMRESIGMA, we quantify the impact of orbital eccentricity on GW signals, showing that next-generation detectors can detect eccentric sources up to 10% louder than quasicircular ones. We also show that current templated LIGO-Virgo-KAGRA searches will lose more than 10% of optimal SNR for about 20% of all eccentric sources by using only quasicircular waveform templates. The same will result in a 25% loss in detection rate for eccentric sources with mass ratios ${m}_{1}/{m}_{2}\ensuremath{\ge}4$. Our results highlight the need for including eccentricity and higher-order modes in GW source models and searches for asymmetric eccentric BBH signals.