Nonlinear quasinormal mode detectability with next-generation gravitational wave detectors

In the aftermath of a binary black hole merger event, the gravitational wave signal emitted by the remnant black hole is modeled as a superposition of damped sinusoids known as quasinormal modes (QNMs). While the dominant QNMs originating from linear black hole perturbation theory have been studied extensively in this post-merger "ringdown" phase, more accurate models of ringdown radiation include the nonlinear modes arising from higher-order perturbations of the remnant black hole spacetime. We explore the detectability of quadratic QNMs with both ground- and space-based next-generation detectors. We demonstrate that accurate predictions of the quadratic mode detectability are highly dependent on the QNM starting times. We then calculate the signal-to-noise ratio (SNR) of quadratic modes for several detectors and binary black hole populations. For the events with the loudest quadratic mode SNRs, we additionally compute statistical errors on the mode parameters in order to further ascertain the distinguishability of the quadratic mode from the linear QNMs. Our results suggest that while we will detect the quadratic mode in at most a few events with ground-based detectors, prospects for detection with the Laser Interferometer Space Antenna (LISA) can be considerably more optimistic, depending on the astrophysical model of binaries in LISA's frequency range.