Enhancing modified gravity detection from gravitational-wave observations using the Parametrized ringdown spin expansion coefficients formalism

Harvesting the full potential of black hole spectroscopy demands realising the importance of casting constraints on modified theories of gravity in a framework as general and robust as possible. Requiring more stringent -- yet well-motivated -- beyond General Relativity (GR) parametrizations improves the inference drawn from available GW data, substantially decreasing the errors on deviation parameters. This implies a reduction in the number of signals needed to detect a deviation from GR predictions and an increase of the number of GR-violating coefficients that can be meaningfully constrained with a given number of signals. To this end, we apply to LIGO-Virgo observations a high-spin version of the Parametrized ringdown spin expansion coefficients (ParSpec) formalism, encompassing large classes of modified theories of gravity. We constrain the lowest-order perturbative deviation of the fundamental ringdown frequency to be $\delta\omega^{0}_{220} = {-0.05}^{+0.05}_{-0.05}$, when assuming adimensional beyond-GR couplings, substantially improving upon previously published results. We also establish upper bounds $\ell_{p=2} < 23 \, \mathrm{km}$, $\ell_{p=4} < 35 \, \mathrm{km}$, $\ell_{p=6} < 42 \, \mathrm{km}$ on the scale $\ell_p$ at which the appearance of new physics is disfavoured, depending on the mass dimension $p$ of the ringdown coupling. These bounds exceed the ones obtained by previous analyses or are competitive with existing ones, depending on the specific alternative theory considered, and promise to quickly improve as the number of detectors, sensitivity and duty-cycle of the gravitational-wave network steadily increases.