Statistical identification of ringdown modes with rational filters

Abstract: Measuring quasinormal modes (QNMs) during the ringdown phase of binary black hole coalescences provides key insights into merger dynamics and enables tests of the no-hair theorem. The QNM rational filter has recently been introduced as a technique to identify specific QNMs in ringdown signals without sampling over mode amplitudes and phases. In this work, we extend the QNM rational filter framework to quantify the statistical confidence of subdominant mode detections in real gravitational wave (GW) observations. We employ a frequentist approach to estimate false-alarm probabilities and propose a workflow for robust identification of specific QNMs. We first validate our methodology using synthetic signals generated from numerical relativity waveforms. We then reanalyze the first GW event, GW150914, finding a marginal detection of an overtone, but at time when the applicability of constant amplitude QNM fits is not fully understood. This extended methodology provides a systematic approach to improving the reliability of QNM detections, paving the way for more precise tests of strong-field gravity with current and future GW observations.