Impact of Detector Calibration Accuracy on Black Hole Spectroscopy

Systematic errors in detector calibration can bias signal analyses and potentially lead to incorrect interpretations suggesting violations of general relativity. In this study, we investigate how calibration systematics affect black hole (BH) spectroscopy, a technique that uses the quasinormal modes (QNMs) emitted during the ringdown phase of gravitational waves (GWs) to study remnant BHs formed in compact binary coalescences. We simulate a series of physically motivated, tunable calibration errors and use them to intentionally miscalibrate numerical relativity waveforms. We then apply a QNM extraction method -- the rational QNM filter -- to quantify the impact of these calibration errors. We find that current calibration standards (errors within $10\%$ in magnitude and $10^\circ$ in phase across the most sensitive frequency range of 20--2000 Hz) are adequate for BH ringdown analyses with existing observations, but insufficient for the accuracy goals of future upgraded and next-generation observatories. Specifically, we show that for events with a high ringdown signal-to-noise ratio of $\sim 120$, calibration errors must remain $\lesssim 4\%$ in magnitude and $\lesssim 4^\circ$ in phase to avoid introducing biases. While this analysis focuses on a particular aspect of BH spectroscopy, the results offer quantitative benchmarks for calibration standards crucial to fully realize the potential of precision tests of general relativity in the next-generation detector era.