The impact of physically motivated calibration errors on search pipeline detection parameters for broadband burst Signals

Imperfections in the calibration of gravitational wave observatories introduce frequency dependent amplitude and phase errors on the measured GW signal. Previous unmodelled burst searches have approximated these effects using prescriptions such as a uniform amplitude rescaling or a constant time shift, which do not capture the frequency-dependent structure of calibration errors. This limitation is problematic for core-collapse supernovae, whose predicted GW signals occupy a wide frequency band and exhibit complex time-frequency morphology. In this work, we investigate how realistic calibration errors affect burst search pipelines by combining analytical modelling with large-scale injection campaigns. First-order estimates are derived to quantify how frequency-dependent amplitude and phase errors influence detection statistics such as the coherent network SNR and the correlation coefficient. These calculations predict that the relative impact on the coherent network SNR scales with the signal strength until it reaches an asymptotic value. The effect on the correlation coefficient is most pronounced near the detection threshold and is entirely suppressed at high SNR ratio. Injection studies confirm that calibration errors do modify the detection statistics, but show that the dominant contribution arises indirectly through changes in the number of time-frequency pixels selected in an event. Despite these measurable variations, detection efficiencies as a function of distance differ by less than one percent across all tested waveforms, and explosion-energy limits remain dominated by astrophysical uncertainties rather than calibration uncertainty. These results demonstrate that, at current detector sensitivity, realistic calibration errors have minimal impact on the detectability of broadband GW burst signals. The impact of calibration errors on parameter estimation is left for future work.