Optimal calibration accuracy for gravitational-wave detectors

Calibration errors in the response function of a gravitational-wave detector degrade its ability to detect and then to measure the properties of any detected signals. This paper derives the needed levels of calibration accuracy for each of these data-analysis tasks. The levels derived here are optimal in the sense that lower accuracy would result in missed detections and/or a loss of measurement precision, while higher accuracy would be made irrelevant by the intrinsic noise level of the detector. Calibration errors affect the data-analysis process in much the same way as errors in theoretical waveform templates. The optimal level of calibration accuracy is expressed therefore as a joint limit on modeling and calibration errors: increased accuracy in one reduces the accuracy requirement in the other.

Figure 1

The curves illustrate $C$, the ratio of the standard signal-to-noise measure $\rho$ to a nonstandard measure defined in Eq. (27), as a function of the total mass for nonspinning equal-mass binary black-hole waveforms. The dashed curve is based on the Initial LIGO noise spectrum [5]; the solid curve is based on an Advanced LIGO noise curve [6].

Figure 2

The curves illustrate $\tilde{C}$, the ratio of the standard signal-to-noise measure $\rho$ to another nonstandard measure defined in Eq. (34), as a function of the total mass for nonspinning equal-mass binary black-hole waveforms. The dashed curve is based on the Initial LIGO noise spectrum; the solid curve is based on an Advanced LIGO noise curve.