A fixed false alarm probability figure of merit for gravitational wave detectors

Performance of gravitational wave (GW) detectors can be characterized by several figures of merit (FOMs) which are used to guide the detector's commissioning and operations, and to gauge astrophysical sensitivity. One key FOM is the range in Mpc, averaged over orientation and sky location, at which a GW signal from binary neutron star inspiral and coalescence would have a signal-to-noise ratio (SNR) of 8 in a single detector. This fixed-SNR approach does not accurately reflect the effects of transient noise (glitches), which can severely limit the detectability of transient GW signals expected from a variety of astrophysical sources. We propose a FOM based instead on a fixed false-alarm probability (FAP). This is intended to give a more realistic estimate of the detectable GW transient range including the effect of glitches. Our approach applies equally to individual interferometers or a network of interferometers. We discuss the advantages of the fixed-FAP approach, present examples from a prototype implementation, and discuss the impact it has had on the recent commissioning of the GW detector GEO 600.