Frequency-dependent responses in third generation gravitational-wave detectors

Interferometric gravitational-wave detectors are dynamic instruments. Changing gravitational-wave strains influence the trajectories of null geodesics and therefore modify the interferometric response. These effects will be important when the associated frequencies are comparable to the round-trip light travel time down the detector arms. The arms of advanced detectors currently in operation are short enough that the strain can be approximated as static, but planned 3rd generation detectors, with arms an order of magnitude longer, will need to account for these effects. We investigate the impact of neglecting the frequency-dependent detector response for compact binary coalescences and show that it can introduce large systematic biases in localization, larger than the statistical uncertainty for 1.4-1.4 Ms at z1.7. Analysis of 3rd generation detectors therefore must account for these effects.