Frequency-Dependent Responses in 3rd 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 3${}^{\mathrm{r}\mathrm{d}}$ 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$M_{\odot }$ neutron star coalescences at $z\lesssim 1.7$. Analysis of $3^{\mathrm{r}\mathrm{d}}$ generation detectors therefore must account for these effects.