The Doppler boosted LISA response to gravitational waves

Future space-based gravitational wave observatories like LISA, TianQin and Taji are expected to detect massive black hole binaries (MBHBs) with high signal-to-noise ratios (SNRs), ranging up to thousands. Such high-precision observations require accurate modeling of the detector response. However, current derivations of the response function neglect the motion of the spacecraft during light travel time, omitting velocity-dependent terms of order $\beta = v/c \sim 10^{-4}$. In this work, we derive the velocity-dependent corrections to the gravitational wave response. Focusing on LISA, we analyze the contribution of the velocity-terms for MBHBs in the mass range $[10^6,10^8]\:\mathrm{M}_{\odot}$ using a modified version of the state-of-the-art response simulator \texttt{lisagwresponse}. We find that corrections introduce residual SNRs up to $\sim 2$ for the loudest events and fractional differences up to $0.02\%$, compared to \texttt{lisagwresponse}. While small, these effects are comparable to current waveform modeling uncertainties and imprint distinctive sky-localization signatures, making them potentially relevant for parameter estimation of high-mass MBHBs and simulation of mock datasets.