Impact of Spacecraft Orbit Uncertainties and Velocity Mismodeling on the LISA Gravitational-Wave Response

Abstract

The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave observatory that consists of three spacecraft in a near-equilateral triangular formation. The spacecraft orbits are typically assumed to be perfectly known in LISA data analysis studies, but in reality, the orbit determination process introduces uncertainties in the spacecraft positions and velocities. In this work, we investigate how these uncertainties propagate into the LISA detector output and the impact of neglecting the spacecraft velocities. We quantify these errors in the knowledge of the LISA response using mismatches and discuss the implications for gravitational wave data analysis. We find that spacecraft orbit uncertainties impact the LISA response knowledge at high frequencies with worst mismatch below $10^{-7}$. The effect of neglecting the spacecraft velocities is largest at frequencies around $10^{-4}$ Hz with mismatches of order $10^{-4}$. For a galactic binary with frequency $10^{-4}$ Hz and SNR=200 observed for one year, we find that neglecting the spacecraft velocities in the response leads to less than 1-$σ$ biases in the parameter estimates. This work provides the first characterization of how errors in the LISA gravitational wave response propagate from gravitational wave strain through detector output to estimated parameters.