Optimal filtering of the LISA data

Abstract

The LISA time-delay-interferometry responses to a gravitational wave signal are rewritten in a form that accounts for the motion of the LISA constellation around the Sun; the responses are given in closed analytic forms valid for any frequency in the band accessible to LISA. We then present a complete procedure, based on the principle of maximum likelihood, to search for stellar-mass binary systems in the LISA data. We define the required optimal filters, the amplitude-maximized detection statistic (analogous to the $\mathcal{F}$ statistic used in pulsar searches with ground-based interferometers), and discuss the false-alarm and detection probabilities. We then test the procedure in numerical simulations of gravitational-wave detection.