Tri-linear representations for the Laser Interferometer Space Antenna

Abstract

Abstract The Laser Interferometer Space Antenna (LISA) is a space-borne observatory of gravitational waves to be launched by ESA and NASA in the 2030s. Interferometric measurements are made between three spacecraft orbiting the Sun. The measurements are dependent on the geometric information due to the relative locations between the spacecraft as well as the intrinsic parameters of the astrophysical objects that generate the gravitational waves. We show that the measurements of mildly chirping gravitational waves can be approximated by means of a tri-linear representation, where the geometric information about the location of the observed object as well as that of the spacecraft locations are separated by different factors. We discuss that for low frequencies the relative approximation error is proportional to the square of the signal’s carrier frequency and illustrate this accuracy in numerical experiments. For the sake of illustration, we outline a simple algorithm for extracting parameters from the observed gravitational waves.