Simulation of the white dwarf white dwarf galactic background in the LISA data

Laser Interferometer Space Antenna (LISA) is a proposed mission to detect and study gravitational radiation in the frequency range from 10<SUP>-4</SUP> to 10<SUP>-1</SUP> Hz. In the low part of its frequency band, the LISA data will contain a stochastic signal consisting of an incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the LISA response to this background, we have simulated a population of white-dwarf binaries recently synthesized by one of us. Our approach relies on an analytic expressions of the LISA Time-Delay Interferometric responses to the gravitational radiation emitted by such systems, and it allows us to implement a computationally efficient and accurate simulation of the background in the LISA data. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time with a period of 1 year, reaching a minimum equal to about twice that of the LISA noise for a period of about 2 months around the time when the Sun LISA direction is roughly oriented towards the Autumn equinox. This modulation means that the galactic white-dwarf background that will be observable by LISA is a cyclostationary random process with a period of 1 year. We summarize the theory of cyclostationary random processes and present the corresponding generalized spectral method needed to characterize such a process in the LISA data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarf binary systems present in our galaxy