White-dwarf–white-dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low part of its frequency band, the LISA strain sensitivity will be dominated by the 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 magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. Our approach relies on entirely analytic expressions of the LISA time-delay interferometric responses to the gravitational radiation emitted by such systems, which 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, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. This suggests that, during this time period, LISA could search for other gravitational wave signals incoming from directions that are away from the galactic plane. Since the galactic white-dwarf background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of 1 yr, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated 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.