Spatially Filtering the Binary Confusion Noise for Space Gravitational Wave Detectors

For the last fifteen years, the limiting noise source at the low frequency end of the sensitivity window for space gravitational wave detectors has been expected to be the confusion background of overlapping galactic binary stars. Here, we present results of a study that investigates the correlation between binary star signals and conclude that there is a spatial filter in the position-dependent Doppler shift of each binary that sharply reduces the contribution of the galactic binary confusion to the noise in the detector when a monochromatic source is being detected. The sensitivity is thus determined by the instrument alone, and the confusion noise may effectively be ignored. It has been nearly 15 years since the first paper [1] was published recognizing the problem that thousands of compact binaries would present in the detection of low frequency (LF) gravitational waves. Since that time, all discussions of the sensitivity of the detectors to gravitational waves have had to take these binaries into account, concluding that at periods longer than about 300 seconds the detectors will likely be limited not by the instruments themselves, but by the inability of the detectors to separate a weak gravitational wave of interest from the background of the gravitational waves from these other, less interesting sources. In this paper we show, for the case where the source of interest is itself a particular monochromatic binary, that there is an inherent spatial filter due to the phase modulation produced by the motion of the detector around the sun that sharply reduces the confusion noise, typically to a level below the instrument noise of the detector. Therefore, for monochromatic sources like these, the confusion noise may simply be ignored. We will consider the two different configurations of space gravitational detectors that have been proposed. These are the ecliptic plane configuration (like the proposed OMEGA [2] detector in which independent probes orbit the earth in the ecliptic plane) and the precessing plane case (like the proposed LISA [3] mission where the heliocentric orbits for the probes are chosen so that the plane of the detector is inclined 60◦ to the ecliptic and precesses around the ecliptic pole once per year). A binary star of total mass M and reduced mass μ, with circular orbit at an angular frequency ω, lying in a direction given by angular coordinates Θ and Φ (measured in the plane of the detector) and with the orbit plane inclined by i to the line-of-sight, will produce a signal in the detector given by