Angular resolution of space-based gravitational wave detectors

Proposed space-based gravitational wave antennas involve satellites arrayed either in an equilateral triangle around the Earth in the ecliptic plane (the ecliptic-plane option) or in an equilateral triangle orbiting the Sun in such a way that the plane of the triangle is tilted at $60°$ relative to the ecliptic (the precessing-plane option). In this paper, we explore the angular resolution of these two classes of detectors for two kinds of sources (essentially monochromatic compact binaries and coalescing massive-black-hole binaries) using time-domain expressions for the gravitational waveform that are accurate to 4/2 PN order. Our results display an interesting effect not previously reported in the literature, and particularly underline the importance of including the higher-order PN terms in the waveform when predicting the angular resolution of ecliptic-plane detector arrays.