Comparison of maximum-likelihood mapping methods for gravitational-wave backgrounds

Detection of a stochastic background of gravitational waves is likely to occur in the next few years. Beyond searches for the isotropic component of a stochastic gravitational-wave background, there have been various mapping methods proposed to target anisotropic backgrounds. Some of these methods have been applied to data taken by the Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo. Specifically, these directional searches have focused on mapping the intensity of the signal on the sky via maximum-likelihood solutions. We compare this intensity mapping approach to a previously proposed, but never employed, amplitude-phase mapping method to understand whether this latter approach may be employed in future searches. We build up our understanding of the differences between these two approaches by analyzing simple toy models of time-stream data, and we run mock-data mapping tests for the two methods. We find that the amplitude-phase method is only applicable to the case of a background which is phase coherent on large scales or, at the very least, has an intrinsic coherence scale that is larger than the resolution of the detector. Otherwise, the amplitude-phase mapping method leads to an overall loss of information, with respect to both phase and amplitude. Since we do not expect these phase-coherent properties to hold for any of the gravitational-wave background signals we hope to detect in the near future, we conclude that intensity mapping is the preferred method for such backgrounds.