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
SGWBs, 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 Observatories (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 analysing simple toy models of time-stream data, and 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 that of the detector. Otherwise, the amplitude-phase mapping method
leads to a loss of overall 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.
