A wide-angle formulation of foreground filters for HI intensity mapping

Abstract

Neutral hydrogen intensity mapping can in principle deliver rapid and large-volume cosmological surveys with exquisitely accurate redshifts that are determined directly from imaging. However, intensity maps suffer from very strong foreground contamination. Future surveys will require efficient data pipelines to remove the foregrounds and reveal the cosmological signal. It is expected that this cleaning will not remove the signal in substantial parts of the available Fourier space and that significant loss of signal due to imperfect cleaning will be confined to specific regions of Fourier space. This suggests a strategy which is useful for simplified estimates and rapid computations — i.e., to apply foreground filters that avoid the regions where loss of signal is significant. The standard Fourier-space power spectrum and foreground filters use a flat-sky approximation and thus exclude wide-angle correlations. We provide a new geometrical formulation of foreground filters in harmonic space, which naturally includes all wide-angle effects in the power spectrum. Foreground filtering leads to a loss of isotropy in Fourier space. In harmonic space this produces off-diagonal correlations. We derive analytical expressions for the generalised HI power spectrum and its cross-power with CMB lensing, for both single-dish and interferometer mode surveys.