Nonlinear Redshift-Space Distortions in the Harmonic-space Galaxy Power
  Spectrum
  Future high spectroscopic resolution galaxy surveys will observe galaxies
with nearly full-sky footprints. Modeling the galaxy clustering for these
surveys, therefore, must include the wide-angle effect with narrow redshift
binning. In particular, when the redshift-bin size is comparable to the typical
peculiar velocity field, the nonlinear redshift-space distortion (RSD) effect
becomes important. A naive projection of the Fourier-space RSD model to
spherical harmonic space leads to diverging expressions. In this paper we
present a general formalism of projecting the higher-order RSD terms into
spherical harmonic space. We show that the nonlinear RSD effect, including the
fingers-of-God (FoG), can be entirely attributed to a modification of the
radial window function. We find that while linear RSD enhances the
harmonic-space power spectrum, unlike the three-dimensional case, the
enhancement decreases on small angular-scales. The fingers-of-God suppress the
angular power spectrum on all transverse scales if the bin size is smaller than
$\Delta r \lesssim \pi \sigma_u$; for example, the radial bin sizes
corresponding to a spectral resolution $R=\lambda/\Delta \lambda$ of a few
hundred satisfy the condition. We also provide the flat-sky approximation which
reproduces the full calculation to sub-percent accuracy.
