Power spectrum modelling of galaxy and radio intensity maps including
  observational effects
  Fluctuations in the large-scale structure of the Universe contain significant
information about cosmological physics, but are modulated in survey datasets by
various observational effects. Building on existing literature, we provide a
general treatment of how fluctuation power spectra are modified by a
position-dependent selection function, noise, weighting, smoothing,
pixelization and discretization. Our work has relevance for the spatial power
spectrum analysis of galaxy surveys with spectroscopic or accurate photometric
redshifts, and radio intensity-mapping surveys of the sky brightness
temperature including generic noise, telescope beams and pixelization. We
consider the auto-power spectrum of a field, the cross-power spectrum between
two fields and the multipoles of these power spectra with respect to a curved
sky, deriving the corresponding power spectrum models, estimators, errors and
optimal weights. We note that "FKP weights" for individual tracers do not in
general provide the optimal weights when measuring the cross-power spectrum. We
validate our models using mock datasets drawn from N-body simulations, and
provide the python code we use for these tests at
https://github.com/cblakeastro/intensitypower. Our treatment should be useful
for modelling and studying cosmological fluctuation fields in observed and
simulated datasets.
