Exploiting the full potential of photometric quasar surveys: Optimal
  power spectra through blind mitigation of systematics
  We present optimal measurements of the angular power spectrum of the XDQSOz
catalogue of photometric quasars from the Sloan Digital Sky Survey. These
measurements rely on a quadratic maximum likelihood estimator that
simultaneously measures the auto- and cross-power spectra of four redshift
samples, and provides minimum-variance, unbiased estimates even at the largest
angular scales. Since photometric quasars are known to be strongly affected by
systematics such as spatially-varying depth and stellar contamination, we
introduce a new framework of extended mode projection to robustly mitigate the
impact of systematics on the power spectrum measurements. This technique
involves constructing template maps of potential systematics, decorrelating
them on the sky, and projecting out modes which are significantly correlated
with the data. Our method is able to simultaneously process several thousands
of nonlinearly-correlated systematics, and mode projection is performed in a
blind fashion. Using our final power spectrum measurements, we find a good
agreement with theoretical predictions, and no evidence for further
contamination by systematics. Extended mode projection not only obviates the
need for aggressive sky and quality cuts, but also provides control over the
level of systematics in the measurements, enabling the search for small signals
of new physics while avoiding confirmation bias.
