Estimators for CMB Statistical Anisotropy
  We use quadratic maximum-likelihood (QML) estimators to constrain models with
Gaussian but statistically anisotropic Cosmic Microwave Background (CMB)
fluctuations, using CMB maps with realistic sky-coverage and instrumental
noise. This approach is optimal when the anisotropy is small, or when checking
for consistency with isotropy. We demonstrate the power of the QML approach by
applying it to the WMAP data to constrain several models which modulate the
observed CMB fluctuations to produce a statistically anisotropic sky. We first
constrain an empirically motivated spatial modulation of the observed CMB
fluctuations, reproducing marginal evidence for a dipolar modulation pattern
with amplitude 7% at L < 60, but demonstrate that the effect decreases at
higher multipoles and is 1% at L~500. We also look for evidence of a
direction-dependent primordial power spectrum, finding a very statistically
significant quadrupole signal nearly aligned with the ecliptic plane; however
we argue this anisotropy is largely contaminated by observational systematics.
Finally, we constrain the anisotropy due to a spatial modulation of adiabatic
and isocurvature primordial perturbations, and discuss the close relationship
between anisotropy and non-Gaussianity estimators.
