Primordial Non-Gaussianity from Minkowski Functionals of the WMAP Temperature Anisotropies

We present an analysis of the Minkowski Functionals (MFs) describing the Wilkinson Microwave Anisotropy Probe (WMAP) 3-yr temperature maps to place limits on possible levels of primordial non-Gaussianity. In particular, we apply perturbative formulae for the MFs to give constraints on the usual non-linear coupling constant fNL. The theoretical predictions are found to agree with the MFs of simulated cosmic microwave background (CMB) maps including the full effects of radiative transfer. The agreement is also very good even when the simulation maps include various observational artefacts, including the pixel window function, beam smearing, inhomogeneous noise and the survey mask. We accordingly find that these analytical formulae can be applied directly to observational measurements of fNL without relying on non-Gaussian simulations. Considering the bin-to-bin covariance of the MFs in WMAP in a chi-square analysis, we find that the primordial non-Gaussianity parameter is constrained to lie in the range -70 < fNL < 91 [95 per cent confidence level (C.L.)] using the Q + V + W co-added maps