Optimal limits on fNLlocal from WMAP 5-year data

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We have applied the optimal estimator for fNLlocal to the 5 year WMAP data. Marginalizing over the amplitude of foreground templates we get -4 < fNLlocal < 80 at 95% CL. Error bars of previous (sub-optimal) analyses are roughly 40% larger than these. The probability that a Gaussian simulation, analyzed using our estimator, gives a result larger in magnitude than the one we find is 7%. Our pipeline gives consistent results when applied to the three and five year WMAP data releases and agrees well with the results from our own sub-optimal pipeline. We find no evidence of any residual foreground contamination.