Optimal constraint on g_NL from CMB

An optimal method to constrain the non-linearity parameter g(NL) of the local-type non-Gaussianity from CMB data is proposed. Our optimal estimator for g(NL) is separable and can be efficiently computed in real space. Combining the exact filtering of CMB maps with the full covariance matrix, our method allows us to extract cosmological information from observed data as much as possible and obtain a tighter constraint on g(NL) than previous studies. Applying our method to the WMAP 9-year data, we obtain the constraint g(NL) = (-3.3 +/- 2.2) x 10(5), which is a few times tighter than previous ones. We also make a forecast for PLANCK data by using the Fisher matrix analysis.