The binned bispectrum estimator: template-based and non-parametric CMB\n non-Gaussianity searches

We describe the details of the binned bispectrum estimator as used for the\nofficial 2013 and 2015 analyses of the temperature and polarization CMB maps\nfrom the ESA Planck satellite. The defining aspect of this estimator is the\ndetermination of a map bispectrum (3-point correlator) that has been binned in\nharmonic space. For a parametric determination of the non-Gaussianity in the\nmap (the so-called fNL parameters), one takes the inner product of this binned\nbispectrum with theoretically motivated templates. However, as a complementary\napproach one can also smooth the binned bispectrum using a variable smoothing\nscale in order to suppress noise and make coherent features stand out above the\nnoise. This allows one to look in a model-independent way for any statistically\nsignificant bispectral signal. This approach is useful for characterizing the\nbispectral shape of the galactic foreground emission, for which a theoretical\nprediction of the bispectral anisotropy is lacking, and for detecting a\nserendipitous primordial signal, for which a theoretical template has not yet\nbeen put forth. Both the template-based and the non-parametric approaches are\ndescribed in this paper.\n