Hot and cold spots counts as probes of non-Gaussianity in the CMB

We introduce the numbers of hot and cold spots, $n_h$ and $n_c$, of excursion sets of the CMB temperature anisotropy maps as statistical observables that can discriminate different non-Gaussian models. We numerically compute them from simulations of non-Gaussian CMB temperature fluctuation maps. The first kind of non-Gaussian model we study is the local type primordial non-Gaussianity. The second kind of models have some specific form of the probability distribution function from which the temperature fluctuation value at each pixel is drawn, obtained using HEALPIX. We find the characteristic non-Gaussian deviation shapes of $n_h$ and $n_c$, which is distinct for each of the models under consideration. We further demonstrate that $n_h$ and $n_c$ carry additional information compared to the genus, which is just their linear combination, making them valuable additions to the Minkowski Functionals in constraining non-Gaussianity.