Analytic Minkowski Functionals of the CMB

Analytic formulas of Minkowski functionals in two-dimensional random
fields are derived, including effects of second-order non-Gaussianity
in the presence of both the bispectrum and trispectrum. The set of
formulas provides a promising method to constrain the primordial
non-Gaussianity of the universe by temperature fluctuations in the
cosmic microwave background radiation. In a case of local-type
non-Gaussianity, the Minkowski functionals are analytically given by
powers of quadratic and cubic parameters, $f_{\rm NL}$ and $g_{\rm
NL}$. Our formulas are not restricted to this particular model, and
applicable to a wide class of non-Gaussian models. The analytic
formulas are compared to numerical realizations of non-Gaussian
temperature maps, showing very good agreements.