Analytic Minkowski Functionals of the Cosmic Microwave Background:
  Second-order Non-Gaussianity with Bispectrum and Trispectrum
  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 evaluations from non-Gaussian realizations of temperature maps,
showing very good agreements.
