Limits on Second-Order Non-Gaussianity from Minkowski Functionals of WMAP Data

We analyze non-Gaussianity (NG) due to the primordial bispectrum and trispectrum using CMB temperature maps of WMAP 7-year data. We first apply the perturbative formulae of Minkowski functionals up to second-order NG derived by Matsubara (2010), which enable us to give limits on cubic NG parametrized with tau_NL and g_NL as well as various types of quadratic NG parametrized with f_NL. We find no signature of primordial NG in WMAP 7-year data, but give constraints on the local-type, equilateral-type, orthogonal-type f_NL: f_NL(loc)=20±42, f_NL(eq)=-121±208, f_NL(ort)=-129±171, respectively, and tau_NL/10^4=-7.6±8.7, and g_NL/10^5=-1.9±6.4. We also find that these constraints are consistent with the limits from skewness and kurtosis parameters which characterize the perturbative corrections of MFs.