Constraining the WMAP9 bispectrum and trispectrum with needlets

We develop a needlet approach to estimate the amplitude of general (including non-separable) bispectra and trispectra in the cosmic microwave background, and apply this to the WMAP 9-year data. We obtain estimates for the 'orthogonal' bispectrum mode, yielding results which are consistent with the WMAP 7-year data. We do not observe the frequency-dependence suggested by the WMAP team's analysis of the 9-year data. We present 1-sigma constraints on the 'local' trispectrum shape gNL/10(5) = -4.1 +/- 2.3, the 'c1' equilateral model g(NL)(c1)/10(6) = -0.8 +/- 2.9, and the constant model g(NL)(cost)/10(6) = -0.2 +/- 1.8, together with a 95% confidence-level upper bound on the multifield local parameter tau(NL) < 22000. We estimate the bias on these parameters produced by point sources. The techniques developed in this paper should prove useful for other datasets such as Planck.