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 9year 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-σ constraints on the ‘local’ trispectrum shape gNL/10 5 = −4.1 ± 2.3, the ‘c1’ equilateral model g1 NL/10 6 = −0.8 ± 2.9, and the constant model g NL /10 6 = −0.2 ± 1.8, together with a 95% confidence-level upper bound on the multifield local parameter τNL < 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.