The CIB-lensing bispectrum: impact on primordial non-Gaussianity and detectability for the Planck mission

We characterize the Cosmic Infrared Background (CIB)-lensing bispectrum which is one of the contributions to the three-point functions of Cosmic Microwave Background (CMB) maps in harmonic space. We show that the CIB-lensing bispectrum has a considerable strength and that it can be detected with high significance in the Planck high-frequency maps. We also present forecasts of the contamination on different shapes of the primordial non-Gaussianity $f_{nl}$ parameter produced by the CIB-lensing bispectrum and by the extragalactic point sources bispectrum in the Planck high-resolution CMB anisotropy maps. The local, equilateral and orthogonal shapes are considered for 'raw' single-frequency (i.e., without applying any component separation technique) and foreground-reduced Planck temperature maps. The CIB-lensing correlation seems to mainly affect orthogonal shapes of the bispectrum - with {\Delta}$f_{nl}$ = -21 and -88 for the 143 and 217 GHz bands respectively - while point sources mostly impact equilateral shapes, with {\Delta}$f_{nl}$ = 160, 54 and 60 at 100, 143 and 217 GHz. However, the results indicate that these contaminants do not induce any relevant bias on Planck $f_{nl}$ estimates when foreground-reduced maps are considered: using SEVEM for the component separation we obtain {\Delta}$f_{nl}$ = 10.5 due to the CIB-lensing and {\Delta}$f_{nl}$ = 30.4 due to point sources, corresponding to 0.30{\sigma} and 0.45{\sigma} in terms of the Planck 2013 $f_{nl}$ uncertainty. The component separation technique is, in fact, able to partially clean the extragalactic source contamination and the bias is reduced for all the shapes. We have further developed single- and multiple-frequency estimators based on the Komatsu, Spergel & Wandelt (2005) formalism that can be implemented to efficiently detect this signal.