On the linear filters for point source extraction of the Planck mission

The manifestation of point sources in the upcoming Planck maps is a direct reflection of the properties of the pixelized antenna beam shape for each frequency, which is related to the scan strategy, pointing accuracy, noise properties and map-making algorithm. In this paper we firstly compare analytically the three filters for the Planck point source extraction, namely, the adaptive top-hat filter (ATHF), the theoretically-optimal filter (TOF), and the so-called pseudo-filter based on wavelet technique. Our analyses are based on the premise that the experiment parameters the TOF and the pseudo-filter assume and require are already known: the CMB and noise power spectrum and a circular Gaussian beam shape and size, whereas the ATHF does not need any a priori knowledge. The analyses show that the TOF is optimal of them all in terms of the gain after the parameter inputs. On the other hand, the wavelet technique is only asymptotic to the TOF. We simulate the Planck HFI 100 GHz channel with elliptical beam in rotation to test the efficiency of the TOF and the ATHF. The uncertainties on the angular power spectrum will hamper the efficiency of the TOF. To tackle the real situations for the Planck point source extraction, most importantly, the elliptical beam shape with slow precession and change of the ellipticity ratio due to possible mirror degradation effect, the adaptive top-hat filter is computationally efficient and well suited to the construction of the Planck Early Release Compact Source Catalogue.