The Mexican Hat Wavelet Family. Application to point source detection in CMB maps

We propose a new detection technique in the plane based on an isotropic wavelet family. This family is naturally constructed as an extension of the Gaussian-Mexican Hat Wavelet pair and for that reason we call it the Mexican Hat Wavelet Family (MHWF). We show the performance of these wavelets when dealing with the detection of extragalactic point sources in cosmic microwave background (CMB) maps: a very important issue within the most general problem of the component separation of the microwave sky. Specifically, flat two-dimensional simulations of the microwave sky comprising all astrophysical components plus instrumental noise have been analyzed for the channels at 30, 44 and 70 GHz of the forthcoming ESA's Planck mission Low Frequency Instrument (LFI). We adopt up-to-date cosmological evolution models of extragalactic sources able to fit well the new data on high-frequency radio surveys and we discuss our current results on point source detection by comparing them with those obtained using the Mexican Hat Wavelet (MHW) technique, which has been already proven a suitable tool for detecting point sources. By assuming a 5% reliability level, the first new members of the MHWF, at their ``optimal scale'', provide three point source catalogues on half of the sky (at galactic latitude |b|> 30) at 30, 44 and 70 GHz of 639, 387 and 340 extragalactic sources, respectively. The corresponding flux detection limits are 0.38, 0.45 and 0.47 Jy . By using the same simulated sky patches and at the same frequencies as before, the MHW at its optimal scale provides 543, 322 and 311 sources with flux detection limits of 0.44, 0.51 and 0.50 Jy, respectively (5% reliability level). These results show a clear improvement when we use the new members of the MHWF and, in particular, the MHW2 with respect to the MHW