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Figure 1: Radial profiles of single frequency and multiple frequency matched filters for a cluster of  arcmin. In the left-hand panel we see the spatial weighting used by the single frequency filter to optimally extract the cluster from the background (radio point sources + CMB) and noise. The filter is arbitrarily normalized to unity at the origin and the beam has a 2 arcmin FWHM. The right-hand panel shows the elements of the 3-band filter with 150, 220 and 300 GHz channels. The three functions are arbitrarily normalized to the peak value of the 150 GHz filter (black curve), and each channel has a 1 arcmin FWHM beam. In this case we see how the filter uses both spatial and spectral information to optimally extract the cluster.

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In the text

Figure 2: Integrated radio and IR source counts. The lower solid red line results from the differential counts of Eq. (6), while the dashed red line corresponds to the model of Eq. (7). Measured counts at 30 GHz from CBI and the VSA are shown as the hashed blue boxes. The upper solid red line gives the submillimeter source counts from Eq. (8). The diamonds show the measured counts at m from the HDF-North (Borys et al. 2003) and the stars those from the 8 mJy-survey (Scott et al. 2002).

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In the text

Figure 3: Noise () on the integrated Compton Y parameter as a function of filter scale. We assume K noise/beam and adopt 1 arcmin beams in all bands, except for the green 3-dot-dashed curve in the right-hand panel. At these frequencies, we only include IR sources below  mJy, following the counts of Eq. (8), and with a spectral index and no dispersion. Left panel: the black dotted line shows the sensitivity at 150 GHz, where the instrumental noise and point source confusion are comparable (see Fig. 4). Confusion is effectively eliminated by a 2-band filter, as demonstrated by the red dot-dashed line lying just above the pure instrumental noise limit (black 3 dot-dashed curve). The upper solid green line shows the result when adding primary CMB anisotropy, in which case the 2-band filter is unable to cleanly separate the three astrophysical components. Addition of a third band at 300 GHz (blue dashed line) does not greatly improve the result, because both the 220 and 300 GHz channels are dominated by point sources, as shown in Fig. 4 (see text). Right panel: artificially removing the point sources from the 300 GHz channel, we see (black dotted line) that the filter gains enough leverage on the three astrophysical signals to drop its noise to the instrumental limit (red dot-dashed line). Source confusion being greatly reduced at lower frequencies, a 3-band filter with 90 GHz (solid green line) performs better; this remains true even when we degrade the 90 GHz beam to a more realistic 2 arcmin FWHM (green 3-dot-dashed curve).

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In the text

Figure 4: Power spectra of the primary CMB anisotropy (solid black line), point source confusion in different bands (as labeled) and instrumental noise; the latter corresponds to K noise/1 arcmin lobe, which we take here to be the same in all bands. Only IR sources with  mJy are included, according to the counts of Eq. (8), and with and no dispersion. The figure shows the that the 300 GHz channel is dominated by sources, explaining why the 3-band filter with 90 GHz performs more efficiently than the one with 300 GHz (see Fig. 3).

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In the text

Figure 5: Minimum detectable mass as a function of redshift. The upper solid blue curve shows the result for the 3-band filter with a 300 GHz channel, while the middle dashed black curve gives the result when this channel is replaced by a 90 GHz band. For reference, the lower red dash-dotted curve gives the ideal detector-noise limited detection mass for the 3-band filter with 90 GHz. The 3-band filter with 90 GHz shows its higher sensitivity (see Fig. 3), but still suffers from residual foreground (CMB) contamination. These results follow for 1 arcmin FWHM beams in all bands. For comparison, the black 3-dot-dashed line gives the mass limit for the 3-band filter with a 90 GHz beam of 2 arcmin FWHM, which continues to perform better than the 3-band filter with 300 GHz despite the loss of angular resolution at the lower frequency.

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In the text