Astron. Astrophys. 346, 1-6 (1999)

1. Introduction

The study of the anisotropy in the Cosmic Microwave Background (CMB) has the potential to teach us a great deal about the background cosmology in which we live, about the formation of structure and about the early universe. Because of this promise, ESA selected the Planck Surveyor ¹ as the third Medium sized mission of its Horizon 2000 Scientific Program. With its wide range of frequencies, superb angular resolution, and high sensitivity, Planck has been hailed as the definitive CMB anisotropy experiment.

While much of the cosmological information is expected to come from the angular power spectrum of primary anisotropies, the sky contains more than this simple imprint of the inhomogeneities at last scattering. In particular the brightness fluctuations should be dominated on the smallest scales by point sources. One of the collateral science goals of Planck is to produce an all sky catalogue of such sources over a wide range of frequencies. Recent observations suggest that there may be many more bright sub-millimetre sources than previously expected, and it is the purpose of this paper to explore the impact of these findings on the Planck mission. While several authors (see below) have looked at the one-point statistics of these sub-mm galaxies, little has been done on the two-point function (or power spectrum) of these sources. It is this statistic which is most familiar to the CMB community, and which we concentrate on here.

The most exciting recent observations in the sub-mm waveband have come from the new Submillimeter Common-User Bolometer Array (SCUBA; Holland et al. 1999) on the James Clerk Maxwell Telescope. A combination of the properties of the sky and the galaxies themselves make the SCUBA 850 µm filter the optimal one for cosmology. This waveband corresponds closely with the 353 GHz channel of the High Frequency Instrument (HFI) of Planck. The central frequencies are almost identical, although the Planck bandwidth will be considerably larger ( rather than the of the SCUBA 850 µm filter). SCUBA has now been used to make several deep integrations which have detected distant sources at 850 µm (Barger et al. 1998, Eales et al. 1998, Holland et al. 1998, Hughes et al. 1998, Smail et al. 1997), and this has radically altered our expectations for the importance of dusty galaxies at high redshift.

A summary of the source count observations is provided in Table 1. These new data thus provide us with direct measurements of the number density of bright sources (albeit currently only over small patches of the sky, and a limited range of flux) at a frequency directly relevant to the Planck science channels. We shall work primarily at 353 GHz, though we shall also extrapolate these counts to nearby frequencies using models of the spectral energy distribution of the sources.

Table 1. SCUBA point source observations at 850 µm (353 GHz). We list the flux level to which each field was searched (generally 3 times the rms level), the number of sources found, the Bayesian 95% confidence level on the mean counts coming from Poisson statistics, the area covered, the number density of sources (with errors also from Poisson statistics). These numbers were taken from Hughes et al. (1998), Barger et al. (1998), Eales et al. (1998), Smail et al. (1997), Chapman et al. (in preparation), and Holland et al. (1998), respectively.

There have been several estimates of how many sub-mm sources Planck might be able to detect (e.g. Bersanelli et al. 1996), as well as estimates of other one-point statistics, often referred to as `confusion noise' (Condon 1974, Blain et al. 1998). As far as the fluctuations are concerned, several studies have already been carried out on the implications of point sources for the measurement of CMB anisotropies. Much of this work dealt more specifically with radio galaxy contributions at low frequency (e.g. Tegmark & Efstathiou 1996), or dealt with far-IR sources, but concentrated on the uniform background contribution and the correlation function (e.g. Franceschini et al. 1991, Bond et al. 1991, Wang 1991, Gawiser & Smoot 1997, Blain et al. 1998). Very similar studies have also been carried out for the X-ray background (see Yamamoto & Sugiyama 1998, and references therein), the optical background (see Vogeley 1998, and references therein), and more exotic backgrounds (e.g. Scott 1993). The most relevant work are the recent papers by Toffolatti et al. (1998) and Guiderdoni et al. (1996) which contain many useful results, and estimates of confusion noise, although they were written before the new series of SCUBA measurements. Our approach here also differs from theirs in that our predictions are based on straightforward extrapolations from observable properties. We deliberately avoid any modelling of the complex galaxy evolution process.

To calculate the impact of these new data on Planck it will be necessary to model the number density of sources as a function of flux, . We shall take care to ensure that our model does not overproduce, when integrated, the far-infrared background (FIB) light detected by (Puget et al. 1996, Fixsen et al. 1998). At 353 GHz the background is approximately , although this is not a directly measured quantity, so the real error bar at 353 GHz may be larger. We construct our fiducial model so that the integrated light from the sources contribute essentially all of this background.

© European Southern Observatory (ESO) 1999

Online publication: May 6, 1999
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