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Table 1:   PEP number counts, normalized to the Euclidean slope.

Appendix A: PACS data

PEP science demonstration data include the GOODS-N and Abell 2218 fields. In addition to these, part of the other PEP blank fields have already been scheduled and observed: Lockman Hole and COSMOS (85% of the planned depth). Observations of all fields were carried out by adopting the intermediate speed (20 arcsec/s) scan-map mode. Table A.1 lists the total exposure times already observed for these fields.

Data have been processed through the standard PACS reduction pipeline, version 2.0.1328, within the HCSS environment (Ott et al. 2010). Additionally, we employed custom procedures aimed at removing of interference patterns, tracking anomalies, re-centering positional offsets, and mapping.

Glitch removal is based on multi-resolution median transform, developed by Starck & Murtagh (1998) to detect faint sources in ISOCAM data. The signal due to real sources and glitches show different signatures in the pixel timeline. These features are recognized using a multi-scale transform, separating the various frequencies of the signal. Once the glitch components are identified, they are replaced by interpolated values in the pixel timeline.

PACS photometers exhibit a noise with a roughly f^-0.5 spectrum at relevant frequencies. To remove the bulk of the noise we apply a ``running-box'' high-pass median filter to each pixel timeline, but mask the position of bright sources. The objects mask is produced iteratively during the reduction by detecting sources on the final map, and then we mask them in a double-pass mapping scheme. Testing shows that this masked filtering method modifies the fluxes of point-like source by less than 5%.

Imperfections, drifts, and errors in the pointing accuracy of the Herschel satellite were corrected by re-centering the data on a grid of known 24 m sources populating the fields. Such objects were stacked for all scan-legs in a given direction in a given map repetition (or for a subset of those, in the very large COSMOS maps). The stacking result was then used to compute the average offset to be applied to this set of scan-legs, for a given direction, in a given map repetition. This procedure also implicitly corrects for small timing offsets between pointing information and data. Absolute, systematic astrometric offsets turned out to be as high as 5 arcsec, while relative corrections between individual submaps are approximately 1 arcsec.

Table A.1:   PEP fields: total exposure times, noise properties, flux levels for 80% completeness and 30% spurious fraction, statistics of blind catalogs, and results of maximum-likelihood match to the multi-wavelength ancillary catalogs (labeled ``multi'', GOODS-N only).

Map reconstruction is done via simple image co-addition, based on a simplified version of the ``drizzle'' method (Fruchter & Hook 2002). Given the high data redundancy in the GOODS-N field, the drop size is set to 1/8 of the input array pixel size. This corresponds to 1/5 and 1/4 of the output pixel size at 100 m and 160 m, respectively, thus reducing the correlated noise in the final map. Fields with lower redundancy were mapped by adopting a smaller drop size (1/4 of the input PACS array pixel size). Images produced from each observation were weighted according to the effective exposure of each pixel and co-added to produce the final maps. The final error map was computed as the standard deviation of the weighted mean. Owing to the nature of scan maps, correlations exist between nearby pixels, in particular along the scan direction. These correlations are close to uniform across the final map, thus we derived a mean correlation correction factor which was then accounted for in the errors on the extracted fluxes.

PACS catalogs were extracted following two different approaches, optimized for the different scientific aims of the PEP project. We performed a blind extraction using the Starfinder PSF-fitting code (Diolaiti et al. 2000) and a guided extraction using 24 m priors, following the method described in Magnelli et al. (2009). The two methods provide similar results: fluxes extracted in the two cases are consistent with each other, the prior extraction leading to slightly deeper - although possibly biased - catalogs. The number counts presented in this paper were built on the blind catalog. Point spread function (PSF) profiles were extracted from the final science maps, and turn out to have an FWHM of 7.5 and 11 arcsec in the 100 m and 160 m bands, respectively. Aperture corrections were characterized on calibration observations of the Vesta asteroid. Absolute flux calibration is based on Dra, Tau, and CMa and makes use of the standard calibration file embedded in the PACS pipeline (version 2.0.1328). Typical absolute flux calibration errors are 10% and include uncertainties on instrumental characterization, PSFs, and reference stars analysis.

Noise in PACS maps was measured with random aperture extractions on residual images and compared to the observed S/N ratio for the detected sources. The rms values thus obtained include both instrumental noise and confusion noise due to undetected sources (i.e., below the 3 threshold). This measured 1 noise is 1.00 mJy at 100 m and 1.90 mJy at 160 m for GOODS-N. Table A.1 includes the noise properties of the SDP fields, as well as the Lockman Hole and COSMOS.

To quantify the reliability of extracted fluxes, the level of incompleteness and the fraction of spurious sources, Monte Carlo simulations were performed, creating 500 images and adding 20 artificial objects onto science maps each, for a total of 10 000 sources. Input and output fluxes are consistent with each other within a few percent. Completeness is defined as the fraction of sources that have been detected with a photometric accuracy of at least 50% (Papovich et al. 2004). Spurious sources are defined as those extracted above 3 with an input flux lower than 3 . The latter is consistent with the spurious fraction inferred by blindly extracting from inverted maps. The GOODS-N blind catalog reaches 80% completeness at 5.5 mJy and 11.0 mJy in the two bands, and a 30% fraction of spurious detections at 2.5 and 7.0 mJy, in green and red respectively (see Table A.1).

The GOODS-N field benefits from an extensive multi-wavelength coverage. Adopting the Grazian et al. (2006) approach, the PEP Team built a reliable multi-wavelength, PSF-matched database, including ACS bviz (Giavalisco et al. 2004), Flamingos JHK and Spitzer IRAC data. Moreover, MIPS 24 m (Magnelli et al. 2009) and Barger et al. (2008) deep U, , and spectroscopic redshifts have been added. When no spectroscopic redshifts were available, photometric redshifts have been derived using the EAZY code (Brammer et al. 2008).

The 100 and 160 m blind catalogs were finally linked to this multi-wavelength catalog through a three-band maximum likelihood procedure (Sutherland & Saunders 1992), starting from the longest wavelength available (160 m, PACS) and progressively matching 100 m (PACS) and 24 m (Spitzer/MIPS) data. Table A.1 summarizes the main properties of blind catalogs, as well as the results of the maximum-likelihood match in GOODS-N.

Confusion is a major concern in deep wide-beam observations, like far-IR or sub-mm imaging of blank fields. PEP Herschel observations are not dispensed from confusion: the high density of detected sources hinders the extraction of fainter objects, in the so-called ``source density confusion criterion'' (SDC, Dole et al. 2003). Adopting the Lagache et al. (2003) definition of beam (i.e., ), the source density in PACS blind catalogs is 40 beams/source at 100 m and 18 beams/source at 160 m. This indicates that PEP GOODS-N is already hitting the SDC limit in the PACS red band, estimated to be 16.7 beams/source by Dole et al. (2003), while the green channel is not affected. By extrapolating integral number counts, we estimate that this limit will be reached at 2.0 mJy at 100 m and 4.7 mJy at 160 m. Nevertheless, this limit is known to be rather conservative, and some authors have already shown that source extraction can be reliably carried out to levels as low as 10 beam/source under favorable conditions (e.g. at 24 m, Magnelli et al. 2009).