FIRBACK: III. Catalog, source counts, and cosmological implications of the 170 mu m ISO

The FIRBACK (Far Infrared BACKground) survey is one of the deepest imaging surveys carried out at 170 mu m with ISOPHOT onboard ISO, and is aimed at the study of the structure of the Cosmic Far Infrared Background. This paper provides the analysis of resolved sources. After a validated process of data reduction and calibration, we perform intensive simulations to optimize the source extraction, measure the confusion noise (sigma_c = 45 mJy), and give the photometric and astrometric accuracies. 196 galaxies with flux S > 3 sigma_c are detected in the area of 3.89 square degrees. Counts of sources with flux S > 4 sigma_c present a steep slope of 3.3 +/- 0.6 on a differential ``log N-log S'' plot between 180 and 500 mJy. As a consequence, the confusion level is high and will impact dramatically on future IR deep surveys. This strong evolution, compared with a slope of 2.5 from Euclidian geometry, is in line with models implying a strongly evolving Luminous Infrared Galaxy population. The resolved sources account for less than 10% of the Cosmic Infrared Background at 170 mu m, which is expected to be resolved into sources in the 1 to 10 mJy range. Based on observations with ISO, an ESA project with instruments funded by ESA Member States (especially the PI countries: France, Germany, The Netherlands and the UK) and with the participation of ISAS and NASA.. Tables 7 to 13 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5)} or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/372/364.