The WIRCam Deep Survey. I. Counts, colours, and mass-functions derived from near-infrared imaging in the CFHTLS deep fields

20 pages, 22 figures, accepted by A&A. Minor corrections plus an extended discussion of the galaxy stellar mass function. Galaxy number counts are also updated (Figs 10-12 and Table 3)International audienceWe present a new near-infrared imaging survey in the four CFHTLS deep fields: the WIRCam Deep Survey or "WIRDS". WIRDS comprises extremely deep, high quality (FWHM ~ 0.6″) J, H, and Ks imaging covering a total effective area of 2.1 deg2 and reaching AB 50% completeness limits of ≈ 24.5. We combine our images with the CFHTLS to create a unique eight-band ugrizJHKS photometric catalogues in the four CFHTLS deep fields; these four separate fields allow us to make a robust estimate of the effect of cosmic variance for all our measurements. We use these catalogues in combination with ≈ 9800 spectroscopic redshifts to estimate precise photometric redshifts (σΔz/(1 + z) ≲ 0.03 at i < 25), galaxy types, star-formation rates and stellar masses for a unique sample of ≈ 1.8 million galaxies. Our JHKs number counts are consistent with previous studies. We apply the "BzK" selection to our gzK filter set and find that the star forming BzK selection successfully selects 76% of star-forming galaxies in the redshift range 1.4 < z < 2.5 in our photometric catalogue, based on our photometric redshift measurement. Similarly the passive BzK selection returns 52% of the passive 1.4 < z < 2.5 population identified in the photometric catalogue. We present the mass functions of the total galaxy population as a function of redshift up to z = 2 and present fits using double Schechter functions. A mass-dependent evolution of the mass function is seen with the numbers of galaxies with masses of M ≲ 1010.75 still evolving at z ≲ 1, but galaxies of higher mass reaching their present day numbers by z ~ 0.8-1. This is consistent with the present picture of downsizing in galaxy evolution. We compare our results with the predictions of the GALFORM semi-analytical galaxy formation model and find that the simulations provide a relatively successful fit to the observed mass functions at intermediate masses (i.e. 10 ≲ log (M/M&sun;) ≲ 11). However, as is common with semi-analytical predictions of the mass function, the GALFORM results under-predict the mass function at low masses (i.e. log (M/M&sun;) ≲ 10), whilst the fit as a whole degrades beyondredshifts of z ~ 1.2. All photometric catalogues and images are made publicly available from TERAPIX and CADC. Based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l'Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS