Accurate photometric redshifts for the CFHT legacy survey calibrated using the VIMOS VLT deep survey

Aims. We present and release photometric redshifts for a uniquely large and deep sample of 522286 objects with i′_AB ≤25 in the Canada-France Hawaii Telescope Legacy Survey (CFHTLS) "Deep Survey" fields D1, D2, D3, and D4, which cover a total effective area of 3.2 deg ². Methods. We use 3241 spectroscopic redshifts with 0 ≤ z ≤ 5 from the VIMOS VLT Deep Survey (VVDS) as a calibration and training set to derive these photometric redshifts. Using the "Le Phare" photometric redshift code, we developed a robust calibration method based on an iterative zero-point refinement combined with a template optimisation procedure and the application of a Bayesian approach. This method removes systematic trends in the photometric redshifts and significantly reduces the fraction of catastrophic errors (by a factor of 2), a significant improvement over traditional methods. We use our unique spectroscopic sample to present a detailed assessment of the robustness of the photometric redshift sample. Results. For a sample selected at i′_AB ≤24, we reach a redshift accuracy of σ_Δz/(1+z)= 0.029 with η = 3.8% of catastrophic errors (η is defined strictly as those objects with |Δz|/(1 + z) > 0.15). The reliability of our photometric redshifts decreases for faint objects: we find σ_Δz/(1+z) = 0.025,0.034 and η = 1.9%, 5.5% for samples selected at i′_AB = 17.5-22.5 and 22.5-24 respectively. We find that the photometric redshifts of starburst galaxies are less reliable: although these galaxies represent only 22% of the spectroscopic sample, they are responsible for 50% of the catastrophic errors. An analysis as a function of redshift demonstrates that our photometric redshifts work best in the redshift range 0.2 ≤; z ≤ 1.5. We find an excellent agreement between the photometric and the VVDS spectroscopic redshift distributions at i′_AB ≤ 24. Finally, we compare the redshift distributions of i′ selected galaxies on the four CFHTLS deep fields, showing that cosmic variance is still present on fields of 0.7-0.9 deg². These photometric redshifts are made publicly available at http://terapix.iap.fr (complete ascii catalogues) and http://cencos.oamp.fr/cencos/CFHTLS/ (searchable database interface).