The photospheric solar oxygen project. IV. 3D-NLTE investigation of the 777 nm triplet lines

International audienceContext. The solar photospheric oxygen abundance is still widely debated. Adopting the solar chemical composition based on the "low" oxygen abundance, as determined with the use of three-dimensional (3D) hydrodynamical model atmospheres, results in a well-known mismatch between theoretical solar models and helioseismic measurements that is so far unresolved. Aims: We carry out an independent redetermination of the solar oxygen abundance by investigating the center-to-limb variation of the O i IR triplet lines at 777 nm in different sets of spectra. Methods: The high-resolution and high signal-to-noise solar center-to-limb spectra are analyzed with the help of detailed synthetic line profiles based on 3D hydrodynamical CO5BOLD model atmospheres and 3D non-LTE line formation calculations with NLTE3D. The idea is to exploit the information contained in the observations at different limb angles to simultaneously derive the oxygen abundance, A(O), and the scaling factor SH that describes the cross-sections for inelastic collisions with neutral hydrogen relative to the classical Drawin formula. Using the same codes and methods, we compare our 3D results with those obtained from the semi-empirical Holweger-Müller model atmosphere as well as from different one-dimensional (1D) reference models. Results: With the CO5BOLD 3D solar model, the best fit of the center-to-limb variation of the triplet lines is obtained when the collisions by neutral hydrogen atoms are assumed to be efficient, i.e., when the scaling factor SH is between 1.2 and 1.8, depending on the choice of the observed spectrum and the triplet component used in the analysis. The line profile fits achieved with standard 1D model atmospheres (with fixed microturbulence, independent of disk position mu) are clearly of inferior quality compared to the 3D case, and give the best match to the observations when ignoring collisions with neutral hydrogen (SH = 0). The results derived with the Holweger-Müller model are intermediate between 3D and standard 1D. Conclusions: The analysis of various observations of the triplet lines with different methods yields oxygen abundance values (on a logarithmic scale where A(H) = 12) that fall in the range 8.7