Very massive star models I. Impact of rotation and metallicity and comparisons with observations

Context. In addition to being spectacular objects, very massive stars (VMSs) are suspected to have a tremendous impact on their environment and on cosmic evolution in general. The nucleosynthesis both during their advanced stages and their final explosion may contribute greatly to the overall enrichment of the Universe. Their resulting supernovae are candidates for the most superluminous events possible and their extreme conditions also lead to very important radiative and mechanical feedback effects, from local to cosmic scale.Aims. We explore the impact of rotation and metallicity on the evolution of VMSs over cosmic time.Methods. With the recent implementation of an equation of state in the GENEC stellar evolution code, which is appropriate for describing the conditions in the central regions of very massive stars in their advanced phases, we present new results on VMS evolution from Population III to solar metallicity.Results. Low-metallicity VMS models are highly sensitive to rotation, while the evolution of higher-metallicity models is dominated by mass-loss effects. The mass loss strongly affects their surface velocity evolution, breaking quickly at high metallicity while reaching the critical velocity for low-metallicity models. Comparison to observed VMSs in the LMC shows that the mass-loss prescriptions used for these models are compatible with observed mass-loss rates. In our framework for modeling rotation, our models of VMS need a high initial velocity in order to reproduce the observed surface velocities. The surface enrichment of these VMSs is difficult to explain with only one initial composition, and could suggest multiple populations in the R136 cluster. At a metallicity typical of R136, only our non- or slowly rotating VMS models may produce pair-instability supernovae. The most massive black holes that can be formed are less massive than about 60 M-circle dot.Conclusions. Direct observational constraints on VMS are still scarce. Future observational campaigns will hopefully gather more pieces of information to guide the theoretical modeling of these objects, whose impacts can be very important. VMS tables are available at the CDS.