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Context. The determination of chemical abundances constitutes a fundamental requirement for obtaining a complete picture of a star. Particularly in massive stars, CNO abundances are of prime interest, due to the nuclear CNO-cycle, and various mixing processes which bring these elements to the surface. The precise determination of carbon abundances, together with N and O, is thus a key ingredient for understanding the different phases of stellar evolution. Aims. We aim to enable a reliable carbon spectroscopy for our unified non-LTE atmosphere code FASTWIND. Methods. We have developed a new carbon model atom including C II/III/IV/V, and we discuss specific problems related to carbon spectroscopy in O-type stars. We describe different tests we have performed to examine the reliability of our implementation, and investigate which mechanisms influence the carbon ionization balance. By comparing with high-resolution spectra from six O-type stars, we verified to what extent observational constraints can be reproduced by our new carbon line synthesis. Results. Carbon lines are even more sensitive to a variation of Teff, log g, and Ṁ, than hydrogen and helium lines. We are able to reproduce most of the observed lines from our stellar sample, and to estimate those specific carbon abundances which bring the lines from different ions into agreement (three stages in parallel for cool objects, two for intermediate O-types). For hot dwarfs and supergiants earlier than O7, X-rays from wind-embedded shocks can have an impact on the synthesized line strengths, particularly for C IV, potentially affecting the abundance determination. Dielectronic recombination has a significant impact on the ionization balance in the wind. Conclusions. We demonstrate our capability to derive realistic carbon abundances by means of FASTWIND, using our recently developed model atom. We find that complex effects can have a strong influence on the carbon ionization balance in hot stars. For a further understanding, the UV range needs to be explored as well. By means of detailed and available nitrogen and oxygen model atoms, we will be able to perform a complete CNO abundance analysis for larger samples of massive stars, and to provide constraints on corresponding evolutionary models and aspects. [ABSTRACT FROM AUTHOR]

Context. Starbursts play an essential role in the evolution of galaxies. In these environments, massive stars, with their short lifetimes, are of particular importance. The stellar winds of massive stars significantly influence not only on their surroundings, but the associated mass loss also profoundly affects the evolution of the stars themselves. The evolution of the dense cores of massive starburst clusters is also affected by dynamical processes induced by N-body interactions, in addition to the evolution of each star, and the formation of very massive stars with masses up to several thousand solar masses may be decisive for the evolution of the cluster. The interpretation of the corresponding observations relies mainly on the theoretical modeling of such starbursts, which is a major challenge. Aims. The primary objective is to introduce an advanced diagnostic method of O-type stellar atmospheres with winds, including an assessment of the accuracy of the determinations of abundances, stellar and wind parameters. Moreover, observational results are interpreted in the framework of our stationary, one-dimensional theory of line driven winds. Possible effects caused by nonhomogeneous time dependent structures are also discussed. Methods. We combine consistent models of expanding atmospheres with stellar evolutionary calculations of massive and very massive (up to several 1000 solar masses) single stars with regard to the evolution of dense stellar clusters. Essential in this context are accurate dynamic parameters of the winds of very massive stars. Because the atmospheric mass outflow has substantial influence on the radiation field and the atomic occupation numbers, and the radiation field and the occupation numbers in turn directly influence the radiative acceleration and thus the strength and velocity of the outflow, the determination of the hydrodynamic structures requires a highly consistent treatment of the statistical equilibrium and the hydrodynamic and radiative processes in the expanding atmospheres. Results. We present computed mass loss rates, terminal wind velocities, and spectral energy distributions of massive and very massive stars of different metallicities, calculated from atmospheric models with an improved level of consistency. These computations have important implications for (i) the primordial chemical enrichment of Population III very massive stars; (ii) the age determination of globular clusters; and (iii) the formation of intermediate mass black holes in dense stellar clusters with respect to the importance of stellar wind mass loss for the evolution of their progenitor stars. Conclusions. Stellar evolutionary calculations, using the mass loss rates of very massive stars obtained in the present paper, show that very massive stars with a low metallicity lose only a very small amount of their mass; thus it is unlikely that very massive population III stars cause a significant helium enrichment of the interstellar medium. Solar-metallicity stars have higher mass-loss rates, but these are not so high to exclude very massive stars of solar metallicity, formed by dynamical processes in dense clusters, from ending their life massive enough to form intermediate-mass black holes. [ABSTRACT FROM AUTHOR]