Context. Mass loss from massive stars forms an important aspect of the evolution of massive stars, as well as for the enrichment of the surrounding interstellar medium. Aims. Our goal is to predict accurate mass-loss rates and terminal wind velocities. These quantities can be compared to empirical values, thereby testing radiation-driven wind models. One specific topical issue is that of the so-called "weak-wind problem", where empirically derived mass-loss rates and (modified) wind momenta fall orders of magnitude short of predicted values. Methods. We employ an established Monte Carlo model and a recently suggested new line acceleration formalism to solve the wind dynamics more consistently. Results. We provide a new grid of mass-loss rates and terminal wind velocities of O-type stars, and compare the values to empirical results. Our models fail to provide mass-loss rates for main-sequence stars below a luminosity of log(L/L ) = 5.2, where we appear to run into a fundamental limit. At luminosities below this critical value there is insufficient momentum transferred to the wind in the region below the sonic point in order to kick-start the acceleration of the flow. This problem occurs at almost the exact location of the onset of the weak-wind problem. For O dwarfs, the boundary between being able to start a wind, and failing to do so, is at spectral type O6/O6.5. The direct cause of this failure for O6.5 stars is a combination of the lower luminosity and a lack of Fe v lines at the base of the wind. This might indicate that -in addition to radiation pressure -another mechanism is required to provide the necessary driving to initiate the wind acceleration. Conclusions. For stars more luminous than 10 5.2 L , our new mass-loss rates are in excellent agreement with the mass-loss prescription by Vink et al. (2000, A&A, 362, 295) using our terminal wind velocities as input to this recipe. This implies that the main assumption entering the method of the Vink et al. prescriptions -i.e. that the momentum equation is not explicitly solved for -does not compromise the reliability of the Vink et al. results for this part of parameter space. Finally, our new models predict terminal velocities that are typically 35 and 45 percent larger than observed values. Such over-predictions are similar to those from (modified) CAK-theory.

Stellar winds are an important aspect of our understanding of the evolution of massive stars and their input into the interstellar medium. Here we present solutions for the velocity field and mass-loss rates for stellar outflows as well as for the case of mass accretion through the use of the so-called Lambert W-function. For the case of a radiation-driven wind, the velocity field is obtained analytically using a parameterised description for the line acceleration that only depends on radius, which we obtain from MonteCarlo multi-line radiative transfer calculations. In our form of the equation of motion the critical point is the sonic point. We also derive an approximate analytical solution for the supersonic flow which closely resembles our exact solution. For the simultaneous solution of the mass-loss rate and velocity field, we describe a new iterative method. We apply our theoretical expressions and our iterative method to the stellar wind from a typical O5-V main sequence star, and find good agreement with empirical values. Our computations represent a self-consistent mass-loss calculation including the effect of multi-line scattering for an O-type star, opening up the possibility of applying Monte Carlo mass-loss calculations in regions of the Universe for which empirical constraints cannot be readily obtained.

We present solutions for the velocity field and mass-loss rates for 2D axisymmetric outflows, as well as for the case of mass accretion through the use of the Lambert W-function. For the case of a rotating radiation-driven wind the velocity field is obtained analytically using a parameterised description of the line acceleration that only depends on radius r at any given latitude θ. The line acceleration g(r) is obtained from Monte-Carlo multi-line radiative transfer calculations. The critical/sonic point of our equation of motion varies with latitude θ. Furthermore, an approximate analytical solution for the supersonic flow of a rotating wind is derived, which is found to closely resemble the exact solution. For the simultaneous solution of the mass-loss rate and velocity field, we use the iterative method of our 1D method extended to the non-spherical 2D case. We apply the new theoretical expressions with our iterative method to the stellar wind from a differentially rotating 40 M O5-V main sequence star as well as to a 60 M O-giant star, and we compare our results to previous studies that are extensions of the Castor et al. (1975, ApJ, 195, 157) CAK formalism. Next, we account for the effects of oblateness and gravity darkening. Our numerical results predict an equatorial decrease of the mass-loss rate, which would imply that (surface-averaged) total mass-loss rates are lower than for the spherical 1D case, in contradiction to the Maeder & Meynet (2000, A&A, 361, 159) formalism that is oftentimes employed in stellar evolution calculations for rotating massive stars. To clarify the situation in nature we discuss observational tests to constrain the shapes of large-scale 2D stellar winds.

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