The R136 star cluster dissected with Hubble Space Telescope/STIS. III. The most massive stars and their clumped winds

Context: The star cluster R136 inside the LMC hosts a rich population of massive stars, including the most massive stars known. The strong stellar winds of these very luminous stars impact their evolution and the surrounding environment. We currently lack detailed knowledge of the wind structure that is needed to quantify this impact. Aims: To observationally constrain the stellar and wind properties of the massive stars in R136, in particular the parameters related to wind clumping. Methods: We simultaneously analyse optical and UV spectroscopy of 53 O-type and 3 WNh-stars using the FASTWIND model atmosphere code and a genetic algorithm. The models account for optically thick clumps and effects related to porosity and velocity-porosity, as well as a non-void interclump medium. Results: We obtain stellar parameters, surface abundances, mass-loss rates, terminal velocities and clumping characteristics and compare these to theoretical predictions and evolutionary models. The clumping properties include the density of the interclump medium and the velocity-porosity of the wind. For the first time, these characteristics are systematically measured for a wide range of effective temperatures and luminosities. Conclusions: We confirm a cluster age of 1.0-2.5 Myr and derive an initial stellar mass of $\geq 250 {\rm M}_\odot$ for the most massive star in our sample, R136a1. The winds of our sample stars are highly clumped, with an average clumping factor of $f_{\rm cl}=29\pm15$. We find tentative trends in the wind-structure parameters as a function of mass-loss rate, suggesting that the winds of stars with higher mass-loss rates are less clumped. We compare several theoretical predictions to the observed mass-loss rates and terminal velocities and find that none satisfactorily reproduces both quantities. The prescription of Krti\v{c}ka & Kub\'at (2018) matches best the observed mass-loss rates.Comment: Accepted for publication in A&A; Appendix I will not be included in the published versio