Hydrodynamical mass-loss rates for very massive stars

Radiation-driven winds are ubiquitous in massive stars, but in very massive stars (VMSs), mass loss dominates their evolution, chemical yields, and ultimate fate. Theoretical predictions have often relied on extrapolations of O-star prescriptions, likely underestimating true VMS mass-loss rates. In the first of a series of papers on VMS wind properties, we investigate a feature predicted by Monte Carlo (MC) simulations: a mass-loss ‘kink’ or upturn where the single-scattering limit is breached and winds transition from optically thin to optically thick. We calculated hydrodynamically consistent wind-atmosphere models in non-local thermodynamic equilibrium using the POWR HD code, with a grid spanning 40-135 M ⊙ and 12-50kK at fixed log( L * / L ⊙ ) = 6.0 and solar-like metallicity with Z = 0.02. Our models confirm the existence of the kink, where the wind optical depth crosses unity and spectral morphology shifts from O-star to WNh types. The predicted location of the kink coincides with the transition stars in the Galactic Arches Cluster and reproduces the model-independent transition mass-loss rate of log( Ṁ trans ) ≈ −5.16 from Vink & Gräfener (2012). For the first time, we locate the kink at Γ e ≈ 0.43 ( M * ≈ 60 M ⊙ ) without relying on uncertain stellar masses. Above the kink, mass-loss rates scale much more steeply with decreasing mass (slope ~10), in qualitative agreement with MC predictions. We additionally identified two bistability jumps in the mass loss driven by Fe ionisation shifts: the first is from Fe IV → Fe III near 25 kK, and the second is from Fe III → Fe II near 15 kK. Our models thus provide the first comprehensive confirmation of the VMS mass-loss kink while establishing a mass-loss relation with complex mass and temperature dependencies with consequences for stellar evolution, chemical yields, and the black hole mass spectrum.