Hydrodynamical mass-loss rates for Very Massive Stars II. New theoretical mass-loss predictions at solar metallicity (Z = 0.02)

The evolutionary pathways and ultimate fates of very massive stars are governed primarily by mass loss through radiatively-driven winds. We present a new theoretical mass-loss prescription for (very) massive stars, capturing the complex dependence on the Eddington parameter e, luminosity, temperature, and hydrogen abundance. We calculated an extensive grid of 178 hydrodynamically consistent wind-atmosphere models in non-local thermodynamic equilibrium using the PoWR-HD code, predicting wind properties such as the mass-loss rate and terminal velocity self-consistently. The grid spans masses M* = 16-500 Msun, luminosities (L*/L) = 5.5-6.8, inner boundary temperatures T* = 12-50 kK, and hydrogen mass fractions X = 0.01-0.9, at a fixed metallicity of Z=0.02. We confirm the presence of a mass-loss kink in the - e relation across the explored parameter space. The kink marks the transition from a shallow scaling (about 2.8) at low e for optically thin O-star winds to a steeper scaling (about 10) for optically thick winds at high e. We derive comprehensive fitting relations capturing both the kink behaviour and two bistability jumps arising from iron ionisation changes, and provide auxiliary relations for implementation into stellar evolutionary calculations. Our prescription correctly reproduces the model-independent transition mass-loss rate in the Arches Cluster, confirming the accuracy of our predicted rates at the O-to-WNh transition. Application of our recipe to the Zero Age Main Sequence provides excellent agreement with recent empirical - e relation obtained for a wide range of temperatures and Eddington parameters. We provide a physically motivated, continuous, and empirically anchored mass-loss recipe for (very) massive stars, suitable for stellar evolution calculations in the 20-500 Msun range.