Empirical mass-loss rates and clumping properties of Galactic early-type O supergiants

We investigate the impact of optically thick clumping on stellar wind diagnostics in O supergiants and constrain wind parameters associated with porosity in velocity space. This is the first time the effects of optically thick clumping have been investigated for a sample of massive hot stars, using models including a full optically thick clumping description. We re-analyse spectroscopic observations of a sample of eight O supergiants. Using a genetic algorithm wrapper around the NLTE atmosphere code FASTWIND we obtain simultaneous fits to optical and UV spectra and determine photospheric and wind properties and surface abundances. We provide empirical constraints on a number of wind parameters including the clumping factors, mass-loss rates and terminal wind velocities. Additionally, we establish the first systematic empirical constraints on velocity filling factors and interclump densities. These parameters describe clump distribution in velocity-space and density of the interclump medium in physical-space, respectively. We observe a mass-loss rate reduction of a factor of 3.6 compared to theoretical predictions from Vink et al. (2000), and mass-loss rates within a factor 1.4 of predictions from Bj\"orklund et al. (2021). We confirm that including optically thick clumping allows simultaneous fitting of recombination lines and resonance lines, including the unsaturated UV phosphorus lines (Pv 1118-1128), without reducing the phosphorus abundance. We find that, on average, half of the wind velocity field is covered by dense clumps. We also find that these clumps are 25 times denser than the average wind, and that the interclump medium is 3-10 times less dense than the mean wind. The former result agrees well with theoretical predictions, the latter suggests that lateral filling-in of radially compressed gas might be critical for setting the scale of the rarefied interclump matter.