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.
