Bright OB stars in the Galaxy -: III.: Constraints on the radial stratification of the clumping factor in hot star winds from a combined Hα, IR and radio analysis

Context. Recent results strongly challenge the canonical picture of massive star winds: various evidence indicates that currently accepted mass-loss rates,. M, may need to be revised downwards, by factors extending to one magnitude or even more. This is because the most commonly used mass-loss diagnostics are affected by clumping (small-scale density inhomogeneities), influencing our interpretation of observed spectra and fluxes. Aims. Such downward revisions would have dramatic consequences for the evolution of, and feedback from, massive stars, and thus robust determinations of the clumping properties and mass-loss rates are urgently needed. We present a first attempt concerning this objective, by means of constraining the radial stratification of the so-called clumping factor. Methods. To this end, we have analyzed a sample of 19 Galactic O-type supergiants/giants, by combining our own and archival data for H-alpha, IR, mm and radio fluxes, and using approximate methods, calibrated to more sophisticated models. Clumping has been included into our analysis in the conventional way, by assuming the inter-clump matter to be void. Because (almost) all our diagnostics depends on the square of density, we cannot derive absolute clumping factors, but only factors normalized to a certain minimum. Results. This minimum was usually found to be located in the outermost, radio-emitting region, i.e., the radio mass-loss rates are the lowest ones, compared to M derived from H-alpha and the IR. The radio rates agree well with those predicted by theory, but are only upper limits, due to unknown clumping in the outer wind. H-alpha turned out to be a useful tool to derive the clumping properties inside r < 3...5 R-*. Our most important result concerns a (physical) difference between denser and thinner winds: for denser winds, the innermost region is more strongly clumped than the outermost one (with a normalized clumping factor of 4.1 +/- 1.4), whereas thinner winds have similar clumping properties in the inner and outer regions. Conclusions. Our findings are compared with theoretical predictions, and the implications are discussed in detail, by assuming different scenarios regarding the still unknown clumping properties of the outer wind.