Atmospheric NLTE models for the spectroscopic analysis of blue stars with winds. IV. Porosity in physical and velocity space

Context. Clumping in the radiation-driven winds of hot, massive stars severly affects the derivation of synthetic observables across the electromagnetic spectrum.
Aims: We implement a formalism for treating wind clumping - focusing in particular on the light-leakage effects associated with a medium that is porous in physical and velocity space - into the global (photosphere + wind) NLTE model atmosphere and spectrum synthesis code FASTWIND.
Methods: The basic method presented here assumes a stochastic, two-component wind consisting of a mixture of optically thick and thin clumps embedded in a rarefied inter-clump medium. We have accounted fully for the reductions in opacity associated with porosity in physical and velocity-space (the latter due to Doppler shifts in an accelerating medium), as well as for the well-known effect that opacities depending on ⟨ρ²⟩ are higher in clumpy winds than in smooth ones of equal mass-loss rate. By formulating our method in terms of suitable mean and effective opacities for the clumpy wind, we are able to compute atmospheric models with the same speed (∼15 min on a modern laptop or desktop) as in previous generations of FASTWIND.
Results: After verifying important analytic limits (smooth, optically thin, completely optically thick), we present some first, generic results of the new models. These include: i) Confirming earlier results that velocity-space porosity is critical for analysis of UV wind resonance lines in O-stars; ii) for the optical Hα line, we show that optically thick clumping effects are small for O-stars, but potentially very important for late B and A-supergiants; iii) in agreement with previous work, we show that spatial porosity is a marginal effect for absorption of high-energy X-rays in O-stars, as long as the mean-free path between clumps are kept at realistic values ≲R_*; iv) whereas radio absorption in O-stars shows strong spatial porosity effects in near photospheric layers, it is negligible at their typical radio-photosphere radii ∼100R_*; v) regarding the wind ionization balance, a general trend is that increased rates of recombination in simulations with optically thin clumps lead to overall lower degrees of ionization than in corresponding smooth models, but that this effect now is counteracted by the increased levels of light-leakage associated with porosity in physical and velocity space (i.e., by an increase of ionization rates). We conclude by discussing future work and some planned applications for this new generation of FASTWIND models.