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Register a new userA proper description of clumping in hot star winds: the key to obtaining reliable mass-loss rates?
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Small-scale inhomogeneities, or `clumping, in the winds of hot, massive stars are conventionally included in spectral analyses by assuming optically thin clumps. To reconcile investigations of different diagnostics using this microclumping technique, very low mass-loss rates must be invoked for O stars. Recently it has been suggested that by using the microclumping approximation one may actually drastically underestimate the mass-loss rates. Here we demonstrate this, present a new, improved description of clumpy winds, and show how corresponding models, in a combined UV and optical analysis, can alleviate discrepancies between previously derived rates and those predicted by the line-driven wind theory. Furthermore, we show that the structures obtained in time-dependent, radiation-hydrodynamic simulations of the intrinsic line-driven instability of such winds, which are the basis to our current understanding of clumping, in their present-day form seem unable to provide a fully self-consistent, simultaneous fit to both UV and optical lines. The reasons for this are discussed.
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We calculate global (unified) wind models of main-sequence, giant, and supergiant O stars from our Galaxy. The models are calculated by solving hydrodynamic, kinetic equilibrium (also known as NLTE) and comoving-frame (CMF) radiative transfer equations from the (nearly) hydrostatic photosphere to the supersonic wind. For given stellar parameters, our models predict the photosphere and wind structure and in particular the wind mass-loss rates without any free parameters. Our predicted mass-loss rates are by a factor of 2--5 lower than the commonly used predictions. A possible cause of the difference is abandoning of the Sobolev approximation for the calculation of the radiative force, because our models agree with predictions of CMF NLTE radiative transfer codes. Our predicted mass-loss rates agree nicely with the mass-loss rates derived from observed near-infrared and X-ray line profiles and are slightly lower than mass-loss rates derived from combined UV and H$alpha$ diagnostics. The empirical mass-loss rate estimates corrected for clumping may therefore be reconciled with theoretical predictions in such a way that the average ratio between individual mass-loss rate estimates is not higher than about $ 1.6 $. On the other hand, our predictions are by factor of $ 4.7 $ lower than pure H$alpha$ mass-loss rate estimates and can be reconciled with these values only assuming a microclumping factor of at least eight.
This review describes the evidence for small-scale structure, `clumping, in the radiation line-driven winds of hot, massive stars. In particular, we focus on examining to what extent simulations of the strong instability inherent to line-driving can explain the multitude of observational evidence for wind clumping, as well as on how to properly account for extensive structures in density and velocity when interpreting the various wind diagnostics used to derive mass-loss rates.
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 Bjorklund 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.
We investigate the effects of stellar limb-darkening and photospheric perturbations for the onset of wind structure arising from the strong, intrinsic line-deshadowing instability (LDI) of a line-driven stellar wind. A linear perturbation analysis shows that including limb-darkening reduces the stabilizing effect of the diffuse radiation, leading to a net instability growth rate even at the wind base. Numerical radiation-hydrodynamics simulations of the non-linear evolution of this instability then show that, in comparison with previous models assuming a uniformly bright star without base perturbations, wind structure now develops much closer ($r la 1.1 R_star$) to the photosphere. This is in much better agreement with observations of O-type stars, which typically indicate the presence of strong clumping quite near the wind base.
We construct helium (He) star models with optically thick winds and compare them with the properties of Galactic Wolf-Rayet (WR) stars. Hydrostatic He-core solutions are connected smoothly to trans-sonic wind solutions that satisfy the regularity conditions at the sonic point. Velocity structures in the supersonic parts are assumed by a simple beta-type law. By constructing a center-to-surface structure, a mass-loss rate can be obtained as an eigenvalue of the equations. Sonic points appear at temperatures ~ 1.8e5 - 2.8e5 K below the Fe-group opacity peak, where the radiation force becomes comparable to the local gravity. Photospheres are located at radii 3-10 times larger than sonic points. The obtained mass-loss rates are comparable to those of WR stars. Our mass-loss rate - luminosity relation agrees well with the relation recently obtained by Graefener et al. (2017). Photospheric temperatures of WR stars tend to be cooler than our predictions. We discuss the effects of stellar evolution, detailed radiation transfer, and wind clumping, which are ignored in this paper.
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