2D wind clumping in hot, massive stars from hydrodynamical line-driven instability simulations using a pseudo-planar approach

Context: Clumping in the radiation-driven winds of hot, massive stars arises naturally due to the strong, intrinsic instability of line-driving (the `LDI'). But LDI wind models have so far mostly been limited to 1D, mainly because of severe computational challenges regarding calculation of the multi-dimensional radiation force. Aims: To simulate and examine the dynamics and multi-dimensional nature of wind structure resulting from the LDI. Methods: We introduce a `pseudo-planar', `box-in-a-wind' method that allows us to efficiently compute the line-force in the radial and lateral directions, and then use this approach to carry out 2D radiation-hydrodynamical simulations of the time-dependent wind. Results: Our 2D simulations show that the LDI first manifests itself by mimicking the typical shell-structure seen in 1D models, but how these shells then quickly break up into complex 2D density and velocity structures, characterized by small-scale density `clumps' embedded in larger regions of fast and rarefied gas. Key results of the simulations are that density-variations in the well-developed wind statistically are quite isotropic and that characteristic length-scales are small; a typical clump size is ~0.01R at 2R, thus resulting also in rather low typical clump-masses ~10^17 g. Overall, our results agree well with the theoretical expectation that the characteristic scale for LDI-generated wind-structure is of order the Sobolev length. We further confirm some earlier results that lateral `filling-in' of radially compressed gas leads to somewhat lower clumping factors in 2D simulations than in comparable 1D models. We conclude by discussing an extension of our method toward rotating LDI wind models that exhibit an intriguing combination of large- and small-scale structure extending down to the wind base.Comment: 9 pages, 7 figures + 1 Appendix with 1 figure. Recommended for publication in A&

Mass loss from inhomogeneous hot star winds III. An effective-opacity formalism for line radiative transfer in accelerating, clumped two-component media, and first results on theory and diagnostics

[Abridged] We develop and benchmark a fast and easy-to-use effective-opacity formalism for line and continuum radiative transfer in an accelerating two-component clumpy medium. The formalism bridges the limits of optically thin and thick clumps, and is here used to i) design a simple vorosity-modified Sobolev with exact integration (vmSEI) method for analyzing UV wind resonance lines in hot, massive stars, and ii) derive simple correction factors to the line force driving the outflows of such stars. We show that (for a given ionization factor) UV resonance doublets may be used to analytically predict the upward corrections in empirically inferred mass-loss rates associated with porosity in velocity space (a.k.a. velocity-porosity, or vorosity), but that severe solution degeneracies exist. For an inter-clump density set to 1 % of the mean density, we for O and B supergiants derive upward empirical mass-loss corrections of typically factors of either ~5 or ~50, depending on which of the two applicable solutions is chosen. Overall, our results indicate this solution dichotomy severely limits the use of UV resonance lines as direct mass-loss indicators of clumped hot stellar winds. We next apply the effective-opacity formalism to the standard CAK theory of line-driven winds. By analytic and numerical hydrodynamics calculations, we show that in cases where vorosity is important at the critical point setting the mass-loss rate, the reduced line-force leads to a lower theoretical mass loss, by a factor scaling with the normalized velocity filling factor fvel. On the other hand, if vorosity is important only above this critical point, the predicted mass loss is not affected, but the wind terminal speed is reduced. This shows that porosity in velocity space can have a significant impact not only on the diagnostics, but also on the dynamics and theory of radiatively driven winds.Comment: 13 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

Constraints On Porosity And Mass Loss In O-Star Winds From The Modeling Of X-Ray Emission Line Profile Shapes

We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both spherical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. However, porosity models with isotropic clumps can provide acceptable fits to observed line shapes, but only if the porosity effect is moderate. We quantify the degeneracy between porosity effects from isotropic clumps and the mass-loss rate inferred from the X-ray line shapes, and we show that only modest increases in the mass-loss rate (less than or similar to 40%) are allowed if moderate porosity effects (h(infinity) less than or similar to R-*) are assumed to be important. Large porosity lengths, and thus strong porosity effects, are ruled out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate estimates are relatively insensitive to both optically thin and optically thick clumping. This supports the use of X-ray spectroscopy as a mass-loss rate calibration for bright, nearby O stars

Mass loss from inhomogeneous hot star winds II. Constraints from a combined optical/UV study

Mass-loss rates currently in use for hot, massive stars have recently been seriously questioned, mainly because of the effects of wind clumping. We investigate the impact of clumping on diagnostic ultraviolet resonance and optical recombination lines. Optically thick clumps, a non-void interclump medium, and a non-monotonic velocity field are all accounted for in a single model. We used 2D and 3D stochastic and radiation-hydrodynamic (RH) wind models, constructed by assembling 1D snapshots in radially independent slices. To compute synthetic spectra, we developed and used detailed radiative transfer codes for both recombination lines (solving the "formal integral") and resonance lines (using a Monte-Carlo approach). In addition, we propose an analytic method to model these lines in clumpy winds, which does not rely on optically thin clumping. Results: Synthetic spectra calculated directly from current RH wind models of the line-driven instability are unable to in parallel reproduce strategic optical and ultraviolet lines for the Galactic O-supergiant LCep. Using our stochastic wind models, we obtain consistent fits essentially by increasing the clumping in the inner wind. A mass-loss rate is derived that is approximately two times lower than predicted by the line-driven wind theory, but much higher than the corresponding rate derived from spectra when assuming optically thin clumps. Our analytic formulation for line formation is used to demonstrate the potential impact of optically thick clumping in weak-winded stars and to confirm recent results that resonance doublets may be used as tracers of wind structure and optically thick clumping. (Abridged)Comment: 14 pages+1 Appendix, 8 figures, 3 tables. Accepted for publication in Astronomy and Astrophysics. One reference updated, minor typo in Appendix correcte

Investigating the origin of cyclical wind variability in hot, massive stars - II. Hydrodynamical simulations of co-rotating interaction regions using realistic spot parameters for the O giant ξ\xi Persei

OB stars exhibit various types of spectral variability historically associated with wind structures, including the apparently ubiquitous discrete absorption components (DACs). These features have been proposed to be caused either by magnetic fields or non-radial pulsations. In this second paper of this series, we revisit the canonical phenomenological hydrodynamical modelling used to explain the formation of DACs by taking into account modern observations and more realistic theoretical predictions. Using constraints on putative bright spots located on the surface of the O giant $\xi$ Persei derived from high precision space-based broadband optical photometry obtained with the Microvariability and Oscillations of STars (MOST) space telescope, we generate two-dimensional hydrodynamical simulations of co-rotating interaction regions in its wind. We then compute synthetic ultraviolet (UV) resonance line profiles using Sobolev Exact Integration and compare them with historical timeseries obtained by the International Ultraviolet Explorer (IUE) to evaluate if the observed behaviour of $\xi$ Persei's DACs is reproduced. Testing three different models of spot size and strength, we find that the classical pattern of variability can be successfully reproduced for two of them: the model with the smallest spots yields absorption features that are incompatible with observations. Furthermore, we test the effect of the radial dependence of ionization levels on line driving, but cannot conclusively assess the importance of this factor. In conclusion, this study self-consistently links optical photometry and UV spectroscopy, paving the way to a better understanding of cyclical wind variability in massive stars in the context of the bright spot paradigm.Comment: 16 pages, 10 figures, accepted for publication by MNRA

A Generalized Porosity Formalism For Isotropic And Anisotropic Effective Opacity And Its Effects On X-Ray Line Attenuation In Clumped O Star Winds

We present a generalized formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealized model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of boundfree absorption of X-rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single-clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates