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

[Abridged] Clumping in the radiation-driven winds of hot, massive stars affects the derivation of synthetic observables across the electromagnetic spectrum. We implement a formalism for treating wind clumping - in particular the light-leakage effects associated with a medium that is porous in physical and velocity space - into the global (photosphere+wind) NLTE model atmosphere code FASTWIND. We assume a stochastic, two-component wind consisting of a mixture of optically thick and thin clumps embedded in a rarefied inter-clump medium. We account fully for the reductions in opacity associated with porosity in physical and velocity-space, and for the well-known effect that opacities depending on rho^2 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 models with the same speed (~15 min. on a modern laptop) as in previous code-generations. Some first, generic results of the new models include: i) Confirming earlier results that velocity-space porosity is critical for analysis of UV wind lines in O-stars; ii) for the optical Halpha line, optically thick clumping effects are small for O-stars, but potentially very important for late B and A-supergiants; iii) 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; iv) porosity is negligible at typical O-star radio-photosphere radii; 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.Comment: 12 pages, 5 figures, accepted for publication in Astronomy & Astrophysic

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

Wind Roche lobe overflow in high mass X-ray binaries : a possible mass transfer mechanism for Ultraluminous X-ray sources

Ultra-luminous X-ray sources (ULX) have so high X-ray luminosities that they were long thought to be accreting intermediate mass black holes. Yet, some ULX have been shown to display periodic modulations and coherent pulsations, suggestive of a neutron star in orbit around a stellar companion and accreting at super-Eddington rates. In this letter, we propose that the mass transfer in ULX could be qualitatively the same as in Supergiant X-ray binaries (SgXB), with a wind from the donor star highly beamed towards the compact object. Since the star does not fill its Roche lobe, this mass transfer mechanism known as "wind Roche lobe overflow" can remain stable even for large mass ratios. Based on realistic acceleration profiles derived from spectral observations and modeling of the stellar wind, we compute the bulk motion of the wind to evaluate the fraction of the stellar mass outflow captured by the compact object. We identify the orbital and stellar conditions for a SgXB to transfer mass at rates matching the expectations for ULX and show that the transition from SgXB to ULX luminosity levels is progressive. These results indicate that a high stellar Roche lobe filling factor is not necessary to funnel large quantities of material into the Roche lobe of the accretor. Large stellar mass loss rates such as the ones from the Wolf-Rayet star in M101 ULX-1 or the late B9 Supergiant in NGC 7793 P13 are enough to lead to a highly beamed wind and a significantly enhanced mass transfer rate

3D radiative transfer: Continuum and line scattering in non-spherical winds from OB stars

Context: State of the art quantitative spectroscopy of OB-stars compares synthetic spectra (calculated by means of 1D, spherically symmetric computer codes) with observations. Certain stellar atmospheres, however, show strong deviations from spherical symmetry, and need to be treated in 3D. Aims: We present a newly developed 3D radiative transfer code, tailored to the solution of the radiation field in rapidly expanding stellar atmospheres. We apply our code to the continuum transfer in wind-ablation models, and to the UV resonance line formation in magnetic winds. Methods: We have used a 3D finite-volume method for the solution of the equation of radiative transfer, to study continuum- and line-scattering problems. Convergence has been accelerated by a non-local approximate Lambda-iteration scheme. Particular emphasis has been put on careful (spherically symmetric) test cases. Results: Typical errors of the source functions, when compared to 1D solutions, are of the order of 10-20 %, and increase for optically thick continua. In circumstellar discs, the radiation temperatures in the (optically thin) transition region from wind to disc are quite similar to corresponding values in the wind. For MHD simulations of dynamical magnetospheres, the line profiles, calculated with our 3D code, agree well with previous solutions using a 3D-SEI method. When compared with profiles resulting from the `analytic dynamical magnetosphere' (ADM) model, significant differences become apparent. Conclusions: Due to similar radiation temperatures in the wind and the transition region to the disc, the same line-strength distribution can be applied within radiation hydrodynamic calculations for circumstellar discs in `accreting high-mass stars'. To properly describe the UV line formation in dynamical magnetospheres, the ADM model needs to be further developed, at least in a large part of the outer wind

The rotation rates of massive stars: How slow are the slow ones?

Context: Rotation plays a key role in the life cycles of stars with masses above 8 Msun. Hence, accurate knowledge of the rotation rates of such massive stars is critical for understanding their properties and for constraining models of their evolution. Aims: This paper investigates the reliability of current methods used to derive projected rotation speeds v sin i from line-broadening signatures in the photospheric spectra of massive stars, focusing on stars that are not rapidly rotating. Methods: We use slowly rotating magnetic O-stars with well-determined rotation periods to test the Fourier transform (FT) and goodness-of-fit (GOF) methods typically used to infer projected rotation rates of massive stars. Results: For our two magnetic test stars with measured rotation periods longer than one year, i.e., with v sin i < 1 km/s, we derive v sin i ~ 40-50 km/s from both the FT and GOF methods. These severe overestimates are most likely caused by an insufficient treatment of the competing broadening mechanisms referred to as microturbulence and macroturbulence. Conclusions: These findings warn us not to rely uncritically on results from current standard techniques to derive projected rotation speeds of massive stars in the presence of significant additional line broadening, at least when v sin i <~ 50 km/s. This may, for example, be crucial for i) determining the statistical distribution of observed rotation rates of massive stars, ii) interpreting the evolutionary status and spin-down histories of rotationally braked B-supergiants, and iii) explaining the deficiency of observed O-stars with spectroscopically inferred v sin i ~ 0 km/s. Further investigations of potential shortcomings of the above techniques are presently under way.Comment: 4 pages, 4 figures, accepted for publication in A&A Letter

Atmospheric NLTE-Models for the Spectroscopic Analysis of Blue Stars with Winds. III. X-ray emission from wind-embedded shocks

X-rays/EUV radiation emitted from wind-embedded shocks in hot, massive stars can affect the ionization balance in their outer atmospheres, and can be the mechanism responsible for the production of highly ionized species. To allow for these processes in the context of spectral analysis, we have implemented such emission into our unified, NLTE model atmosphere/spectrum synthesis code FASTWIND. The shock structure and corresponding emission is calculated as a function of user-supplied parameters. We account for a temperature and density stratification inside the post-shock cooling zones, calculated for radiative and adiabatic cooling in the inner and outer wind, respectively. The high-energy absorption of the cool wind is considered by adding important K-shell opacities, and corresponding Auger ionization rates have been included into the NLTE network. We tested and verified our implementation carefully against corresponding results from various alternative model atmosphere codes, and studied the effects from shock emission for important ions from He, C, N, O, Si, and P. Surprisingly, dielectronic recombination turned out to play an essential role for the ionization balance of OIV/OV around Teff = 45,000 K. Finally, we investigated the behavior of the mass absorption coefficient, kappa_nu(r), important in the context of X-ray line formation in massive star winds. In almost all considered cases, direct ionization is of major influence, and Auger ionization significantly affects only NVI and OVI. The approximation of a radially constant kappa_nu is justified for r > 1.2 Rstar and lambda < 18 A, and also for many models at longer wavelengths. To estimate the actual value of this quantity, however, the HeII opacities need to be calculated from detailed NLTE modeling, at least for wavelengths longer than 18 to 20 A, and information on the individual CNO abundances has to be present.Comment: accepted by A&