Neglecting the porosity of hot-star winds can lead to underestimating mass-loss rates

Context: The mass-loss rate is a key parameter of massive stars. Adequate stellar atmosphere models are required for spectral analyses and mass-loss determinations. Present models can only account for the inhomogeneity of stellar winds in the approximation of small-scale structures that are optically thin. This treatment of ``microclumping'' has led to reducing empirical mass-loss rates by factors of two and more. Aims: Stellar wind clumps can be optically thick in spectral lines. We investigate how this ``macroclumping'' impacts on empirical mass-loss rates. Methods: The Potsdam Wolf-Rayet (PoWR) model atmosphere code is generalized in the ``formal integral'' to account for clumps that are not necessarily optically thin. Results: Optically thick clumps reduce the effective opacity. This has a pronounced effect on the emergent spectrum. Our modeling for the O-type supergiant zeta Puppis reveals that the optically thin H-alpha line is not affected by wind porosity, but that the PV resonance doublet becomes significantly weaker when macroclumping is taken into account. The reported discrepancies between resonance-line and recombination-line diagnostics can be resolved entirely with the macroclumping modeling without downward revision of the mass-loss rate. Conclusions: Mass-loss rates inferred from optically thin emission, such as the H-alpha line in O stars, are not influenced by macroclumping. The strength of optically thick lines, however, is reduced because of the porosity effects. Therefore, neglecting the porosity in stellar wind modeling can lead to underestimating empirical mass-loss rates.Comment: A&A (in press), see full abstract in the tex

High resolution X-ray spectroscopy of bright O type stars

Archival X-ray spectra of the four prominent single, non-magnetic O stars Zeta Pup, Zeta Ori, Ksi Per and Zeta Oph, obtained in high resolution with Chandra HETGS/MEG have been studied. The resolved X-ray emission line profiles provide information about the shocked, hot gas which emits the X-radiation, and about the bulk of comparably cool stellar wind material which partly absorbs this radiation. In this paper, we synthesize X-ray line profiles with a model of a clumpy stellar wind. We find that the geometrical shape of the wind inhomogeneities is important: better agreement with the observations can be achieved with radially compressed clumps than with spherical clumps. The parameters of the model, i.e. chemical abundances, stellar radius, mass-loss rate and terminal wind velocity, are taken from existing analyses of UV and optical spectra of the programme stars. On this basis, we also calculate the continuum-absorption coefficient of the cool-wind material, using the Potsdam Wolf-Rayet (PoWR) model atmosphere code. The radial location of X-ray emitting gas is restricted from analysing the fir line ratios of helium-like ions. The only remaining free parameter of our model is the typical distance between the clumps; here, we assume that at any point in the wind there is one clump passing by per one dynamical time-scale of the wind. The total emission in a model line is scaled to the observation. There is a good agreement between synthetic and observed line profiles. We conclude that the X-ray emission line profiles in O stars can be explained by hot plasma embedded in a cool wind which is highly clumped in the form of radially compressed shell fragments.Comment: a typo corrected, 14 pages, MNRAS, in pres

The metallicity dependence of WR winds

Wolf-Rayet (WR) stars are the most advanced stage in the evolution of the most massive stars. The strong feedback provided by these objects and their subsequent supernova (SN) explosions are decisive for a variety of astrophysical topics such as the cosmic matter cycle. Consequently, understanding the properties of WR stars and their evolution is indispensable. A crucial but still not well known quantity determining the evolution of WR stars is their mass-loss rate. Since the mass loss is predicted to increase with metallicity, the feedback provided by these objects and their spectral appearance are expected to be a function of the metal content of their host galaxy. This has severe implications for the role of massive stars in general and the exploration of low metallicity environments in particular. Hitherto, the metallicity dependence of WR star winds was not well studied. In this contribution, we review the results from our comprehensive spectral analyses of WR stars in environments of different metallicities, ranging from slightly super-solar to SMC-like metallicities. Based on these studies, we derived empirical relations for the dependence of the WN mass-loss rates on the metallicity and iron abundance, respectively.Comment: 5 pages, 4 figures, to be published in the Proceedings of the IAU Symposium No. 329 "The lives and death-throes of massive stars

Wind-Interaction Models for the Early Afterglows of Gamma-Ray Bursts: The Case of GRB 021004

Wind-interaction models for gamma-ray burst afterglows predict that the optical emission from the reverse shock drops below that from the forward shock within 100s of seconds of the burst. The typical frequency $\nu_m$ of the synchrotron emission from the forward shock passes through the optical band typically on a timescale of minutes to hours. Before the passage of $\nu_m$, the optical flux evolves as $t^{-1/4}$ and after the passage, the decay steepens to $t^{-(3p-2)/4}$, where $p$ is the exponent for the assumed power-law energy distribution of nonthermal electrons and is typically $\sim 2$. The steepening in the slope of temporal decay should be readily identifiable in the early afterglow light curves. We propose that such a steepening was observed in the R-band light curve of GRB 021004 around day 0.1. Available data at several radio frequencies are consistent with this interpretation, as are the X-ray observations around day~1. The early evolution of GRB 021004 contrasts with that of GRB 990123, which can be described by emission from interaction with a constant density medium.Comment: 16 pages, 1 figure, submitted to ApJ

Wolf-Rayet stars in the Small Magellanic Cloud: I. Analysis of the single WN stars

Wolf-Rayet (WR) stars have a severe impact on their environments owing to their strong ionizing radiation fields and powerful stellar winds. Since these winds are considered to be driven by radiation pressure, it is theoretically expected that the degree of the wind mass-loss depends on the initial metallicity of WR stars. Following our comprehensive studies of WR stars in the Milky Way, M31, and the LMC, we derive stellar parameters and mass-loss rates for all seven putatively single WN stars known in the SMC. Based on these data, we discuss the impact of a low-metallicity environment on the mass loss and evolution of WR stars. The quantitative analysis of the WN stars is performed with the Potsdam Wolf-Rayet (PoWR) model atmosphere code. The physical properties of our program stars are obtained from fitting synthetic spectra to multi-band observations. In all SMC WN stars, a considerable surface hydrogen abundance is detectable. The majority of these objects have stellar temperatures exceeding 75 kK, while their luminosities range from 10^5.5 to 10^6.1 Lsun. The WN stars in the SMC exhibit on average lower mass-loss rates and weaker winds than their counterparts in the Milky Way, M31, and the LMC. By comparing the mass-loss rates derived for WN stars in different Local Group galaxies, we conclude that a clear dependence of the wind mass-loss on the initial metallicity is evident, supporting the current paradigm that WR winds are driven by radiation. A metallicity effect on the evolution of massive stars is obvious from the HRD positions of the SMC WN stars at high temperatures and high luminosities. Standard evolution tracks are not able to reproduce these parameters and the observed surface hydrogen abundances. Homogeneous evolution might provide a better explanation for their evolutionary past.Comment: 18+12 pages; 22+8 figures; accepted for publication in A&

Comparison of Global and Local Adaptive Coordinates for Density Functional Calculations

A globally-adaptive curvilinear coordinate formalism is shown to be easily convertible to a class of curvilinear transformations locally optimized around atom sites by a few parameters. Parameter transferability is established for a demanding test case, and the results of the two methods are shown to be comparable. Computational efficiencies realized in the local method are discussed.Comment: 21 pages, 4 figure

X-ray emission from hydrodynamical simulations in non-LTE wind models

Hot stars are sources of X-ray emission originating in their winds. Although hydrodynamical simulations that are able to predict this X-ray emission are available, the inclusion of X-rays in stationary wind models is usually based on simplifying approximations. To improve this, we use results from time-dependent hydrodynamical simulations of the line-driven wind instability (seeded by the base perturbation) to derive the analytical approximation of X-ray emission in the stellar wind. We use this approximation in our non-LTE wind models and find that an improved inclusion of X-rays leads to a better agreement between model ionization fractions and those derived from servations. Furthermore, the slope of the L_x-L relation is in better agreement with observations, however the X-ray luminosity is underestimated by a factor of three. We propose a possible solution for this discrepancy.Comment: 9 pages, accepted for publication in Astronomy and Astrophysic