Achim Feldmeier

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. Compared to previous homogeneous models, this treatment of “microclumping” has led to reducing empirical mass-loss rates by factors of two to three. Further reductions are presently discussed in the literature, with far-reaching consequences e.g. for stellar evolution and stellar yields. Aims. Stellar wind clumps can be optically thick in spectral lines. We investigate how this “macroclumping” influences the radiative transfer and the emergent line spectra and discuss its impact 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. The stellar wind is characterized by the filling factor of the dense clumps and by their average separation. An effective opacity is obtained by adopting a statistical distribution of clumps and applied in the radiative transfer. Results. Optically thick clumps reduce the effective opacity. This has a pronounced effect on the emergent spectrum. Our modeling for the O-type supergiant ζ Puppis reveals that the optically thin Hα line is not affected by wind porosity, but that the P v 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. In the case of Wolf-Rayet stars, we demonstrate for two representative models that stronger lines are typically reduced by a factor of two in intensity, while weak lines remain unchanged by porosity effects. Conclusions. Mass-loss rates inferred from optically thin emission, such as the Hα 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.

High resolution X-ray spectroscopy of bright O type stars

Archival X-ray spectra of the four prominent single, non-magnetic O stars ζ Pup, ζ Ori, ξ Per, ζ Oph, obtained in high resolution with Chandra HETGS/MEG have been studied. The resolved X-ray emission line profiles prov ide 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 the pr esent 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 a nd terminal wind velocity, are taken from existing analyses of UV and optical spectra of the program 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 analyzing 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 timescale 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 th at 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.

X-ray line emission from a fragmented stellar wind

We discuss X-ray line formation in dense O star winds. A random distribution of wind shocks is assumed to emit X-rays that are partially absorbed by cooler wind gas. The cool gas resides in highly compressed fragments oriented perpendicular to the radial flow direction. For fully opaque fragments, we find that the blueshifted part of X-ray line profiles remains flat-topped even after severe wind attenuation, whereas the red part shows a steep decline. These box- type, blueshifted profiles resemble recent Chandra observations of the O3 star zeta Pup. For partially transparent fragments, the emission lines become similar to those from a homogeneous wind.

Mass loss from inhomogeneous hot star winds - I. Resonance line formation in 2D models

Context. The mass-loss rate is a key parameter of hot, massive stars. Small-scale inhomogeneities (clumping) in the winds of these stars are conventionally included in spectral analyses by assuming optically thin clumps, a void inter-clump medium, and a smooth velocity field. To reconcile investigations of different diagnostics (in particular, unsaturated UV resonance lines vs. Hα/radio emission) within such models, a highly clumped wind with very low mass-loss rates needs to be invoked, where the resonance lines seem to indicate rates an order of magnitude (or even more) lower than previously accepted values. If found to be realistic, this would challenge the radiative line-driven wind theory and have dramatic consequences for the evolution of massive stars. Aims. We investigate basic properties of the formation of resonance lines in small-scale inhomogeneous hot star winds with nonmonotonic velocity fields. Methods. We study inhomogeneous wind structures by means of 2D stochastic and pseudo-2D radiation-hydrodynamic wind models, constructed by assembling 1D snapshots in radially independent slices. A Monte-Carlo radiative transfer code, which treats the resonance line formation in an axially symmetric spherical wind (without resorting to the Sobolev approximation), is presented and used to produce synthetic line spectra. Results. The optically thin clumping limit is only valid for very weak lines. The detailed density structure, the inter-clump medium, and the non-monotonic velocity field are all important for the line formation. We confirm previous findings that radiationhydrodynamic wind models reproduce observed characteristics of strong lines (e.g., the black troughs) without applying the highly supersonic “microturbulence” needed in smooth models. For intermediate strong lines, the velocity spans of the clumps are of central importance. Current radiation-hydrodynamic models predict spans that are too large to reproduce observed profiles unless a very low mass-loss rate is invoked. By simulating lower spans in 2D stochastic models, the profile strengths become drastically reduced, and are consistent with higher mass-loss rates. To simultaneously meet the constraints from strong lines, the inter-clump medium must be non-void. A first comparison to the observed Phosphorus V doublet in the O6 supergiant λ Cep confirms that line profiles calculated from a stochastic 2D model reproduce observations with a mass-loss rate approximately ten times higher than that derived from the same lines but assuming optically thin clumping. Tentatively this may resolve discrepancies between theoretical predictions, evolutionary constraints, and recent derived mass-loss rates, and suggests a re-investigation of the clump structure predicted by current radiation-hydrodynamic models.

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

Context. Mass loss is essential for massive star evolution, thus also for the variety of astrophysical applications relying on it s predictions. However, mass-loss rates currently in use for hot, massive stars have recently been seriously questioned, mainl y because of the effects of wind clumping. Aims. We investigate the impact of clumping on diagnostic ultraviolet resonance and optical recombination lines often used to derive empirical mass-loss rates of hot stars. Optically thick clu mps, a non-void interclump medium, and a non-monotonic velocity field are all accounted for in a single model. The line formation is firs t theoretically studied, after which an exemplary multi-di agnostic study of an O-supergiant is performed. Methods. We used 2D and 3D stochastic and radiation-hydrodynamic 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. The importance of the ‘vorosity’ effect for line formation in clumpy winds is emphasized. Resonance lines are generally more affected by optically thick clumping than recombination lines. Synthetic spectra calculated directly from current radia tionhydrodynamic wind models of the line-driven instability are unable to in parallel reproduce strategic optical and ultr aviolet lines for

Clumped stellar winds in supergiant high‐mass X‐ray binaries: X‐ray variability and photoionization

ABSTRACT The clumping of massive star winds is an established paradigm confirmed by multiple lines ofevidence and supported by stellar wind theory. The purpose of this paper is to bridge the gapbetween detailed models of inhomogeneous stellar winds in single stars and the phenomeno-logical description of donor winds in supergiant high-massX-ray binaries (HMXBs). We useresults from time-dependent hydrodynamicalmodels of the instability in the line-driven windof a massive supergiant star to derive the time-dependentaccretion rate onto a compact objectin the Bondi-Hoyle-Lyttleton approximation. The strong density and velocity fluctuations inthe wind result in strong variability of the synthetic X-raylight curves. The model predicts alarge scale X-ray variability, up to eight orders of magnitude, on relatively short timescales.The apparent lack of evidence for such strong variability in the observed HMXBs indicatesthat the details of accretion process act to reducethe variability due to the stellar wind velocityand density jumps.We study the absorptionof X-rays in the clumpedstellar windby means of a 2-D stochas-tic wind model. The monochromatic absorption in cool stellar wind in dependence on orbitalphase is computed for realistic stellar wind opacity. We find that absorption of X-rays changesstrongly at different orbital phases. The degree of the variability due to the absorption in thewind depends on the shape of the wind clumps and is stronger in case of oblate clumps.We address the photoionization in the clumped wind, and show that the degree of ioniza-tion is affected by the wind clumping. A correction factor for the photoionization parameteris derived. It is shown that the photoionization parameter is reduced by a factor X comparedto the smooth wind models with the same mass-loss rate, whereXis the wind inhomogeneityparameter. We conclude that wind clumping must also be taken into account when comparingthe observed and model spectra of the photoionized stellar wind.Key words: accretion, X-rays: binaries, instabilities, stars: neutron, X-rays: stars

X-ray emission lines from inhomogeneous stellar winds

It is commonly adopted that X-rays from O stars are produced deep inside the stellar wind, and transported outwards through the bulk of the expanding matter which attenuates the radiation and affects the shape of emission line profiles. The ability of the X-ray observatories Chandra and XMM-Newton to resolve these lines spectroscopically provided a stringent test for the theory of the X-ray production. It turned out that none of the existing models was able to fit the observations consistently. The possible caveat of these models was the underlying assumption of a smooth stellar wind. Motivated by the evidence that the stellar winds are in fact structured, we present a 2-D numerical model of a stochastic, inhomogeneous wind. Small parcels of hot, X-ray emitting gas are permeated by cool, absorbing wind material which is compressed into thin shell fragments. Wind fragmentation alters the radiative transfer drastically, compared to homogeneous models of the same mass-loss rate. X-rays produced deep inside the wind, which would be totally absorbed in a homogeneous flow, can effectively escape from a fragmented wind. The wind absorption becomes wavelength independent if the individual fragments are optically thick. The X-ray line profiles are flat-topped in the blue part and decline steeply in the red part for the winds with a short acceleration zone. For the winds where the acceleration extends over significant distances, the lines can appear nearly symmetric and only slightly blueshifted, in contrast to the skewed, triangular line profiles typically obtained from homogeneous wind models of high optical depth. We show that profiles from a fragmented wind model can reproduce the observed line profiles from ζ Orionis. The present numerical modeling confirms the results from a previous study, where we derived analytical formulae from a statistical treatment.

Three-dimensional radiative transfer in clumped hot star winds - I. Influence of clumping on the resonance line formation

Context. The true mass-loss rates from massive stars are important for many branches of astrophysics. For the correct modeling of the resonance lines, which are among the key diagnostics of stellar mass-loss, the stellar wind clumping has been found to be very important. To incorporate clumping into a radiative transfer calculation, three-dimensional (3D) models are required. Various properties of the clumps may have a strong impact on the resonance line formation and, therefore, on the determination of empirical mass-loss rates. Aims. We incorporate the 3D nature of the stellar wind clumping into radiative transfer calculations and investigate how different model parameters influence the resonance line formation. Methods. We develop a full 3D Monte Carlo radiative transfer code for inhomogeneous expanding stellar winds. The number density of clumps follows the mass conservation. For the first time, we use realistic 3D models that describe the dense as well as the tenuous wind components to model the formation of resonance lines in a clumped stellar wind. At the same time, we account for nonmonotonic velocity fields. Results. The 3D density and velocity wind inhomogeneities show that there is a very strong impact on the resonance line formation. The different parameters describing the clumping and the velocity field results in different line strengths and profiles. We present a set of representative models for various sets of model parameters and investigate how the resonance lines are affected. Our 3D models show that the line opacity is lower for a larger clump separation and shallower velocity gradients within the clumps. Conclusions. Our model demonstrates that to obtain empirically correct mass-loss rates from the UV resonance lines, the wind clumping and its 3D nature must be taken into account.

Dynamics of Line-driven Winds from Disks in Cataclysmic Variables. I. Solution Topology and Wind Geometry

We analyze the dynamics of two-dimensional stationary, line-driven winds from accretion disks in cataclysmic variable stars. The driving force is that of line radiation pressure, in the formalism developed by Castor, Abbott, & Klein for O stars. Our main assumption is that wind helical streamlines lie on straight cones. We Ðnd that the Euler equation for the disk wind has two eigenvalues, the mass-loss rate and the Now-tilt angle with the disk. Both are calculated self-consistently. The wind is characterized by two distinct regions, an outer wind launched beyond four white dwarf radii from the rotation axis and an inner wind launched within this radius. The inner wind is very steep, up to 80i with the disk plane, while the outer wind has a typical tilt of 60i. In both cases, the wind cone dispersion is small because of a good alignment between the wind and the radiative Nux vectors from the disk. We, therefore, provide an insight into the formation of the biconical geometry of disk winds as suggested by observations and kinematical modeling. The wind collimation angle appears to be robust and depends on the disk tem- perature stratiÐcation only. The Now critical points lie high above the disk for the inner wind but close to the disk photosphere for the outer wind. Comparison with existing kinematical and dynamical models is provided. Mass-loss rates from the disk as well as wind velocity laws are discussed in the second paper in this series. Subject headings : accretion, accretion disks E novae, cataclysmic variables E stars : mass loss E stars : winds, outNows

On the wavelength drift of spectral features from structured hot star winds

Spectral lines formed in stellar winds from OB stars are observed to exhibit profile variations. Discrete Absorption Components (DACs) show a remarkably slow wavelength drift with time. In a straightforward interpretation, this is in sharp contradiction to the steep velocity law predicted by the radiation-driven wind theory, and by semi- empirical profile fitting. In the present paper we re-discuss the interpretation of the drift rate. We show that the Co- rotating Interaction Region (CIR) model for the formation of DACs does not explain their slow drift rate as a consequence of rotation. On the contrary, the apparent acceleration of a spectral CIR feature is even higher than for the corresponding kinematical model without rotation. However, the observations can be understood by distinguishing between the velocity field of the matter flow, and the velocity law for the motion of the patterns in which the DAC features are formed. If the latter propagate upstream against the matter flow, the resulting wavelength drift mimics a much slower acceleration although the matter is moving fast. Additional to the DACs, a second type of recurrent structures is present in observed OB star spectra, the so-called modulations. In contrast to the DACs, these structures show a steep acceleration compatible with the theoretically predicted velocity law. We see only two possible consistent scenarios. Either, the wind is accelerated fast, and the modulations are formed in advected structures, while the DACs come from structures which are propagating upstream. Or, alternatively, steep and shallow velocity laws may co-exist at the same time in different spatial regions or directions of the wind.