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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 non-monotonic 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.
Clumped stellar winds in supergiant high-mass X-ray binaries: X-ray variability and photoionization
(2012)
The clumping of massive star winds is an established paradigm, which is confirmed by multiple lines of evidence and is supported by stellar wind theory. The purpose of this paper is to bridge the gap between detailed models of inhomogeneous stellar winds in single stars and the phenomenological description of donor winds in supergiant high-mass X-ray binaries (HMXBs). We use the results from time-dependent hydrodynamical models of the instability in the line-driven wind of a massive supergiant star to derive the time-dependent accretion rate on to a compact object in the BondiHoyleLyttleton approximation. The strong density and velocity fluctuations in the wind result in strong variability of the synthetic X-ray light curves. The model predicts a large-scale X-ray variability, up to eight orders of magnitude, on relatively short time-scales. The apparent lack of evidence for such strong variability in the observed HMXBs indicates that the details of the accretion process act to reduce the variability resulting from the stellar wind velocity and density jumps.
X-ray spectroscopy is a sensitive probe of stellar winds. X-rays originate from optically thin shock-heated plasma deep inside the wind and propagate outwards throughout absorbing cool material. Recent analyses of the line ratios from He-like ions in the X-ray spectra of O-stars highlighted problems with this general paradigm: the measured line ratios of highest ions are consistent with the location of the hottest X-ray emitting plasma very close to the base of the wind, perhaps indicating the presence of a corona, while measurements from lower ions conform with the wind-embedded shock model. Generally, to correctly model the emerging Xray spectra, a detailed knowledge of the cool wind opacities based on stellar atmosphere models is prerequisite. A nearly grey stellar wind opacity for the X-rays is deduced from the analyses of high-resolution X-ray spectra. This indicates that the stellar winds are strongly clumped. Furthermore, the nearly symmetric shape of X-ray emission line profiles can be explained if the wind clumps are radially compressed. In massive binaries the orbital variations of X-ray emission allow to probe the opacity of the stellar wind; results support the picture of strong wind clumping. In high-mass X-ray binaries, the stochastic X-ray variability and the extend of the stellar-wind part photoionized by X-rays provide further strong evidence that stellar winds consist of dense clumps.
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 zeta Orionis. The present numerical modeling confirms the results from a previous study, where we derived analytical formulae from a statistical treatment
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.
We discuss the connection between wind overloading and discrete absorption components in P Cygni line profiles from O stars. Overloading can create horizontal plateaus in the radial wind speed that cause the extra absorption in the line profile. The upstream propagation speed of these velocity plateaus is analyzed. The second part of the paper deals with X-ray emission from O stars. X-ray line profiles observed with Chandra and XMM are often symmetric, contrary to what is expected for lines from a homogeneous wind. We discuss the influence on line symmetry of photon escape channels in a strongly clumped 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.
Clumps in hot star winds can originate from shock compression due to the line driven instability. One-dimensional hydrodynamic simulations reveal a radial wind structure consisting of highly compressed shells separated by voids, and colliding with fast clouds. Two-dimensional simulations are still largely missing, despite first attempts. Clumpiness dramatically affects the radiative transfer and thus all wind diagnostics in the UV, optical, and in X-rays. The microturbulence approximation applied hitherto is currently superseded by a more sophisticated radiative transfer in stochastic media. Besides clumps, i.e. jumps in the density stratification, so-called kinks in the velocity law, i.e. jumps in dv/dr, play an eminent role in hot star winds. Kinks are a new type of radiative-acoustic shock, and propagate at super-Abbottic speed.
Modeling expanding atmospheres is a difficult task because of the extreme non-LTE situation, the need to account for complex model atoms, especially for the iron-group elements with their millions of lines, and because of the supersonic expansion. Adequate codes have been developed e.g. by Hillier (CMFGEN), the Munich group (Puls, Pauldrach), and in Potsdam (PoWR code, Hamann et al.). While early work was based on the assumption of a smooth and homogeneous spherical stellar wind, the need to account for clumping became obvious about ten years ago. A relatively simple first-order clumping correction was readily implemented into the model codes. However, its simplifying assumptions are severe. Most importantly, the clumps are taken to be optically thin at all frequencies (”microclumping”). We discuss the consequences of this approximation and describe an approach to account for optically thick clumps (“macroclumping”). First results demonstrate that macroclumping can generally reduce the strength of spectral features, depending on their optical thickness. The recently reported discrepancy between the Hα diagnostic and the Pv resonance lines in O star spectra can be resolved without decreasing the mass-loss rates, when macroclumping is taken into account.