Winds Of Hot Stars Research Articles

Modelling the clumping-induced polarimetric variability of hot star winds

Clumping in the winds of massive stars may significantly reduce empirical mass-loss rates, and which in turn may have a large impact on our understanding of massive star evolution. Here, we investigate wind-clumping through the linear polarization induced by light scattering off the clumps. Through the use of an analytic wind clumping model, we predict the time evolution of the linear polarimetry over a large parameter space. We concentrate on the Luminous Blue Variables, which display the greatest amount of polarimetric variability and for which we recently conducted a spectropolarimetric survey. Our model results indicate that the observed level of polarimetric variability can be reproduced for two regimes of parameter space: one of a small number of massive, optically-thick clumps; and one of a very large number of low-mass clumps. Although a systematic time-resolved monitoring campaign is required to distinguish between the two scenarios, we currently favour the latter, given the short timescale of the observed polarization variability. As the polarization is predicted to scale linearly with mass-loss rate, we anticipate that all hot stars with very large mass-loss rates should display polarimetric variability. This is consistent with recent findings that intrinsic polarization is more common in stars with strong H$\alpha$ emission.

A Clumping-independent Diagnostic of Stellar Mass-Loss Rates: Rapid Clump Destruction in Adiabatic Colliding Winds

Clumping in hot star winds can significantly affect estimates of mass-loss rates, the inferred evolution of the star, and the environmental impact of the wind. A hydrodynamical simulation of a colliding winds binary (CWB) with clumpy winds reveals that the clumps are rapidly destroyed after passing through the confining shocks of the wind-wind collision region (WCR) for reasonable parameters of the clumps if the flow in the WCR is adiabatic. Despite large density and temperature fluctuations in the postshock gas, the overall effect of the interaction is to smooth the existing structure in the winds. Averaged over the entire interaction region, the resulting X-ray emission is very similar to that from the collision of smooth winds. The insensitivity of the X-ray emission to clumping suggests it is an excellent diagnostic of the stellar mass-loss rates () in wide CWBs and may prove to be a useful addition to existing techniques for deriving , many of which are extremely sensitive to clumping. Clumpy winds also have implications for a variety of phenomena at the WCR: particle acceleration may occur throughout the WCR due to supersonic MHD turbulence, reacceleration at multiple shocks, and reconnection; a statistical description of the properties of the WCR may be required for studies of nonequilibrium ionization and the rate of electron heating; and the physical mixing of the two winds will be enhanced, as seems necessary to trigger dust formation.

Modeling the magnetospheres of luminous stars: Interactions between supersonic radiation-driven winds and stellar magnetic fields

Hot, luminous stars (spectral types O and B) lack the hydrogen recombination convection zones that drive magnetic dynamo generation in the sun and other cool stars. Nonetheless, observed rotational modulation of spectral lines formed in the strong, radiatively driven winds of hot stars suggests magnetic perturbations analogous to those that induce “co-rotating interaction regions” in the solar wind. Indeed, recent advances in spectropolarimetric techniques have now led to direct detection of moderate to strong (100–10 000G), tilted dipole magnetic fields in several hot stars. Using a combination of analytic and numerical magnetohydrodynamic models, this paper focuses on the role of such magnetic fields in channeling, and sometimes confining, the radiatively driven mass outflows from such stars. The results show how “magnetically confined wind shocks” can explain the moderately hard x-ray emission seen from the O7V star Theta-1 Ori C, and how the trapping of material in a “rigidly rotating magnetosphere” can explain the periodically modulated Balmer line emission seen from the magnetic B2pV star Sigma Ori E. In addition, magnetic reconnection heating from episodic centrifugal breakout events might explain the occasional very hard x-ray flares seen from the latter star. The paper concludes with a brief discussion on the generation of hot-star fields and the broader relationship to other types of magnetospheres.

Hot star wind models with new solar abundances

We compare the hot star wind models calculated assuming older solar abundance determination with models calculated using the recently published values derived from 3D hydrodynamical model atmospheres. We show that the use of new abundances with lower metallicity improves the agreement between wind observation and theory in several aspects: (1) The predicted wind mass-loss rates are lower by a factor of 0.76. This leads to a better agreement with mass-loss rate determinations derived from observations with account of clumping. (2) As a result of the lowering of mass-loss rates, there is a better agreement between predicted modified wind momentum-luminosity relationship and that derived from observations with account of clumping. (3) Both the lower mass fraction of heavier elements and lower mass-loss rates lead to a decrease of the opacity in the X-ray region. This has influence on the prediction of the X-ray line profile shapes. (4) There is a better agreement between predicted PV ionization fractions and those derived from observations.

Non-LTE models for synthetic spectra of type Ia supernovae / hot stars with extremely extended atmospheres

Context. Realistic atmospheric models that link the properties and the physical conditions of supernova ejecta to observable spectra are required for the quantitative interpretation of observational data of type Ia supernovae (SN Ia) and the assessment of the physical merits of theoretical supernova explosion models. The numerical treatment of the radiation transport – yielding the synthetic spectra – in models of SN Ia ejecta in early phases is usually carried out in analogy to atmospheric models of “normal” hot stars. Applying this analogy indiscriminately leads to inconsistencies in SN Ia models because a diffusive lower boundary, while justified for hot stars, is invalid for hydrogen and helium-deficient supernova ejecta. In type Ia supernovae the radiation field does not thermalize even at large depths, and large optical depths are not reached at all wavelengths. Aims. We aim to derive an improved description of the lower boundary that allows a more consistent solution of the radiation transfer in SN Ia and therefore yields more realistic synthetic spectra. Methods. We analyze the conditions that lead to a breakdown of the conventional diffusion approximation as the lower boundary in SN Ia. For the radiative transfer, we use a full non-LTE code originally developed for radiatively driven winds of hot stars, with adaptations for the physical conditions in SN Ia. In addition to a well-tested treatment of the underlying microphysical processes, this code allows a direct comparison of the results for SN Ia and hot stars. Results. We develop a semi-analytical description that allows us to overcome some of the limiting assumptions in the conventional treatment of the lower boundary in SN Ia radiative transfer models. We achieve good agreement in a comparison between the synthetic spectrum of our test model and an observed spectrum.

Non‐LTE Monte Carlo Radiative Transfer. I. The Thermal Properties of Keplerian Disks around Classical Be Stars

We present a 3-D NLTE Monte Carlo radiative transfer code that we use to study the temperature and ionization structure of Keplerian disks around Classical Be stars. The method we employ is largely similiar to the Monte Carlo transition probability method developed by Lucy. Here we present a simplification of his method that avoids the use of the macro atom concept. Our investigations of the temperature structure of Be star disks show that the disk temperature behavior is a hybrid between the behavior of Young Stellar Object (YSO) disks and Hot Star winds. The optically thick inner parts of Be star disks have temperatures that are similar to YSO disks, while the optically thin outer parts are like stellar winds. Thus, the temperature at the disk midplane initially drops, reaching a minimum at 3--5 stellar radii, after which it rises back to the optically thin radiative equilibrium temperature at large distances. On the other hand, the optically thin upper layers of the disk are approximately isothermal -- a behavior that is analogous to the hot upper layers of YSO disks. We also find that the disks are fully ionized, as expected, but there is an ionization minimum in the vicinity of the temperature minimum. Finally, we find that, despite the complex temperature structure, the infrared excess is well-approximated by an equivalent isothermal disk model whose temperature is about 60% of the stellar temperature. This is largely because, at long wavelengths, the effective photosphere of the disk is located in its isothermal regions.

The Discordance of Mass‐Loss Estimates for Galactic O‐Type Stars

We have determined accurate values of the product of the mass-loss rate and the ion fraction of P+4, Mq(P+4), for a sample of 40 Galactic O-type stars by fitting stellar wind profiles to observations of the P v resonance doublet obtained with FUSE, ORFEUS BEFS, and Copernicus. When P+4 is the dominant ion in the wind [i.e., 0.5 less than or similar to q(P+4) <= 1],. Mq(P+4) approximates the mass-loss rate to within a factor of less than or similar to 2. Theory predicts that P+4 is the dominant ion in the winds of O7-O9.7 stars, although an empirical estimator suggests that the range O4-O7 may be more appropriate. However, we find that the mass-loss rates obtained from P v wind profiles are systematically smaller than those obtained from fits to H alpha emission profiles or radio free-free emission by median factors of similar to 130 (if P+4 is dominant between O7 and O9.7) or similar to 20 (if P+4 is dominant between O4 and O7). These discordant measurements can be reconciled if the winds of O stars in the relevant temperature range are strongly clumped on small spatial scales. We use a simplified two-component model to investigate the volume filling factors of the denser regions. This clumping implies that mass-loss rates determined from rho(2)'' diagnostics have been systematically overestimated by factors of 10 or more, at least for a subset of O stars. Reductions in the mass-loss rates of this size have important implications for the evolution of massive stars and quantitative estimates of the feedback that hot-star winds provide to their interstellar environments.

2D simulations of the line-driven instability in hot-star winds

2D simulations of the line-driven instability in hot-star winds

A pseudo-planar, periodic-box formalism for modelling the outer evolution of structure in spherically expanding stellar winds

We present an efficient technique to study the 1D evolution of instability-generated structure in winds of hot stars out to very large distances (∼1000 stellar radii). This technique makes use of our previous finding that external forces play little rôle in the outer evolution of structure. Rather than evolving the entire wind, as is traditionally done, the technique focuses on a representative portion of the structure and follows it as it moves out with the flow. This requires the problem to be formulated in a moving reference frame. The lack of Galilean invariance of the spherical equations of hydrodynamics is circumvented by recasting them in a pseudo-planar form. By applying the technique to a number of problems we show that it is fast and accurate, and has considerable conceptual advantages. It is particularly useful to test the dependence of solutions on the Galilean frame in which they were obtained. As an illustration, we show that, in a one-dimensional approximation, the wind can remain structured out to distances of more than 1300 stellar radii from the central star.

Ion‐by‐Ion Differential Emission Measure Determination of Collisionally Ionized Plasma. I. Method

We describe a technique to derive constraints on the differential emission measure (DEM) distribution, a measure of the temperature distribution, of collisionally ionized hot plasmas from their X-ray emission-line spectra. This technique involves fitting spectra using a number of components, each of which is the entire X-ray emission-line spectrum for a single ion. It is applicable to high-resolution X-ray spectra of any collisionally ionized plasma, and it is particularly useful for spectra in which the emission lines are broadened and blended, such as those of the winds of hot stars. This method does not require that any explicit assumptions about the form of the DEM distribution be made and is easily automated.

Optically thick clumps – not the solution to the Wolf-Rayet wind momentum problem?

The hot star wind momentum problem is revisited, and it is shown that the conventional belief, that it can be solved by a combination of clumping of the wind and multiple scattering of photons, is not self-consistent for optically thick clumps. Clumping does reduce the mass loss rate , and hence the momentum supply, required to generate a specified radio emission measure ε, while multiple scattering increases the delivery of momentum from a specified stellar luminosity L. However, in the case of thick clumps, when combined the two effects act in opposition rather than in unison since clumping reduces multiple scattering. From basic geometric considerations, it is shown that this reduction in momentum delivery by clumping more than offsets the reduction in momentum required, for a specified ε. Thus the ratio of momentum deliverable to momentum required is maximal for a smooth wind and the momentum problem remains for the thick clump case. In the case of thin clumps, all of the benefit of clumping in reducing η lies in reducing for a given ε so that extremely small filling factors are needed. It is also shown that clumping affects the inference of from radio ε not only by changing the emission measure per unit mass but also by changing the radio optical depth unity radius , and hence the observed wind volume, at radio wavelengths. In fact, for free-free opacity , contrary to intuition, increases with increasing clumpiness.

3D hydrodynamical simulations of corotating interaction regions in rotating line-driven stellar winds

I present radiation hydrodynamics simulations of rotating line-driven O-star winds subject to surface variations tak- ing the shape of localized bright Gaussian spots. Following the original work of Cranmer & Owocki, I investigate the influence on resulting corotating interaction regions (CIRs) of 1) extending the simulation domain from 2D (equatorial plane) to 3D (oc- tant of a sphere) and 2) explicitly account for the lateral components of the radiative acceleration, computed using a multiple-ray quadrature of the visible stellar disk at all wind locations. I identify the wind spin down effect of Gayley & Owocki, present in unperturbed rotating hot star winds. In 2D simulations, the perturbed azimuthal component of the radiative acceleration does not change the gross properties of CIRs. However, the resulting perturbed azimuthal velocity extrema are enhanced by a factor of 50 compared to unperturbed models, so that its magnitude is now a few times greater than the adopted isothermal sound speed. This lateral broadening of wind material at the vertical of a spot leads to an overall weakening of the CIR compression compared to Cranmer & Owocki. In 3D, the extra dimension weakens further the CIR compression and associated velocity kink compared to equivalent 2D simulations. 3D simulations confirm the assumption of Cranmer & Owocki that the angular extent of a surface spot influence is similar in the azimuthal and latitudinal directions. 3D simulations for off-equatorial spots reveal the presence of CIRs advecting out along a fixed latitude, i.e. centred on the spot latitude and contained within a conic shell whose latitudinal thickness is of the order of the full-width-half-maximum of the Gaussian spot. Thus, the CIR properties are essentially independent of the latitude of base perturbations. These results suggest that the key properties of a line-driven wind subject to base brightness variations are well described by considering only the perturbation on the radial radiative ac- celeration, with, for a Gaussian spot, an angular modulation solely dependent on the distance to the spot location, irrespective of the latitudinal or azimuthal direction. Following the technique of Cranmer & Owocki, I have performed spectroscopic line synthesis computations based on 2D hydrodynamical inputs obtained using the multi-ray computation of the multi-component perturbed radiative acceleration or its perturbed radial component. For both P-Cygni and emission line profiles, the differences in hydrodynamical inputs have unnoticeable effects on profile shapes. The method developed in Cranmer & Owocki is therefore adequate for extensive investigations of the large-amplitude long-term line profile variability identified in many O-star spectra.

Radiation-driven winds of hot luminous stars

Radiation-driven winds of hot luminous stars

Structure and dynamics of hot star winds

Hot luminous stars are characterized by their fast, dense and persistent outflows. Here, we analyze the unambiguous spectroscopic signatures of the presence of these winds. We then present various observational elements that suggest that hot star winds are not smoothly expanding outflows. The unstable nature of line-driving could be at the origin of these properties of radiatively-driven outflows and we investigate here its ability to explain the Line Profile Variability (LPV) observed in hot star spectra. Such variability features profile sub-peaks migrating away from line center, and with characteristic velocity scales increasing from 50 to 100-200 km s -1 (from center to edge). Based on radiation-hydrodynamics simulations, we compute the average and temporal evolution of the emissivity of a hot star wind, and compare with LPV datasets of Wolf-Rayet (WR) spectra. The inferred inadequacy of the spherically-symmetric assumption suggests a globally asymmetrical wind structure, which we model by mapping the 3D wind volume with closely-packed star-centered cones. We find that the cone-angle α , which represents the lateral extent of wind structures, controls the sub-peak width at line center. Given the absence of an explicit lateral velocity in our simulations, the best match to observations suggest an upper limit of ca. 1-3 deg to these structures. At line edge, synthetic sub-peaks are narrower than observed by a factor 2-3, suggesting the lack of radial velocity dispersion of computed wind structures, a likely artifact of our 1D simulations. Additionally, assuming that sub-peak lifetimes in LPV time-series represents the crossing-time of the Line Emission Region (LER), we determine the wind acceleration in the LER. Contrary to previous findings, we find no firm evidence for very extended acceleration of WR winds, which would require using spectral diagnostics with LER located distinctly below v ∞ . Although the best candidates, WR objects and their optically thick outflows constitute a big challenge for constraining observationally the velocity law of radiatively-driven winds.

Inference of hot star density stream properties from data on rotationally recurrent DACs

The information content of data on rotationally periodic recurrent discrete absorption components (DACs) in hot star wind emission lines is discussed. The data comprise optical depths τ(w, φ) as a function of dimensionless Doppler velocity w = (∆λ/λ0)(c/v∞) and of time expressed in terms of stellar rotation angle φ. This is used to study the spatial distributions of density, radial and rotational velocities, and ionisation structures of the corotating wind streams to which recurrent DACs are conventionally attributed. The simplifying assumptions made to reduce the degrees of freedom in such structure distribution functions to match those in the DAC data are discussed and the problem then posed in terms of a bivariate relationship between τ(w, φ) and the radial velocity vr(r), transverse rotation rate Ω(r) and density ρ(r ,φ ) structures of the streams. The discussion applies to cases where: the streams are equatorial; the system is seen edge on; the ionisation structure is approximated as uniform; the radial and transverse velocities are taken to be functions only of radial distance but the stream density is allowed to vary with azimuth. The last kinematic assumption essentially ignores the dynamical feedback of density on velocity and the relationship of this to fully dynamical models is discussed. The case of narrow streams is first considered, noting the result of Hamann et al. (2001) that the apparent acceleration of a narrow stream DAC is higher than the acceleration of the matter itself, so that the apparent slow acceleration of DACs cannot be attributed to the slowness of stellar rotation. Thus DACs either involve matter which accelerates slower than the general wind flow, or they are formed by structures which are not advected with the matter flow but propagate upstream (such as Abbott waves). It is then shown how, in the kinematic model approximation, the radial speed of the absorbing matter can be found by inversion of the apparent acceleration of the narrow DAC, for a given rotation law. The case of broad streams is more complex but also more informative. The observed τ(w, φ) is governed not only by vr(r) and Ω(r) of the absorbing stream matter but also by the density profile across the stream, determined by the azimuthal (φ0) distribution function F0(φ0) of mass loss rate around the stellar equator. When F0(φ0 )i s fairly wide inφ0, the acceleration of the DAC peak τ(w, φ )i nw is generally slow compared with that of a narrow stream DAC and the information on vr(r), Ω(r) and F0(φ0) is convoluted in the data τ(w, φ). We show that it is possible, in this kinematic model, to recover by inversion, complete information on all three distribution functions vr(r), Ω(r )a ndF0(φ0) from data on τ(w, φ )o f sufficiently high precision and resolution since vr(r )a ndΩ(r) occur in combination rather than independently in the equations. This is demonstrated for simulated data, including noise effects, and is discussed in relation to real data and to fully hydrodynamic models.

Understanding the High‐Resolution X‐Ray Spectra of Early‐Type Stars

Fig. 1.—Chandra Medium Energy Grating spectra of the six target stars, showing emission from Hand He-like S, Si, Ne, Mg, and O, along with a number of Fe ions (principally Fe xvii). Note the variety of emission line profile shapes. The jump in X-ray spectral resolution made possible by the orbiting Chandra X-Ray Observatory has inspired a host of new techniques for determining the locations, motions, and temperature structures of the X-ray–emitting plasma of hot stars. Although steady-state models of stellar winds are relatively well developed, X-rays offer a unique window on small-scale inhomogeneous structures in hot star winds. Currently, the most viable theory of X-ray generation in hot stars relies on small instabilities growing into X-ray–emitting shocks distributed throughout the wind. The advent of high-resolution X-ray data allows many new ways to test this paradigm that are applied here. In a detailed study of the O4f star z Pup (J. P. Cassinelli et al. 2001, ApJ, 554, L55), X-ray–emitting gas is found extremely close to the photosphere, a region where it would be difficult to generate strong shocks. The X-ray line profiles of z Pup do conform well to what would be expected from an Xray source embedded in an expanding, absorbing wind: they are broad because of the wind expansion, and their centroids are blueshifted because of wind absorption of X-rays originating on the far side of the wind. Achieving an understanding of the line profiles of the O9 III star d Ori is not as straightforward, however. The emission lines are surprisingly narrow and do not show the expected blueshift (N. A. Miller et al. 2002, ApJ, 577, 951). Detailed comparisons to theories of line profile generation are not able to resolve this discrepancy. A study of the six normal hot stars observed with Chandra (see Fig. 1) reveals that the good agreement found between the line profiles of z Pup and theoretical expectations is the exception, not the rule. Perhaps most puzzling, the X-ray line profiles of the two B stars studied are broadened by less than a couple of hundred kilometers per second, making it difficult to imagine how the X-ray–emitting gas can be related to the rapid outflow of the wind as a whole. A recently proposed infalling clump model for the B star t Sco (J. C. Howk et al. 2000, ApJ, 534, 348) can explain nearly all of its X-ray properties. However, this model probably does not explain all B star X-ray emission, for the other B star studied (b Cru) is a much dimmer and softer X-ray emitter.

STRUCTURE AND VARIABILITY OF HOT-STAR WINDS

A study of the structure of hot stars and the nature of their variability is presented. We propose a three-phase model for hot-star winds and calculate the X-ray line emission of the hot component of the wind in comparison with the XMM Newton X-ray spectrum of O4f star κ Puppis. The results of high-resolution spectroscopy for some bright O stars are also presented. The line profile variability of bright O stars 19 Cep and λ Ori A is detected.

Two-dimensional simulations of the line-driven instability in hot-star winds

We report initial results of two-dimensional simulations of the nonlinear evolution of the line-driven instability (LDI) in hot-star winds. The method is based on the Smooth Source Function (SSF) formalism for nonlocal evaluation of the radial line-force, implemented separately within each of a set of radiatively isolated azimuthal grid zones. The results show that radially compressed shells that develop initially from the LDI are systematically broken up by Rayleigh-Taylor or thin-shell instabilities as these structures are accelerated outward. Through radial feedback of backscattered radiation, this leads ultimately to a flow structure characterized by nearly complete lateral incoherence, with structure extending down to the lateral grid scale, which here corresponds to angle sizes of order a fifth of a degree. We briefly discuss the implications for interpreting various observational diagnostics of wind structure, but also emphasize the importance of future extensions to include lateral line-drag effects of diffuse radiation, which may set a minimum lateral scale for break-up of flow structure.

Instabilities in the winds of hot stars

We present work investigating the stability of line-driven winds using a non-Sobolev approach. We find that the dense shell structures which characterise the growth of radiation-driven instabilities in one dimensional simulations break up into numerous bow-shaped clumps in two-dimensions.

Magnetically confined winds of hot stars

We discuss the interplay between radiatively driven winds and magnetic fields in hot stars. In late main sequence B stars, radiatively driven winds are likely to occur but with a mass loss rate strongly affected by the magnetic field structure at the stellar surface. Away from the stellar surface, the interaction of a radiatively driven wind with a dipolar magnetic field lead to the formation of a large magnetosphere consisting of an extended hot postshock region as well as a dense cooling disk forming near the magnetic equator (Magnetically Confined Wind Shock Model, MCWS). In the context of this model, we try to interpret an extensive set of observations (X-ray, UV and optical data) available for the O7V star Θ1 Ori C as well as the pulsating B star β Cep. We finally show how observations of X-ray lines with the XMM or Chandra spacecrafts could help us to obtain a clearer picture of the interaction between magnetic fields and the winds of hot stars.