We examine radiatively driven mass loss from stars near and above the Eddington limit. Building on the standard CAK theory of driving by scattering in an ensemble of lines with a power-law distribution of opacity, we first show that the formal divergence of such line-driven mass loss as a star approaches the Eddington limit is actually limited by the ''photon tiring'' associated with the work needed to lift material out of the star's gravitational potential. We also examine such tiring in simple continuum-driven models in which a specified outward increase in opacity causes a net outward acceleration above the radius where the generalized Eddington parameter exceeds unity. When the density at this radius implies a mass loss too close to the tiring limit, the overall result is flow stagnation at a finite radius. Since escape of a net steady wind is precluded, such circumstances are expected to lead to extensive variability and spatial structure. After briefly reviewing convective and other instabilities that also can be expected to lead to extensive structure in the envelope and atmosphere of a star near or above the Eddington limit, we investigate how the porosity of such a structured medium can reduce the effective coupling between the matter and radiation. Introducing a new ''porosity-length'' formalism, we derive a simple scaling for the reduced effective opacity and use this to derive an associated scaling for the porosity-moderated, continuumdriven mass-loss rate from stars that formally exceed the Eddington limit. For a simple super-Eddington model with a single porosity length that is assumed to be on the order of the gravitational scale height, the overall mass loss is similar to that derived in previous porosity models, given roughly by L à =a à c (where L * is the stellar luminosity and c and a * are the speed of light and the atmospheric sound speed). This is much higher than is typical of line-driven winds but is still only a few percent of the tiring limit. To obtain still stronger mass loss that approaches observationally inferred values near this limit, we draw on an analogy with the power-law distribution of line-opacity in the standard CAK model of line-driven winds and thereby introduce a ''power-law-porosity'' model in which the associated structure has a broad range of scales. We show that for power indices p < 1, the mass-loss rate can be enhanced over the single-scale model by a factor that increases with the Eddington parameter as À À1þ1= p . For lower p (%0.5-0.6) and/or moderately large À (>3-4), such models lead to mass-loss rates that approach the photon-tiring limit. Together with the ability to drive quite fast outflow speeds (of order the surface escape speed), the derived, near-tiring-limited mass loss offers a potential dynamical basis to explain the observationally inferred large mass loss and flow speeds of giant outbursts in Carinae and other luminous blue variable stars.

Abstract. We investigate stochastic structure in hot-star winds. The structure (i.e. inhomogeneities such as clumps and shocks) is generated by the instability of the line driving mechanism in the inner wind. It is self-excited in the sense that it persists even in the absence of explicit perturbations. The evolution of structure as it moves out with the flow is quantified by the radial dependence of statistical properties such as the clumping factor and the velocity dispersion. We find that structure evolves under the influence of two competing mechanisms. Dense clumps pressure-expand into the rarefied gas that separates them, but this expansion is counteracted by supersonic collisions among the clumps, which tend to compress them further. Because of such ongoing collisions, clumps can survive over an extended region out of pressure equilibrium with the rarefied surrounding gas. Moreover, the linedriving force has little rôle in maintaining the structure beyond about 20-30 R * , implying that the outer evolution can be simplified as a pure gasdynamical problem. In modelling the distant wind structure we find it is necessary to maintain a relatively fine constant grid spacing to resolve the often quite narrow dense clumps. We also find that variations in the heating and cooling, particularly the "floor" temperature to which shock-compressed gas is allowed to cool, can affect both the density and temperature variation. Finally, we find that increasing the value of the line-driving cut-off parameter κmax can significantly enhance the level of flow structure. Overall, the results of our work suggest that structure initiated in the inner wind acceleration region can survive to substantial distances (∼100 R * ), and thus can have an important influence on observational diagnostics (e.g. infrared and radio emission) formed in the outer wind.

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Motivated by recent detections by the XMM and Chandra satellites of X-ray line emission from hot, luminous stars, we present synthetic line profiles for X-rays emitted within parameterized models of a hot-star wind. The X-ray line emission is taken to occur at a sharply defined co-moving-frame resonance wavelength, which is Doppler-shifted by a stellar wind outflow parameterized by a 'beta' velocity law, v(r) = v ∞ (1 − R * /r) β . Above some initial onset radius R o for X-ray emission, the radial variation of the emission filling factor is assumed to decline as a power-law in radius, f (r) ∼ r −q . The computed emission profiles also account for continuum absorption within the wind, with the overall strength characterized by a cumulative optical depth τ * . In terms of a wavelength shift from line-center scaled in units of the wind terminal speed v ∞ , we present normalized X-ray line profiles for various combinations of the parameters β, τ * , q and R o , and including also the effect of instrumental and/or macroturbulent broadening as characterized by a Gaussian with a parameterized width σ. We discuss the implications for interpreting observed hot-star X-ray spectra, with emphasis on signatures for discriminating between "coronal" and "wind-shock" scenarios. In particular, we note that in profiles observed so far the substantial amount of emission longward of line center will be difficult to reconcile with the expected attenuation by the wind and stellar core in either a wind-shock or coronal model.

We investigate the degree to which the nearly symmetric form of X-ray emission lines seen in Chandra spectra of early-type supergiant stars could be explained by a possibly porous nature of their spatially structured stellar winds. Such porosity could effectively reduce the bound-free absorption of X-rays emitted by embedded wind shocks, and thus allow a more similar transmission of red-vs. blue-shifted emission from the back vs. front hemispheres. To obtain the localized self-shielding that is central to this porosity effect, it is necessary that the individual clumps be optically thick. In a medium consisting of clumps of size ℓ and volume filling factor f , we argue that the general modification in effective opacity should scale approximately as κ ef f ≈ κ/(1 + τ c ), where, for a given atomic opacity κ and mean density ρ, the clump optical thickness scales as τ c = κρℓ/f . For a simple wind structure parameterization in which the 'porosity length' h ≡ ℓ/f increases with local radius r as h = h ′ r, we find that a substantial reduction in wind absorption requires a quite large porosity scale factor, h ′ ∼ > 1, implying large porosity lengths h ∼ > r. The associated wind structure must thus have either a relatively large scale ℓ ∼ < r, or a small volume filling factor f ≈ ℓ/r ≪ 1, or some combination of these. We argue that the relatively small-scale, moderate compressions generated by intrinsic instabilities in line-driving are unlikely to give such large porosity lengths. This raises questions about whether porosity effects could play a significant role in explaining nearly symmetric X-ray line profiles, leaving again the prospect of instead having to invoke a substantial (ca. factor 5) downward revision in the assumed mass-loss rates.

-Results from the most extensive study of the time-evolving dust structure around the prototype "Pinwheel" nebula WR 104 are presented. Encompassing 11 epochs in three near-infrared filter bandpasses, a homogeneous imaging data set spanning more than 6 years (or 10 orbits) is presented. Data were obtained from the highly successful Keck Aperture Masking Experiment, which can recover high fidelity images at extremely high angular resolutions, revealing the geometry of the plume with unprecedented precision. Inferred properties for the (unresolved) underlying binary and wind system are orbital period 241.5±0.5 days and angular outflow velocity of 0.28±0.02 mas/day. An optically thin cavity of angular size 13.3 ± 1.4 mas was found to lie between the central binary and the onset of the spiral dust plume. Rotational motion of the wind system induced by the binary orbit is found to have important ramifications: entanglement of the winds results in strong shock activity far downstream from the nose of the bowshock. The far greater fraction of the winds participating in the collision may play a key role in gas compression and the nucleation of dust at large radii from the central binary and shock stagnation point. Investigation of the effects of radiative braking pointed towards significant modifications of the simple hydrostatic colliding wind geometry, extending the relevance of this phenomena to wider binary systems than previously considered. Limits placed on the maximum allowed orbital eccentricity of e < ∼ 0.06 argue strongly for a prehistory of tidal circularization in this system. Finally we discuss the implications of Earth's polar (i < ∼ 16 • ) vantage point onto a system likely to host supernova explosions at future epochs.

The highly eccentric binary system, η Car, provides clues to the transition of massive stars from hydrogen-burning via the CNO cycle to a helium-burning evolutionary state. The fastmoving wind of η Car B creates a cavity in η Car A's slower, but more massive, stellar wind, providing an in situ probe. lines extend only 0.3 arcsec (700 au) from NE to SW and are blue shifted from −500 to +200 km s −1 . All observed spectral features vary with the 5.54-year orbital period. The highly ionized, forbidden emission disappears during the low state, associated with periastron passage. The high-ionization emission originates in the outer wind interaction region that is directly excited by the far-ultraviolet radiation from η Car B. The HST/STIS spectra reveal a time-varying, distorted paraboloidal structure, caused by the interaction of the massive stellar winds. The model and observations are consistent with the orbital plane aligned with the skirt of the Homunculus. However, the axis of the distorted paraboloid, relative to the major axis of the binary orbit, is shifted in a prograde rotation along the plane, which projected on the sky is from NE to NW.

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