On the behaviour of stellar winds that exceed the photon-tiring limit

Stars can produce steady-state winds through radiative driving as long as the mechanical luminosity of the wind does not exceed the radiative luminosity at its base. This upper bound on the mass loss rate is known as the photon-tiring limit. Once above this limit, the radiation field is unable to lift all the material out of the gravitational potential of the star, such that only part of it can escape and reach infinity. The rest stalls and falls back toward the stellar surface, making a steady-state wind impossible. Photon-tiring is not an issue for line-driven winds since they cannot achieve sufficiently high mass loss rates. It can however become important if the star exceeds the Eddington limit and continuum interaction becomes the dominant driving mechanism. This paper investigates the time-dependent behaviour of stellar winds that exceed the photon-tiring limit, using 1-D numerical simulations of a porosity moderated, continuum-driven stellar wind. We find that the regions close to the star show a hierarchical pattern of high density shells moving back and forth, unable to escape the gravitational potential of the star. At larger distances, the flow eventually becomes uniformly outward, though still quite variable. Typically, these winds have a very high density but a terminal flow speed well below the escape speed at the stellar surface. Since most of the radiative luminosity of the star is used to drive the stellar wind, such stars would appear much dimmer than expected from the super-Eddington energy generation at their core. The visible luminosity typically constitutes less then half of the total energy flow and can become as low as ten percent or less for those stars that exceed the photon-tiring limit by a large margin.Comment: Accepted for publication in MNRA

Luminous Blue Variables & Mass Loss near the Eddington Limit

During the course of their evolution, massive stars lose a substantial fraction of their initial mass, both through steady winds and through relatively brief eruptions during their Luminous Blue Variable (LBV) phase. This talk reviews the dynamical driving of this mass loss, contrasting the line-driving of steady winds to the potential role of continuum driving for eruptions during LBV episodes when the star exceeds the Eddington limit. A key theme is to emphasize the inherent limits that self-shadowing places on line-driven mass loss rates, whereas continuum driving can in principle drive mass up to the "photon-tiring" limit, for which the energy to lift the wind becomes equal to the stellar luminosity. We review how the "porosity" of a highly clumped atmosphere can regulate continuum-driven mass loss, but also discuss recent time-dependent simulations of how base mass flux that exceeds the tiring limit can lead to flow stagnation and a complex, time-dependent combination of inflow and outflow regions. A general result is thus that porosity-mediated continuum driving in super-Eddington phases can explain the large, near tiring-limit mass loss inferred for LBV giant eruptions.Comment: Conference proceedings, Massive Stars as Cosmic Engines, IAU Symp 250, ed. F. Bresolin, P. A. Crowther, & J. Puls (Cambridge Univ. Press

2D Simulations of the Line-Driven Instability in Hot-Star Winds: II. Approximations for the 2D Radiation Force

We present initial attempts to include the multi-dimensional nature of radiation transport in hydrodynamical simulations of the small-scale structure that arises from the line-driven instability in hot-star winds. Compared to previous 1D or 2D models that assume a purely radial radiation force, we seek additionally to treat the lateral momentum and transport of diffuse line-radiation, initially here within a 2D context. A key incentive is to study the damping effect of the associated diffuse line-drag on the dynamical properties of the flow, focusing particularly on whether this might prevent lateral break-up of shell structures at scales near the lateral Sobolev angle of ca. $1^{\rm o}$. We first explore nonlinear simulations that cast the lateral diffuse force in the simple, local form of a parallel viscosity. Second, to account for the lateral mixing of radiation associated with the radial driving, we next explore models in which the radial force is azimuthally smoothed over a chosen scale. Third, to account for both the lateral line-drag and the lateral mixing in a more self-consistent way, we explore further a method first proposed by Owocki (1999), which uses a restricted 3-ray approach that combines a radial ray with two oblique rays set to have an impact parameter $p < R_{\ast}$ within the stellar core. From numerical simulations, we find that, compared to equivalent 1-ray simulations, the high-resolution 3-ray models show systematically a much higher lateral coherence.... (Full abstract in paper)Comment: Accepted by A&A, 12 pages, 7 figures, 3 only shown in version available at http://www.mpa-garching.mpg.de/~luc/2778.ps.g

Interpreting the solar wind ionization state

The ionization state of the solar coronal expansion is frozen within a few solar radii of the solar photosphere, and spacecraft measurements of the solar wind heavy ion charge state can therefore yield information about coronal conditions (e.g., electron temperature). Previous interpretations of the frozen-in ionization state have always assumed that in the coronal freezing-in region, (1) all heavy ions flow at the same bulk speed as protons, (2) the electron velocity distribution function is Maxwellian, and (3) conditions vary in space but not in time. The consequences of relaxing these assumptions for the interpretation of solar wind charge state measurements are examined. It is found that: (1) the temperature inferred by traditional interpretation of the interplanetary ionization state overestimates (underestimate) the actual coronal electron temperature if higher ion charge stages flow systematically faster (slower) than lower stages at the coronal freezing radius; (2) temperatures inferred from relative abundance measurements of ion-charge-stages with high ionization potentials moderately overestimate the actual coronal electron temperature if the high-energy tail of the coronal electron velocity distribution is enhanced relative to a Maxwellian distribution; (3) the propagation of a disturbance, e.g., a shock wave, through the corona can strongly affect the frozen-in charge state, but only over a time (a few times ten minutes) corresponding to the coronal transit time for the disturbance

Dynamical Simulations of Magnetically Channeled Line-Driven Stellar Winds: II. The Effects of Field-Aligned Rotation

Building upon our previous MHD simulation study of magnetic channeling in radiatively driven stellar winds, we examine here the additional dynamical effects of stellar {\em rotation} in the (still) 2-D axisymmetric case of an aligned dipole surface field. In addition to the magnetic confinement parameter $\eta_{\ast}$ introduced in Paper I, we characterize the stellar rotation in terms of a parameter $W \equiv V_{\rm{rot}}/V_{\rm{orb}}$ (the ratio of the equatorial surface rotation speed to orbital speed), examining specifically models with moderately strong rotation $W =$ 0.25 and 0.5, and comparing these to analogous non-rotating cases. Defining the associated Alfv\'{e}n radius R_{\rm{A}} \approx \eta_{\ast}^{1/4} \Rstar and Kepler corotation radius R_{\rm{K}} \approx W^{-2/3} \Rstar, we find rotation effects are weak for models with $R_{\rm{A}} < R_{\rm{K}}$, but can be substantial and even dominant for models with R_{\rm{A}} \gtwig R_{\rm{K}}. In particular, by extending our simulations to magnetic confinement parameters (up to $\eta_{\ast} = 1000$) that are well above those ($\eta_{\ast} = 10$) considered in Paper I, we are able to study cases with $R_{\rm{A}} \gg R_{\rm{K}}$; we find that these do indeed show clear formation of the {\em rigid-body} disk predicted in previous analytic models, with however a rather complex, dynamic behavior characterized by both episodes of downward infall and outward breakout that limit the buildup of disk mass. Overall, the results provide an intriguing glimpse into the complex interplay between rotation and magnetic confinement, and form the basis for a full MHD description of the rigid-body disks expected in strongly magnetic Bp stars like $\sigma$ Ori E.Comment: 14 pp, visit this http://shayol.bartol.udel.edu/massivewiki-media/publications/rotation.pdf for full figure version of the paper. MNRAS, in pres

Gamma-ray variability from wind clumping in HMXBs with jets

In the subclass of high-mass X-ray binaries known as "microquasars", relativistic hadrons in the jets launched by the compact object can interact with cold protons from the star's radiatively driven wind, producing pions that then quickly decay into gamma rays. Since the resulting gamma-ray emissivity depends on the target density, the detection of rapid variability in microquasars with GLAST and the new generation of Cherenkov imaging arrays could be used to probe the clumped structure of the stellar wind. We show here that the fluctuation in gamma rays can be modeled using a "porosity length" formalism, usually applied to characterize clumping effects. In particular, for a porosity length defined by h=l/f, i.e. as the ratio of the characteristic size l of clumps to their volume filling factor f, we find that the relative fluctuation in gamma-ray emission in a binary with orbital separation a scales as sqrt(h/pi a) in the "thin-jet" limit, and is reduced by a factor 1/sqrt(1 + phi a/(2 l)) for a jet with a finite opening angle phi. For a thin jet and quite moderate porosity length h ~ 0.03 a, this implies a ca. 10 % variation in the gamma-ray emission. Moreover, the illumination of individual large clumps might result in isolated flares, as has been recently observed in some massive gamma-ray binaries.Comment: Accepted for publication in ApJ; 5 pages, 1 figur

Modeling broadband X-ray absorption of massive star winds

We present a method for computing the net transmission of X-rays emitted by shock-heated plasma distributed throughout a partially optically thick stellar wind from a massive star. We find the transmission by an exact integration of the formal solution, assuming that the emitting plasma and absorbing plasma are mixed at a constant mass ratio above some minimum radius, below which there is assumed to be no emission. This model is more realistic than either the slab absorption associated with a corona at the base of the wind or the exospheric approximation that assumes that all observed X-rays are emitted without attenuation from above the radius of optical depth unity. Our model is implemented in XSPEC as a pre-calculated table that can be coupled to a user-defined table of the wavelength dependent wind opacity. We provide a default wind opacity model that is more representative of real wind opacities than the commonly used neutral interstellar medium (ISM) tabulation. Preliminary modeling of \textit{Chandra} grating data indicates that the X-ray hardness trend of OB stars with spectral subtype can largely be understood as a wind absorption effect.Comment: 9 pages, 9 figures. Includes minor corrections made in proof

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

Mass-loss rates currently in use for hot, massive stars have recently been seriously questioned, mainly because of the effects of wind clumping. We investigate the impact of clumping on diagnostic ultraviolet resonance and optical recombination lines. Optically thick clumps, a non-void interclump medium, and a non-monotonic velocity field are all accounted for in a single model. We used 2D and 3D stochastic and radiation-hydrodynamic (RH) 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: Synthetic spectra calculated directly from current RH wind models of the line-driven instability are unable to in parallel reproduce strategic optical and ultraviolet lines for the Galactic O-supergiant LCep. Using our stochastic wind models, we obtain consistent fits essentially by increasing the clumping in the inner wind. A mass-loss rate is derived that is approximately two times lower than predicted by the line-driven wind theory, but much higher than the corresponding rate derived from spectra when assuming optically thin clumps. Our analytic formulation for line formation is used to demonstrate the potential impact of optically thick clumping in weak-winded stars and to confirm recent results that resonance doublets may be used as tracers of wind structure and optically thick clumping. (Abridged)Comment: 14 pages+1 Appendix, 8 figures, 3 tables. Accepted for publication in Astronomy and Astrophysics. One reference updated, minor typo in Appendix correcte