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

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

2D wind clumping in hot, massive stars from hydrodynamical line-driven instability simulations using a pseudo-planar approach

Context: Clumping in the radiation-driven winds of hot, massive stars arises naturally due to the strong, intrinsic instability of line-driving (the `LDI'). But LDI wind models have so far mostly been limited to 1D, mainly because of severe computational challenges regarding calculation of the multi-dimensional radiation force. Aims: To simulate and examine the dynamics and multi-dimensional nature of wind structure resulting from the LDI. Methods: We introduce a `pseudo-planar', `box-in-a-wind' method that allows us to efficiently compute the line-force in the radial and lateral directions, and then use this approach to carry out 2D radiation-hydrodynamical simulations of the time-dependent wind. Results: Our 2D simulations show that the LDI first manifests itself by mimicking the typical shell-structure seen in 1D models, but how these shells then quickly break up into complex 2D density and velocity structures, characterized by small-scale density `clumps' embedded in larger regions of fast and rarefied gas. Key results of the simulations are that density-variations in the well-developed wind statistically are quite isotropic and that characteristic length-scales are small; a typical clump size is ~0.01R at 2R, thus resulting also in rather low typical clump-masses ~10^17 g. Overall, our results agree well with the theoretical expectation that the characteristic scale for LDI-generated wind-structure is of order the Sobolev length. We further confirm some earlier results that lateral `filling-in' of radially compressed gas leads to somewhat lower clumping factors in 2D simulations than in comparable 1D models. We conclude by discussing an extension of our method toward rotating LDI wind models that exhibit an intriguing combination of large- and small-scale structure extending down to the wind base.Comment: 9 pages, 7 figures + 1 Appendix with 1 figure. Recommended for publication in A&

Mass loss from inhomogeneous hot star winds III. An effective-opacity formalism for line radiative transfer in accelerating, clumped two-component media, and first results on theory and diagnostics

[Abridged] We develop and benchmark a fast and easy-to-use effective-opacity formalism for line and continuum radiative transfer in an accelerating two-component clumpy medium. The formalism bridges the limits of optically thin and thick clumps, and is here used to i) design a simple vorosity-modified Sobolev with exact integration (vmSEI) method for analyzing UV wind resonance lines in hot, massive stars, and ii) derive simple correction factors to the line force driving the outflows of such stars. We show that (for a given ionization factor) UV resonance doublets may be used to analytically predict the upward corrections in empirically inferred mass-loss rates associated with porosity in velocity space (a.k.a. velocity-porosity, or vorosity), but that severe solution degeneracies exist. For an inter-clump density set to 1 % of the mean density, we for O and B supergiants derive upward empirical mass-loss corrections of typically factors of either ~5 or ~50, depending on which of the two applicable solutions is chosen. Overall, our results indicate this solution dichotomy severely limits the use of UV resonance lines as direct mass-loss indicators of clumped hot stellar winds. We next apply the effective-opacity formalism to the standard CAK theory of line-driven winds. By analytic and numerical hydrodynamics calculations, we show that in cases where vorosity is important at the critical point setting the mass-loss rate, the reduced line-force leads to a lower theoretical mass loss, by a factor scaling with the normalized velocity filling factor fvel. On the other hand, if vorosity is important only above this critical point, the predicted mass loss is not affected, but the wind terminal speed is reduced. This shows that porosity in velocity space can have a significant impact not only on the diagnostics, but also on the dynamics and theory of radiatively driven winds.Comment: 13 pages, 8 figures, accepted for publication in Astronomy and Astrophysic

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

Continuum driven winds from super-Eddington stars. A tale of two limits

Continuum driving is an effective method to drive a strong stellar wind. It is governed by two limits: the Eddington limit and the photon-tiring limit. A star must exceed the effective Eddington limit for continuum driving to overcome the stellar gravity. The photon-tiring limit places an upper limit on the mass loss rate that can be driven to infinity, given the energy available in the radiation field of the star. Since continuum driving does not require the presence of metals in the stellar atmosphere it is particularly suited to removing mass from low- and zero-metallicity stars and can play a crucial part in their evolution. Using a porosity length formalism we compute numerical simulations of super-Eddington, continuum driven winds to explore their behaviour for stars both below and above the photon-tiring limit. We find that below the photon tiring limit, continuum driving can produce a large, steady mass loss rate at velocities on the order of the escape velocity. If the star exceeds the photon-tiring limit, a steady solution is no longer possible. While the effective mass loss rate is still very large, the wind velocity is much smallerComment: to be published in the conference proceedings of: First Stars III, Santa Fe, 200

X-Ray Emission-Line Profile Modeling Of O Stars: Fitting A Spherically Symmetric Analytic Wind-Shock Model To The Chandra Spectrum Of Zeta Puppis

X-ray emission-line profiles provide the most direct insight into the dynamics and spatial distribution of the hot, X-ray-emitting plasma above the surfaces of OB stars. The O supergiant zeta Puppis shows broad, blueshifted, and asymmetric line profiles, generally consistent with the wind-shock picture of OB star X-ray production. We model the profiles of eight lines in the Chandra HETGS spectrum of this prototypical hot star. The fitted lines indicate that the plasma is distributed throughout the wind starting close to the photosphere, that there is significantly less attenuation of the X-rays by the overlying wind than is generally supposed, and that there is not a strong trend in wind absorption with wavelength

On the spatial distribution of electron energy loss due to gyro-cooling in hot-star magnetospheres

Hot magnetic stars often exhibit incoherent circularly polarized radio emission thought to arise from gyro-synchrotron emission by energetic electrons trapped in the circumstellar magnetosphere. Theoretical scalings for electron acceleration by magnetic reconnection driven by centrifugal breakout match well the empirical scalings for observed radio luminosity with both the magnetic field strength and the stellar rotation rate. This paper now examines how energetic electrons introduced near the top of closed magnetic loops are subsequently cooled by the energy loss associated with their gyro-synchrotron radio emission. For sample assumed distributions for energetic electron deposition about the loop apex, we derive the spatial distribution of the radiated energy from such "gyro-cooling". For sub-relativistic electrons, we show explicitly that this is independent of the input energy, but also find that even extensions to the relativistic regime still yield a quite similar spatial distribution. However, cooling by coulomb collisions with even a modest ambient density of thermal electrons can effectively quench the emission from sub-relativistic electrons, indicating that the observed radio emission likely stems from relativistic electrons that are less affected by such collisional cooling. The overall results form an initial basis for computing radio emission spectra in future models that account for such cooling and multimode excitation about the fundamental gyro-frequency. Though motivated in the context of hot-stars, the basic results here could also be applied to gyro-emission in any dipole magnetospheres, including those of ultra-cool dwarfs and even (exo)-planets.Comment: 9 pages, 7 figures; accepted for publication in MNRA