Constraints on porosity and mass loss in O-star winds from modeling of X-ray emission line profile shapes

We fit X-ray emission line profiles in high resolution XMM-Newton and Chandra grating spectra of the early O supergiant Zeta Pup with models that include the effects of porosity in the stellar wind. We explore the effects of porosity due to both spherical and flattened clumps. We find that porosity models with flattened clumps oriented parallel to the photosphere provide poor fits to observed line shapes. However, porosity models with isotropic clumps can provide acceptable fits to observed line shapes, but only if the porosity effect is moderate. We quantify the degeneracy between porosity effects from isotropic clumps and the mass-loss rate inferred from the X-ray line shapes, and we show that only modest increases in the mass-loss rate (<~ 40%) are allowed if moderate porosity effects (h_infinity <~ R_*) are assumed to be important. Large porosity lengths, and thus strong porosity effects, are ruled out regardless of assumptions about clump shape. Thus, X-ray mass-loss rate estimates are relatively insensitive to both optically thin and optically thick clumping. This supports the use of X-ray spectroscopy as a mass-loss rate calibration for bright, nearby O stars.Comment: 20 pages, 20 figures. Accepted by Ap

Feminists really do count : the complexity of feminist methodologies

We are delighted to be presenting this special issue on the topic of feminism and quantitative methods. We believe that such an issue is exceptionally timely. This is not simply because of ongoing debates around quantification within the field of feminism and women‟s studies. It is also because of debates within the wider research community about the development of appropriate methodologies that take account of new technological and philosophical concerns and are fit-for-purpose for researching contemporary social, philosophical, cultural and global issues. Two areas serve as exemplars in this respect and both speak to these combined wider social science and specifically feminist methodological concerns. The first is the increasing concern amongst social scientists with how the complexity of social life can be captured and analysed. Within feminism, this can be seen in debates about intersectionality that recognise the concerns arising from multiple social positions/divisions and associated power issues. As Denis (2008: 688) comments in respect of intersectional analysis „The challenge of integrating multiple, concurrent, yet often contradictory social locations into analyses of power relations has been issued. Theorising to accomplish this end is evolving, and we are struggling to develop effective methodological tools in order to marry theorising with necessary complex analyses of empirical data.‟ Secondly, new techniques and new data sources are now coming on line. This includes work in the UK of the ESRC National Data Strategy which has been setting out the priorities for the development of research data resources both within and across the boundaries of the social sciences. This will facilitate historical, longitudinal, interdisciplinary and mixed methodological research. And it may be the case that these developments facilitate the achievement of a longstanding feminist aim not simply for interdisciplinarity but for transdisciplinarity in epistemological and methodological terms

The Effect of Porosity on X-ray Emission Line Profiles from Hot-Star Winds

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. For a medium consisting of clumps of size l and volume filling factor f, in which the `porosity length' h=l/f increases with local radius 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. The relatively small-scale, moderate compressions generated by intrinsic instabilities in line-driving seem unlikely to give such large porosity lengths, leaving again the prospect of instead having to invoke a substantial (ca. factor 5) downward revision in assumed mass-loss rates.Comment: 6 pages in apj-emulate; 3 figures; submitted to Ap

Atomic Physics of Shocked Plasma in Winds of Massive Stars

High resolution diffraction grating spectra of X-ray emission from massive stars obtained with Chandra and XMM-Newton have revolutionized our understanding of their powerful, radiation-driven winds. Emission line shapes and line ratios provide diagnostics on a number of key wind parameters. Modeling of resolved emission line velocity profiles allows us to derive independent constraints on stellar mass-loss rates, leading to downward revisions of a factor of a few from previous measurements. Line ratios in He-like ions strongly constrain the spatial distribution of Xray emitting plasma, confirming the expectations of radiation hydrodynamic simulations that X-ray emission begins moderately close to the stellar surface and extends throughout the wind. Some outstanding questions remain, including the possibility of large optical depths in resonance lines, which is hinted at by differences in line shapes of resonance and intercombination lines from the same ion. Resonance scattering leads to nontrivial radiative transfer effects, and modeling it allows us to place constraints on shock size, density, and velocity structur

Statistical keyword detection in literary corpora

Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means of statistical information referring to the "spatial" use of the words. Shannon's entropy of information is used as a tool for automatic keyword extraction. By using The Origin of Species by Charles Darwin as a representative text sample, we show the performance of our detector and compare it with another proposals in the literature. The random shuffled text receives special attention as a tool for calibrating the ranking indices.Comment: Published version. 11 pages, 7 figures. SVJour for LaTeX2

Graph Partitioning Induced Phase Transitions

We study the percolation properties of graph partitioning on random regular graphs with N vertices of degree $k$. Optimal graph partitioning is directly related to optimal attack and immunization of complex networks. We find that for any partitioning process (even if non-optimal) that partitions the graph into equal sized connected components (clusters), the system undergoes a percolation phase transition at $f=f_c=1-2/k$ where $f$ is the fraction of edges removed to partition the graph. For optimal partitioning, at the percolation threshold, we find $S \sim N^{0.4}$ where $S$ is the size of the clusters and $\ell\sim N^{0.25}$ where $\ell$ is their diameter. Additionally, we find that $S$ undergoes multiple non-percolation transitions for $f<f_c$

A Simple Scaling Analysis of X-ray Emission and Absorption in Hot-Star Winds

We present a simple analysis of X-ray emission and absorption for hot-star winds, designed to explore the natural scalings of the observed X-ray luminosity with wind and sstellar properties. We show that an exospheric approximation, in which all of the emission above the optical depth unity radius escapes the wind, reproduces very well the detailed expression for radiation transport through a spherically symmetric wind. Using this approximation we find that the X-ray luminosity $L_x$ scales naturally with the wind density parameter \Mdot/\vinf, obtaining L_x \sim (\Mdot/\vinf)^2 for optically thin winds, and L_x \sim (\Mdot/\vinf)^{1+s} for optically thick winds with an X-ray filling factor that varies in radius as $f \sim r^s$. These scalings with wind density contrast with the commonly inferred empirical scalings of X-ray luminosity $L_x$ with bolometric luminosity $L_B$. The empirically derived linear scaling of $L_x \sim L_B$ for thick winds can however be reproduced, through a delicate cancellation of emission and absorption, if one assumes modest radial fall-off in the X-ray filling factor ($s \approx -0.25$ or $s \approx -0.4$, depending on details of the secondary scaling of wind density with luminosity). We also explore the nature of the X-ray spectral energy distribution in the context of this model, and find that the spectrum is divided into a soft, optically thick part and a hard, optically thin part. Finally, we conclude that the energy-dependent emissivity must have a high-energy cut-off, corresponding to the maximum shock energy, in order to reproduce the general trends seen in X-ray spectral energy distributions of hot stars.Comment: 16 pages, 2 figures, requiress aaspp4.sty, accepted by Astrophysical Journal, to appear in the Aug 10, 1999 issue. Several minor changes have been made at the suggestion of the referee. We have added an appendix in which we consider winds with beta-velocity laws, rather than simply constant velocitie

A Generalised Porosity Formalism for Isotropic and Anisotropic Effective Opacity and its Effects on X-ray Line Attenuation in Clumped O Star Winds

We present a generalised formalism for treating the porosity-associated reduction in continuum opacity that occurs when individual clumps in a stochastic medium become optically thick. As in previous work, we concentrate on developing bridging laws between the limits of optically thin and thick clumps. We consider geometries resulting in either isotropic or anisotropic effective opacity, and, in addition to an idealised model in which all clumps have the same local overdensity and scale, we also treat an ensemble of clumps with optical depths set by Markovian statistics. This formalism is then applied to the specific case of bound-free absorption of X- rays in hot star winds, a process not directly affected by clumping in the optically thin limit. We find that the Markov model gives surprisingly similar results to those found previously for the single clump model, suggesting that porous opacity is not very sensitive to details of the assumed clump distribution function. Further, an anisotropic effective opacity favours escape of X-rays emitted in the tangential direction (the venetian blind effect), resulting in a bump of higher flux close to line centre as compared to profiles computed from isotropic porosity models. We demonstrate how this characteristic line shape may be used to diagnose the clump geometry, and we confirm previous results that for optically thick clumping to significantly influence X-ray line profiles, very large porosity lengths, defined as the mean free path between clumps, are required. Moreover, we present the first X-ray line profiles computed directly from line-driven instability simulations using a 3-D patch method, and find that porosity effects from such models also are very small. This further supports the view that porosity has, at most, a marginal effect on X-ray line diagnostics in O stars, and therefore that these diagnostics do indeed provide a good clumping insensitive method for deriving O star mass-loss rates

Numerical evaluation of the upper critical dimension of percolation in scale-free networks

We propose a numerical method to evaluate the upper critical dimension $d_c$ of random percolation clusters in Erd\H{o}s-R\'{e}nyi networks and in scale-free networks with degree distribution ${\cal P}(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ is the broadness of the degree distribution. Our results report the theoretical prediction, $d_c = 2(\lambda - 1)/(\lambda - 3)$ for scale-free networks with $3 < \lambda < 4$ and $d_c = 6$ for Erd\H{o}s-R\'{e}nyi networks and scale-free networks with $\lambda > 4$. When the removal of nodes is not random but targeted on removing the highest degree nodes we obtain $d_c = 6$ for all $\lambda > 2$. Our method also yields a better numerical evaluation of the critical percolation threshold, $p_c$, for scale-free networks. Our results suggest that the finite size effects increases when $\lambda$ approaches 3 from above.Comment: 10 pages, 5 figure