Spectral Evolution Models for the Next Decade

Spectral evolution models are a widely used tool for determining the stellar content of galaxies. I provide a review of the latest developments in stellar atmosphere and evolution models, with an emphasis on massive stars. In contrast to the situation for low- and intermediate mass stars, the current main challenge for spectral synthesis models are the uncertainties and rapid revision of current stellar evolution models. Spectral libraries, in particular those drawn from theoretical model atmospheres for hot stars, are relatively mature and can complement empirical templates for larger parameter space coverage. I introduce a new ultraviolet spectral library based on theoretical radiation-hydrodynamic atmospheres for hot massive stars. Application of this library to star-forming galaxies at high redshift, i.e., Lyman-break galaxies, will provide new insights into the abundances, initial mass function and ages of stars in the very early universe.Comment: 8 pages, to appear in IAU Symp. 262, Stellar Populations - Planning for the Next Decade, eds. G. Bruzual & S. Charlo

Graphs of bounded degree and the pp-harmonic boundary

Let $p$ be a real number greater than one and let $G$ be a connected graph of bounded degree. In this paper we introduce the $p$-harmonic boundary of $G$. We use this boundary to characterize the graphs $G$ for which the constant functions are the only $p$-harmonic functions on $G$. It is shown that any continuous function on the $p$-harmonic boundary of $G$ can be extended to a function that is $p$-harmonic on $G$. Some properties of this boundary that are preserved under rough-isometries are also given. Now let $\Gamma$ be a finitely generated group. As an application of our results we characterize the vanishing of the first reduced $\ell^p$-cohomology of $\Gamma$ in terms of the cardinality of its $p$-harmonic boundary. We also study the relationship between translation invariant linear functionals on a certain difference space of functions on $\Gamma$, the $p$-harmonic boundary of $\Gamma$ with the first reduced $\ell^p$-cohomology of $\Gamma$.Comment: Give a new proof for theorem 4.7. Change the style of the text in the first two section

Atmospheric NLTE-models for the spectroscopic analysis of blue stars with winds. IV. Porosity in physical and velocity space

[Abridged] Clumping in the radiation-driven winds of hot, massive stars affects the derivation of synthetic observables across the electromagnetic spectrum. We implement a formalism for treating wind clumping - in particular the light-leakage effects associated with a medium that is porous in physical and velocity space - into the global (photosphere+wind) NLTE model atmosphere code FASTWIND. We assume a stochastic, two-component wind consisting of a mixture of optically thick and thin clumps embedded in a rarefied inter-clump medium. We account fully for the reductions in opacity associated with porosity in physical and velocity-space, and for the well-known effect that opacities depending on rho^2 are higher in clumpy winds than in smooth ones of equal mass-loss rate. By formulating our method in terms of suitable mean and effective opacities for the clumpy wind, we are able to compute models with the same speed (~15 min. on a modern laptop) as in previous code-generations. Some first, generic results of the new models include: i) Confirming earlier results that velocity-space porosity is critical for analysis of UV wind lines in O-stars; ii) for the optical Halpha line, optically thick clumping effects are small for O-stars, but potentially very important for late B and A-supergiants; iii) spatial porosity is a marginal effect for absorption of high-energy X-rays in O-stars, as long as the mean-free path between clumps are kept at realistic values; iv) porosity is negligible at typical O-star radio-photosphere radii; v) regarding the wind ionization balance, a general trend is that increased rates of recombination in simulations with optically thin clumps lead to overall lower degrees of ionization than in corresponding smooth models, but that this effect now is counteracted by the increased levels of light-leakage associated with porosity in physical and velocity space.Comment: 12 pages, 5 figures, accepted for publication in Astronomy & Astrophysic