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We present XMM-Newton results for the X-ray spectrum from the N-rich Wolf-Rayet (WR) star WR 1. The EPIC instrument was used to obtain a medium-resolution spectrum. The following features characterize this spectrum: (a) significant emission "bumps" appear that are coincident with the wavelengths of typical strong lines, such as Mg XI, Si XIII and S XV; (b) little emission is detected above 4 keV, in contrast to recent reports of a hard component in the stars WR 6 and WR 110 which are of similar subtype; and (c) evidence for sulfur K-edge absorption at about 2.6 keV, which could only arise from absorption of X-rays by the ambient stellar wind. The lack of hard emission in our dataset is suggestive that WR 1 may truly be a single star, thus representing the first detailed X-ray spectrum that isolates the WR wind alone (in contrast to colliding wind zones). Although the properties of the S-edge are not well-constrained by our data, it does appear to be real, and its detection indicates that at least some of the hot gas in WR 1 must reside interior to the radius of optical depth unity for the total absorptive opacity at the energy of the edge.
We discuss X-ray line formation in dense O star winds. A random distribution of wind shocks is assumed to emit X-rays that are partially absorbed by cooler wind gas. The cool gas resides in highly compressed fragments oriented perpendicular to the radial flow direction. For fully opaque fragments, we find that the blueshifted part of X-ray line profiles remains flat-topped even after severe wind attenuation, whereas the red part shows a steep decline. These box- type, blueshifted profiles resemble recent Chandra observations of the O3 star zeta Pup. For partially transparent fragments, the emission lines become similar to those from a homogeneous wind.
WR Central Stars
(2003)
The Potsdam Non-LTE code for expanding atmospheres, which accounts for clumping and iron-line blanketing, has been used to establish a grid of model atmospheres for WC stars. A parameter degeneracy is discovered for early-type WC models which do not depend on the "stellar temperature". 15 galactic WC4-7 stars are analyzed, showing a very uniform carbon abundance (He:C=55:40) with only few exceptions.
Valuations of Terms
(2003)
Let tau be a type of algebras. There are several commonly used measurements of the complexity of terms of type tau, including the depth or height of a term and the number of variable symbols appearing in a term. In this paper we formalize these various measurements, by defining a complexity or valuation mapping on terms. A valuation of terms is thus a mapping from the absolutely free term algebra of type tau into another algebra of the same type on which an order relation is defined. We develop the interconnections between such term valuations and the equational theory of Universal Algebra. The collection of all varieties of a given type forms a complete lattice which is very complex and difficult to study; valuations of terms offer a new method to study complete sublattices of this lattice
We investigate the relationship between the loss of synchronization and the onset of shadowing breakdown via unstable dimension variability in complex systems. In the neighborhood of the critical transition to strongly nonhyperbolic behavior, the system undergoes on-off intermittency with respect to the synchronization state. There are potentially severe consequences of these facts on the validity of the computer-generated trajectories obtained from dynamical systems whose synchronization manifolds share the same nonhyperbolic properties