The Discovery and Physical Parameterization of a New Type of Wolf-Rayet Star

As part of our ongoing Wolf-Rayet (WR) Magellanic Cloud survey, we have discovered 13 new WRs. However, the most exciting outcome of our survey is not the number of new WRs, but their unique characteristics. Eight of our discoveries appear to belong to an entirely new class of WRs. While one might naively classify these stars as WN3+O3V binaries, such a pairing is unlikely. Preliminary CMFGEN modeling suggests physical parameters similar to early-type WNs in the Large Magellanic Cloud except with mass-loss rates three to five times lower and slightly higher temperatures. The evolution status of these stars remains an open question.

Procrustes problems and Parseval quasi-dual frames

Parseval frames have particularly useful properties, and in some cases, they can be used to reconstruct signals which were analyzed by a non-Parseval frame. In this paper, we completely describe the degree to which such reconstruction is feasible. Indeed, notice that for fixed frames $cF$ and $cX$ with synthesis operators $F$ and $X$, the operator norm of $FX^*-I$ measures the (normalized) worst-case error in the reconstruction of vectors when analyzed with $cX$ and synthesized with $cF$. Hence, for any given frame $cF$, we compute explicitly the infimum of the operator norms of $FX^*-I$, where $cX$ is any Parseval frame. The $cX$s that minimize this quantity are called Parseval quasi-dual frames of $cF$. Our treatment considers both finite and infinite Parseval quasi-dual frames.

Optimal completions of a frame

Given a finite sequence of vectors $mathcal F_0$ in $C^d$ we describe the spectral and geometrical structure of optimal completions of $mathcal F_0$ obtained by adding a finite sequence of vectors with prescribed norms, where optimality is measured with respect to a general convex potential. In particular, our analysis includes the so-called Mean Square Error (MSE) and the Benedetto-Fickus frame potential. On a first step, we reduce the problem of finding the optimal completions to the computation of the minimum of a convex function in a convex compact polytope in $R^d$. As a second step, we show that there exists a finite set (that can be explicitly computed in terms of a finite step algorithm that depends on $cF_0$ and the sequence of prescribed norms) such that the optimal frame completions with respect to a given convex potential can be described in terms of a distinguished element of this set. As a byproduct we characterize the cases of equality in Lindskiis inequality from matrix theory.

Nitrogen line spectroscopy in O-stars -- III. The earliest O-stars

This is the third paper in a series aiming at the analysis of nitrogen abundances in O-type stars, to enable further constraints on the early evolution of massive stars. We provide first theoretical predictions for the NIV4058/NIII4640 emission line ratio in dependence of various parameters, and confront them with results from the analysis of a sample of early LMC/SMC O-stars. Stellar and wind parameters are determined by line profile fitting of H/He/N lines, exploiting the helium and nitrogen ionization balance. Corresponding synthetic spectra are calculated using the NLTE atmospheric code FASTWIND. Though there is a monotonic relationship between the emission line ratio and Teff, all other parameters being equal, theoretical predictions indicate additional dependencies, most notably, on the nitrogen abundance. These basic predictions are confirmed by results from atmospheric code CMFGEN. The effective temperatures for the earliest O-stars, inferred from the nitrogen ionization balance, are partly considerably hotter than indicated by previous studies. Consistent with earlier results, effective temperatures increase from supergiants to dwarfs for all spectral types in the LMC. The relation between observed NIV4058/NIII4640 emission line ratio and Teff, for a given luminosity class, turned out to be quite monotonic for our sample stars, and fairly consistent with our model predictions. The scatter within a spectral sub-type is mainly produced by abundance effects. Our findings suggest that the Walborn et al. (2002) classification scheme is able to provide a meaningful relation between spectral type and Teff, provided that it is possible to discriminate for the luminosity class. This might be difficult to achieve in low-Z environments such as the SMC, owing to rather low wind-strengths. According to our predictions, the major bias of the classification scheme is due to nitrogen content.