Carbon line formation and spectroscopy in O-type stars

The determination of chemical abundances constitutes a fundamental requirement for obtaining a complete picture of a star. Particularly in massive stars, CNO abundances are of prime interest, due to the nuclear CNO-cycle and various mixing processes which bring these elements to the surface. We aim at enabling a reliable carbon spectroscopy for our unified NLTE atmosphere code FASTWIND. We develop a new carbon model atom including CII/III/IV/V, and discuss problems related to carbon spectroscopy in O-type stars. We describe different tests to examine the reliability of our implementation, and investigate which mechanisms influence the carbon ionization balance. By comparing with high-resolution spectra from six O-type stars, we check in how far observational constraints can be reproduced by our new carbon line synthesis. Carbon lines are even more sensitive to a variation of temperature, gravity, and mass-loss rate, than hydrogen/helium lines. We are able to reproduce most of the observed lines from our stellar sample, and to estimate those specific carbon abundances which bring the lines from different ions into agreement. For hot dwarfs and supergiants earlier than O7, X-rays from wind-embedded shocks can impact the synthesized line strengths, particularly for CIV, potentially affecting the abundance determination. We have demonstrated our capability to derive realistic carbon abundances by means of FASTWIND, using our recently developed model atom. We found that complex effects can have a strong influence on the carbon ionization balance in hot stars. For a further understanding, the UV range needs to be explored as well. By means of detailed nitrogen and oxygen model atoms available to use, we will be able to perform a complete CNO abundance analysis for larger samples of massive stars, and to provide constraints on corresponding evolutionary models and aspects.Comment: 22 pages, 16 figures, 6 table

Atmospheric NLTE-Models for the Spectroscopic Analysis of Blue Stars with Winds. III. X-ray emission from wind-embedded shocks

X-rays/EUV radiation emitted from wind-embedded shocks in hot, massive stars can affect the ionization balance in their outer atmospheres, and can be the mechanism responsible for the production of highly ionized species. To allow for these processes in the context of spectral analysis, we have implemented such emission into our unified, NLTE model atmosphere/spectrum synthesis code FASTWIND. The shock structure and corresponding emission is calculated as a function of user-supplied parameters. We account for a temperature and density stratification inside the post-shock cooling zones, calculated for radiative and adiabatic cooling in the inner and outer wind, respectively. The high-energy absorption of the cool wind is considered by adding important K-shell opacities, and corresponding Auger ionization rates have been included into the NLTE network. We tested and verified our implementation carefully against corresponding results from various alternative model atmosphere codes, and studied the effects from shock emission for important ions from He, C, N, O, Si, and P. Surprisingly, dielectronic recombination turned out to play an essential role for the ionization balance of OIV/OV around Teff = 45,000 K. Finally, we investigated the behavior of the mass absorption coefficient, kappa_nu(r), important in the context of X-ray line formation in massive star winds. In almost all considered cases, direct ionization is of major influence, and Auger ionization significantly affects only NVI and OVI. The approximation of a radially constant kappa_nu is justified for r > 1.2 Rstar and lambda < 18 A, and also for many models at longer wavelengths. To estimate the actual value of this quantity, however, the HeII opacities need to be calculated from detailed NLTE modeling, at least for wavelengths longer than 18 to 20 A, and information on the individual CNO abundances has to be present.Comment: accepted by A&

Variations of the Energy of Free Particles in the pp-Wave Spacetimes

We consider the action of exact plane gravitational waves, or pp-waves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the Kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the Kinetic energy with respect to the width $\lambda$ of the gaussian that represents the wave. The variation of the energy of the free particle is expected to be exactly minus the variation of the energy of the gravitational field, and therefore provides an estimation of the local variation of the gravitational energy. The investigation is carried out in the context of short bursts of gravitational waves, and of waves described by normalised gaussians, that yield impulsive waves in a certain limit.Comment: 20 pages, 18 figures, further arguments supporting the localizability of the gravitational energy are presented, published in Univers

Equality of opportunity and educational achievement in Portugal

Portugal has one of the highest levels of income inequality in Europe, and low wages and unemployment are concentrated among low skill individuals. Education is an important determinant of inequality. However, there are large differences in the educational attainment of different individuals in the population, and the sources of these differences emerge early in the life-cycle when families play a central role in individual development. We estimate that most of the variance of school achievement at age 15 is explained by family characteristics. Observed school inputs explain very little of adolescent performance. Children from highly educated parents benefit of rich cultural environments in the home and become highly educated adults. Education policy needs to be innovative: (1) it needs to explicitly recognize the fundamental long run role of families on child development; (2) it needs to acknowledge the failure of traditional input based policies

Non-singular inflation with vacuum decay

On the basis of a semi-classical analysis of vacuum energy in an expanding spacetime, we describe a non-singular cosmological model in which the vacuum density decays with time, with a concomitant production of matter. During an infinitely long period we have an empty, inflationary universe, with H \approx 1. This primordial era ends in a fast phase transition, during which H and \Lambda decrease to nearly zero in a few Planck times, with release of a huge amount of radiation. The late-time scenario is similar to the standard model, with the radiation phase followed by a long dust era, which tends asymptotically to a de Sitter universe, with vacuum dominating again. An analysis of the redshift-distance relation for supernovas Ia leads to cosmological parameters in agreement with other current estimations.Comment: Work presented at IRGAC 2006, Barcelona, July 11-15 2006. To appear in a special issue of Journal of Physics

Bandlimited approximations to the truncated Gaussian and applications

In this paper we extend the theory of optimal approximations of functions $f: \R \to \R$ in the $L^1(\R)$-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and fine properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work \cite{CLV}, where the case of even functions is treated.Comment: to appear in Const. Appro