Casimir energy of finite width mirrors: renormalization, self-interaction limit and Lifshitz formula

We study the field theoretical model of a scalar field in presence of spacial inhomogeneities in form of one and two finite width mirrors (material slabs). The interaction of the scalar field with the defect is described with position-dependent mass term. Within this model we derive the interaction of two finite width mirrors, establish the correspondence of the model to the Lifshitz formula and construct limiting procedure to obtain finite self-energy of a single mirror without any normalization condition.Comment: 5 pages, based on the presentation on the Ninth Conference on Quantum Field Theory under the influence of External Conditions, Oklahoma, 200

Spectroscopic and physical parameters of Galactic O-type stars. II. Observational constraints on projected rotational and extra broadening velocities as a function of fundamental parameters and stellar evolution

Rotation is of key importance for the evolution of hot massive stars, however, the rotational velocities of these stars are difficult to determine. Based on our own data for 31 Galactic O stars and incorporating similar data for 86 OB supergiants from the literature, we aim at investigating the properties of rotational and extra line-broadening as a function of stellar parameters and at testing model predictions about the evolution of stellar rotation. Fundamental stellar parameters were determined by means of the code FASTWIND. Projected rotational and extra broadening velocities originate from a combined Ft + GOF method. Model calculations published previously were used to estimate the initial evolutionary masses. The sample O stars with Minit > 50 Msun rotate with less that 26% of their break-up velocity, and they also lack objects with v sin i 35 Msun on the hotter side of the bi-stability jump, the observed and predicted rotational rates agree quite well; for those on the cooler side of the jump, the measured velocities are systematically higher than the predicted ones. In general, the derived extra broadening velocities decrease toward cooler Teff, whilst for later evolutionary phases they appear, at the same v sin i, higher for high-mass stars than for low-mass ones. None of the sample stars shows extra broadening velocities higher than 110 km/s. For the majority of the more massive stars, extra broadening either dominates or is in strong competition with rotation. Conclusions: For OB stars of solar metallicity, extra broadening is important and has to be accounted for in the analysis. When appearing at or close to the zero-age main sequence, most of the single and more massive stars rotate slower than previously thought. Model predictions for the evolution of rotation in hot massive stars may need to be updated.Comment: 15 pages, 10 figures, accepted for publication in A &