Macroturbulent and rotational broadening in the spectra of B-type supergiants.

The absorption-line spectra of early B-type supergiants show significant broadening that implies that an additional broadening mechanism (characterized here as `macroturbulence') is present in addition to rotational broadening. Using high-resolution spectra with signal-to-noise ratios of typically 500, we have attempted to quantify the relative contributions of rotation and macroturbulence, but even with data of this quality significant problems were encountered. However, for all our targets, a model where macroturbulence dominates and rotation is negligible is acceptable; the reverse scenario leads to poor agreement between theory and observation. Additionally, there is marginal evidence for the degree of broadening increasing with line strength, possibly a result of the stronger lines being formed higher in the atmosphere. Acceptable values of the projected rotational velocity are normally less than or equal to 50 km s-1, which may also be a typical upper limit for the rotational velocity. Our best estimates for the projected rotational velocity are typically 10-20 km s-1 and hence compatible with this limit. These values are compared with those predicted by single star evolutionary models, which are initially rapidly rotating. It is concluded that either these models underestimate the rate of rotational breaking or some of the targets may be evolving through a blue loop or are binaries.

Early-type stars in the Galactic halo from the Palomar-Green survey - III. Completion of a magnitude range limited sample

High-resolution (R approximate to 40 000) echelle spectroscopic observations of 13 high-latitude early-type stars are presented. These stars comprise the final part of a complete magnitude range limited sample based on low-resolution spectroscopy of targets drawn from the Palomar-Green survey. The magnitude range under consideration is 13 less than or equal to B-PG less than or equal to 14.6, corresponding to an approximate distance limit for main-sequence B-type objects of 5 less than or equal to d less than or equal to 40 kpc. Three stars are found to be apparently normal, young stars, based on their positions on the (T-eff, log g) diagram, normal abundance patterns and relatively large projected rotational velocities. A further star, PG 1209+263, was found to belong to the chemically peculiar (CP) silicon star class of objects. The remainder are evolved subluminous stars lying on post- horizontal branch (post-HB) tracks, with the exception of PG 2120+062, which appears to be in a post-asymptotic giant branch evolutionary stage. For the young stars in the sample, we have derived distance and age estimates through comparison of the atmospheric parameters with recent theoretical evolutionary models. We discuss formation scenarios by comparing times-of- flight and evolutionary time-scales. It is found that all stars could have formed in the Galactic disc and been ejected from there soon after their birth, with the exception of PG 1209+263. The adopted proper motion is found to be a crucial factor in the kinematical analysis. We also present some number densities for young B-type halo stars, which indicate that they are extremely scarce objects.

Boron abundances in B-type stars: A test of rotational depletion during main-sequence evolution

Boron abundances have been derived for seven main-sequence B- type stars from Hubble Space Telescope STIS spectra around the B III lambda2066 line. In two stars, boron appears to be undepleted with respect to the presumed initial abundance. In one star, boron is detectable but is clearly depleted. In the other four stars, boron is undetectable, implying depletions of 1-2 dex. Three of these four stars are nitrogen enriched, but the fourth shows no enrichment of nitrogen. Only rotationally induced mixing predicts that boron depletions are unaccompanied by nitrogen enrichments. The inferred rate of boron depletion from our observations is in good agreement with these predictions. Other boron-depleted nitrogen-normal stars are identified from the literature. In addition, several boron- depleted nitrogen-rich stars are identified, and while all fall on the boron-nitrogen trend predicted by rotationally induced mixing, a majority have nitrogen enrichments that are not uniquely explained by rotation. The spectra have also been used to determine iron group (Cr, Mn, Fe, and Ni) abundances. The seven B-type stars have near-solar iron group abundances, as expected for young stars in the solar neighborhood. We have also analyzed the halo B-type star PG 0832 + 676. We find [Fe/H] = -0.88 +/- 0.10, and the absence of the B III line gives the upper limit [B/H] <-2.5. These and other published abundances are used to infer the star's evolutionary status as a post-asymptotic giant branch star.

Rotational excitation of H2O by cold electrons

Experimental data are presented for the scattering of electrons by H2O between 17 and 250 meV impact energy. These results are used in conjunction with a generally applicable method, based on a quantum defect theory approach to electron-polar molecule collisions, to derive the first set of data for state-to-state rotationally inelastic scattering cross sections based on experimental values.

The role of Mittag-Leffler functions in anomalous relaxation

The inertia-corrected Debye model of rotational Brownian motion of polar molecules was generalized by Coffey et al. [Phys. Rev. E, 65, 32 102 (2002)] to describe fractional dynamics and anomalous rotational diffusion. The linear- response theory of the normalized complex susceptibility was given in terms of a Laplace transform and as a function of frequency. The angular-velocity correlation function was parametrized via fractal Mittag-Leffler functions. Here we apply the latter method and complex-contour integral- representation methods to determine the original time-dependent amplitude as an inverse Laplace transform using both analytical and numerical approaches, as appropriate. (C) 2004 Elsevier B.V. All rights reserved.

Interpolation formula between very low and intermediate-to-high damping Kramers escape rates for single-domain ferromagnetic particles

It is shown that the Mel'nikov-Meshkov formalism for bridging the very low damping (VLD) and intermediate-to-high damping (IHD) Kramers escape rates as a function of the dissipation parameter for mechanical particles may be extended to the rotational Brownian motion of magnetic dipole moments of single-domain ferromagnetic particles in nonaxially symmetric potentials of the magnetocrystalline anisotropy so that both regimes of damping, occur. The procedure is illustrated by considering the particular nonaxially symmetric problem of superparamagnetic particles possessing uniaxial anisotropy subject to an external uniform field applied at an angle to the easy axis of magnetization. Here the Mel'nikov-Meshkov treatment is found to be in good agreement with an exact calculation of the smallest eigenvalue of Brown's Fokker-Planck equation, provided the external field is large enough to ensure significant departure from axial symmetry, so that the VLD and IHD formulas for escape rates of magnetic dipoles for nonaxially symmetric potentials are valid.

Microscopic models for dielectric relaxation in disordered systems

It is shown how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended to yield the empirical Havriliak-Negami (HN) equation of anomalous dielectric relaxation from a microscopic model based on a kinetic equation just as in the Debye model. This kinetic equation is obtained by means of a generalization of the noninertial Fokker-Planck equation of conventional Brownian motion (generally known as the Smoluchowski equation) to fractional kinetics governed by the HN relaxation mechanism. For the simple case of noninteracting dipoles it may be solved by Fourier transform techniques to yield the Green function and the complex dielectric susceptibility corresponding to the HN anomalous relaxation mechanism.

B-type supergiants in the Small Magellanic Cloud: rotational velocities and implications for evolutionary models

High-resolution spectra for 24 SMC and Galactic B-type supergiants have been analysed to estimate the contributions of both macroturbulence and rotation to the broadening of their metal lines. Two different methodologies are considered, viz. goodness-of-fit comparisons between observed and theoretical line profiles and identifying zeros in the Fourier transforms of the observed profiles. The advantages and limitations of the two methods are briefly discussed with the latter techniques being adopted for estimating projected rotational velocities ( v sin i) but the former being used to estimate macroturbulent velocities. The projected rotational velocity estimates range from approximately 20 to 60 kms(-1), apart from one SMC supergiant, Sk 191, with a v sin i similar or equal to 90 km s(-1). Apart from Sk 191, the distribution of projected rotational velocities as a function of spectral type are similar in both our Galactic and SMC samples with larger values being found at earlier spectral types. There is marginal evidence for the projected rotational velocities in the SMC being higher than those in the Galactic targets but any differences are only of the order of 5 - 10 km s(-1), whilst evolutionary models predict differences in this effective temperature range of typically 20 to 70 km s(-1). The combined sample is consistent with a linear variation of projected rotational velocity with effective temperature, which would imply rotational velocities for supergiants of 70 kms(-1) at an effective temperature of 28 000 K ( approximately B0 spectral type) decreasing to 32 km s(-1) at 12 000 K (B8 spectral type). For all targets, the macroturbulent broadening would appear to be consistent with a Gaussian distribution ( although other distributions cannot be discounted) with an 1/e half-width varying from approximately 20 km s(-1) at B8 to 60 km s(-1) at B0 spectral types.

The VLT-FLAMES survey of massive stars: stellar parameters and rotational velocities in NGC 3293, NGC 4755 and NGC 6611

An analysis is presented of VLT-FLAMES spectroscopy for three Galactic clusters, NGC3293, NGC4755 and NGC6611. Non-LTE model atmosphere calculations have been used to estimate effective temperatures (from either the helium spectrum or the silicon ionization equilibrium) and gravities (from the hydrogen spectrum). Projected rotational velocities have been deduced from the helium spectrum (for fast and moderate rotators) or the metal line spectrum (for slow rotators). The origin of the low gravity estimates for apparently near main sequence objects is discussed and is related to the stellar rotational velocity. The atmospheric parameters have been used to estimate cluster distances (which are generally in good agreement with previous determinations) and these have been used to estimate stellar luminosities and evolutionary masses. The observed Hertzsprung-Russell diagrams are compared with theoretical predictions and some discrepancies including differences in the main sequence luminosities are discussed. Cluster ages have been deduced and evidence for non-coeval star formation is found for all three of the clusters. Projected rotational velocities for targets in the older clusters, NGC3293 and NGC4755, have been found to be systematically larger than those for the field, confirming recent results in other similar age clusters. The distribution of projected rotational velocities are consistent with a Gaussian distribution of intrinsic rotational velocities. For the relatively unevolved targets in the older clusters, NGC3293 and NGC4755, the peak of the velocity distribution would be 250 km s(-1) with a full-width-half-maximum of approximately 180 km s(-1). For NGC6611, the sample size is relatively small but implies a lower mean rotational velocity. This may be evidence for the spin-down effect due to angular momentum loss through stellar winds, although our results are consistent with those found for very young high mass stars. For all three clusters we deduce present day mass functions with Gamma-values in the range of -1.5 to -1.8, which are similar to other young stellar clusters in the Milky Way.

Correlated electron-ion dynamics: the excitation of atomic motion by energetic electrons

Correlated electron-ion dynamics (CEID) is an extension of molecular dynamics that allows us to introduce in a correct manner the exchange of energy between electrons and ions. The formalism is based on a systematic approximation: small amplitude moment expansion. This formalism is extended here to include the explicit quantum spread of the ions and a generalization of the Hartree-Fock approximation for incoherent sums of Slater determinants. We demonstrate that the resultant dynamical equations reproduce analytically the selection rules for inelastic electron-phonon scattering from perturbation theory, which control the mutually driven excitations of the two interacting subsystems. We then use CEID to make direct numerical simulations of inelastic current-voltage spectroscopy in atomic wires, and to exhibit the crossover from ionic cooling to heating as a function of the relative degree of excitation of the electronic and ionic subsystems.

Time dependence of rotational state populations of excited hydrogen molecules in an RF excited plasma reactor

We report on time-dependent population distributions of excited rotational states of hydrogen in a capacitively coupled RF discharge. The common model to obtain the gas temperature from the rotational distribution is not applicable at all times during the discharge cycle due to the time dependence of the EEDF. The apparent temperature within a cycle assumes values between 350 K and 450 K for the discharge parameters of this experiment. We discuss the optimum time window within the discharge cycle that yields the best approximation to the actual temperature. Erroneous results can be obtained, in principle, with time-integrated measurements; we find, however, that in the present case the systematic error amounts to only approximately 20 K. This is due to the fact that the dominant contribution to the average intensity arises during that time window for which the assumptions underlying the analysis are best fulfilled. A similar analysis can be performed for N+2 rotational bands with a small amount of nitrogen added to the discharge gas. These populations do not exhibit the time variations found in the case of H2.