Weak local Nash equilibrium

In this paper, we consider a concept of local Nash equilibrium for non-cooperative games - the so-called weak local Nash equilibrium. We prove its existence for a significantly more general class of sets of strategies than compact convex sets. The theorems on existence of the weak local equilibrium presented here are applications of Brouwer and Lefschetz fixed point theorems. © 2013 Juliusz Schauder Centre for Nonlinear Studies Nicolaus Copernicus University.

Analysis of the influence of the plasma thermodynamic regime in the spectrally resolved and mean radiative opacity calculations of carbon plasmas in a wide range of density and temperature

In this work the spectrally resolved, multigroup and mean radiative opacities of carbon plasmas are calculated for a wide range of plasma conditions which cover situations where corona, local thermodynamic and non-local thermodynamic equilibrium regimes are found. An analysis of the influence of the thermodynamic regime on these magnitudes is also carried out by means of comparisons of the results obtained from collisional-radiative, corona or Saha–Boltzmann equations. All the calculations presented in this work were performed using ABAKO/RAPCAL code.

A peculiar metal-rich star, HD 135485

Local thermodynamic equilibrium (LTE) absolute and differential abundances are presented for a peculiar metal-rich B-type star, HD 135485. These suggest that HD 135485 has a general enrichment of similar to0.5 dex in all the metals observed (C, N, O, Ne, Mg, Al, Si, P, S, Cl, Ar, Sc, Ti, Cr, Mn, Fe and Sr), except for nickel. The helium enhancement and hence hydrogen deficiency can account for less than or equal to 0.2 dex of this enhancement of metals, with the additional enhancement probably being representative of the progenitor gas. However, some of the metals appear to have greater enhancements, which may have occurred during the star's evolution. The significantly larger nitrogen abundance coupled with a modest helium enhancement observed in HD 135485 indicates that carbon- nitrogen (CN) processed material has possibly contaminated the stellar surface. Neon and carbon enhancements may indicate that helium core flashes have also occurred in HD 135485. Some of the iron-group elements (viz. Mn and Ni) appear to have similar abundance patterns to that of silicon Ap stars, but it is uncertain how these abundance patterns formed if they were not present in the progenitor gas. From a kinematical investigation it is unclear whether this star formed in a metal-rich region as implied by its chemical composition. From its position in the Hertzsprung-Russell diagram, HD 135485 would appear to be an evolved star lying close to or on the horizontal branch.

High-resolution spectroscopic observations of post-asymptotic giant branch candidates from the Edinburgh-Cape Survey

High spectral resolution ( R similar to 40 000) and signal-to-noise optical spectra, obtained at the Very Large Telescope ( VLT), are presented for three post-asymptotic giant branch ( AGB) candidates selected from the Edinburgh-Cape ( EC) Faint Blue Object Survey. The stellar atmospheric parameters and chemical compositions, derived using sophisticated non-local thermodynamic equilibrium calculations, reveal that EC 14102-1337 and EC 20068-7324 are both in an evolved post-horizontal branch ( HB) evolutionary state. However, EC 11507-2253 is most likely a post-AGB star.

A non-LTE abundance analysis of the post-AGB star ROA 5701

An analysis of high-resolution Anglo-Australian Telescope (AAT)/University College London Echelle Spectrograph (UCLES) optical spectra for the ultraviolet (UV)-bright star ROA 5701 in the globular cluster omega Cen (NGC 5139) is performed, using non-local thermodynamic equilibrium (non-LTE) model atmospheres to estimate stellar atmospheric parameters and chemical composition. Abundances are derived for C, N, O, Mg, Si and S, and compared with those found previously by Moehler et al. We find a general metal underabundance relative to young B-type stars, consistent with the average metallicity of the cluster. Our results indicate that ROA 5701 has not undergone a gas-dust separation scenario as previously suggested. However, its abundance pattern does imply that ROA 5701 has evolved off the asymptotic giant branch (AGB) prior to the onset of the third dredge-up.

Chemical abundances and winds of massive stars in M31: a B-type supergiant and a WC star in OB 10

We present high quality spectroscopic data for two massive stars in the OB 10 association of M31, OB 10-64 (B0 la) and OB 10-WRI (WC6). Medium resolution spectra of both stars were obtained using the ISIS spectrograph on the William Herschel Telescope. This is supplemented with Hubble Space Telescope STIS UV spectroscopy and Keck I HIRES data for OB 10-64. A non- local thermodynamic equilibrium (LTE) model atmosphere and abundance analysis for OB 10-64 is presented, indicating that this star has similar photospheric CNO, Mg and Si abundances to solar neighbourhood massive stars. A wind analysis of this early B-type supergiant reveals a mass-loss rate of (M)over dot = 1.6 x 10(-6) M-circle dot yr(-1), and v(infinity) = 1650 km s(-1). The corresponding wind momentum is in good agreement with the wind momentum-luminosity relationship found for Galactic early-B supergiants. Observations of OB 10-WRI are analysed using a non-LTE, line-blanketed code, to reveal approximate stellar parameters of log L/L-circle dot similar to 5.7, T-* - 75 kK, v(infinity) similar to 3000 km s(-1), (M)over dot/(M-circle dot yr(-1)) similar to 10(-4.3) adopting a clumped wind with a filling factor of 10 per cent. Quantitative comparisons are made with the Galactic WC6 star HD 92809 (WR23) revealing that OB 10-WR1 is 0.4 dex more luminous, though it has a much lower C/He ratio (similar to0.1 versus 0.3 for HD 92809). Our study represents the first detailed, chemical model atmosphere analysis for either a B-type supergiant or a Wolf- Rayet (WR) star in Andromeda, and shows the potential of how such studies can provide new information on the chemical evolution of galaxies and the evolution of massive stars in the local Universe.

Australia Telescope Compact Array 1.2cm Observations of the Massive Star Forming Region G305.2+0.2

We report on Australia Telescope Compact Array observations of the massive star-forming region G305.2+0.2 at 1.2 cm. We detected emission in five molecules towards G305A, confirming its hot core nature. We determined a rotational temperature of 26 K for methanol. A non-local thermodynamic equilibrium excitation calculation suggests a kinematic temperature of the order of 200 K. A time-dependent chemical model is also used to model the gas-phase chemistry of the hot core associated with G305A. A comparison with the observations suggest an age of between 2 × 104 and 1.5 × 105 yr. We also report on a feature to the south-east of G305A which may show weak Class I methanol maser emission in the line at 24.933 GHz. The more evolved source G305B does not show emission in any of the line tracers, but strong Class I methanol maser emission at 24.933 GHz is found 3 arcsec to the east. Radio continuum emission at 18.496 GHz is detected towards two H ii regions. The implications of the non-detection of radio continuum emission towards G305A and G305B are also discussed.

Spectral simulation of laser ablated magnesium plasmas

We describe a collisional-radiative equilibrium model for predicting the optical emission spectrum of low-temperature magnesium plasmas, specifically those created by laser ablation. In the model, levels are populated by a balance of collisional and radiative rates. We include Stark widths of lines and trapping of radiation in the calculations. By use of this model we discuss various issues of importance in spectral analysis of laser ablated plasma plumes, such as the partial local thermodynamic equilibrium approximation, line trapping and time dependence.

Iron abundances from optical FeIII absorption lines in B-type stellar spectra

The role of optical FeIII absorption lines in B-type stars as iron abundance diagnostics is considered. To date, ultraviolet Fe lines have been widely used in B-type stars, although line blending can severely hinder their diagnostic power. Using optical spectra, covering a wavelength range ~3560-9200Å, a sample of Galactic B-type main-sequence and supergiant stars of spectral types B0.5 to B7 are investigated. A comparison of the observed FeIII spectra of supergiants, and those predicted from the model atmosphere codes TLUSTY [plane-parallel, non-local thermodynamic equilibrium (LTE)], with spectra generated using SYNSPEC (LTE), and CMFGEN (spherical, non-LTE), reveal that non-LTE effects appear small. In addition, a sample of main-sequence and supergiant objects, observed with the Fiber-fed Extended Range Optical Spectrograph (FEROS), reveal LTE abundance estimates consistent with the Galactic environment and previous optical studies. Based on the present study, we list a number of FeIII transitions which we recommend for estimating the iron abundance from early B-type stellar spectra.

The iron abundance of the Magellanic Bridge

High-resolution Hubble Space Telescope ultraviolet spectra for five B-type stars in the Magellanic Bridge and in the Large (LMC) and Small (SMC) Magellanic Clouds have been analysed to estimate their iron abundances. Those for the Clouds are lower than estimates obtained from late-type stars or the optical lines in B-type stars by approximately 0.5 dex. This may be due to systematic errors possibly arising from non-local thermodynamic equilibrium (non-LTE) effects or from errors in the atomic data, as similar low Fe abundances have previously been reported from the analysis of the ultraviolet spectra of Galactic early-type stars. The iron abundance estimates for all three Bridge targets appear to be significantly lower than those found for the SMC and LMC by approximately -0.5 and -0.8 dex, respectively, and these differential results should not be affected by any systematic errors present in the absolute abundance estimates. These differential iron abundance estimates are consistent with the underabundances for C, N, O, Mg and Si of approximately -1.1 dex relative to our Galaxy previously found in our Bridge targets. The implications of these very low metal abundances for the Magellanic Bridge are discussed in terms of metal deficient material being stripped from the SMC.

Cyanopolyynes in hot cores: modelling G305.2+0.2

We present results from a time-dependent gas-phase chemical model of a hot core based on the physical conditions of G305.2+0.2. While the cyanopolyyne HC3N has been observed in hot cores, the longer chained species, HC5N, HC7N and HC9N, have not been considered as the typical hot-core species. We present results which show that these species can be formed under hot core conditions. We discuss the important chemical reactions in this process and, in particular, show that their abundances are linked to the parent species acetylene which is evaporated from icy grain mantles. The cyanopolyynes show promise as ‘chemical clocks’ which may aid future observations in determining the age of hot core sources. The abundance of the larger cyanopolyynes increases and decreases over relatively short time-scales, ~10^2.5 yr. We present results from a non-local thermodynamic equilibrium statistical equilibrium excitation model as a series of density, temperature and column density dependent contour plots which show both the line intensities and several line ratios. These aid in the interpretation of spectral-line data, even when there is limited line information available. In particular, non-detections of HC5N and HC7N in Walsh et al. are analysed and discussed.

Atmospheric parameters and rotational velocities for a sample of Galactic B-type supergiants

High-resolution optical spectra of 57 Galactic B-type supergiant stars have been analysed to determine their rotational and macroturbulent velocities. In addition, their atmospheric parameters (effective temperature, surface gravity and microturbulent velocity) and surface nitrogen abundances have been estimated using a non-local thermodynamic equilibrium grid of model atmospheres. Comparisons of the projected rotational velocities have been made with the predictions of stellar evolutionary models and in general good agreement was found. However, for a small number of targets, their observed rotational velocities were significantly larger than predicted, although their nitrogen abundances were consistent with the rest of the sample. We conclude that binarity may have played a role in generating their large rotational velocities. No correlation was found between nitrogen abundances and the current projected rotational velocities. However, a correlation was found with the inferred projected rotational velocities of the main-sequence precursors of our supergiant sample. This correlation is again in agreement with the predictions of single star evolutionary models that incorporate rotational mixing. The origin of the macroturbulence and microturbulent velocity fields is discussed and our results support previous theoretical studies that link the former to subphotospheric convection and the latter to non-radial gravity mode oscillations. In addition, we have attempted to identify differential rotation in our most rapidly rotating targets.

Chemical evolution of protoplanetary disks - the effects of viscous accretion, turbulent mixing and disk winds

We calculate the chemical evolution of protoplanetary disks considering radial viscous accretion, vertical turbulent mixing, and vertical disk winds. We study the effects on the disk chemical structure when different models for the formation of molecular hydrogen on dust grains are adopted. Our gas-phase chemistry is extracted from the UMIST Database for Astrochemistry (Rate06) to which we have added detailed gas-grain interactions. We use our chemical model results to generate synthetic near- and mid-infrared local thermodynamic equilibrium line emission spectra and compare these with recent Spitzer observations. Our results show that if H2 formation on warm grains is taken into consideration, the H2O and OH abundances in the disk surface increase significantly. We find that the radial accretion flow strongly influences the molecular abundances, with those in the cold midplane layers particularly affected. On the other hand, we show that diffusive turbulent mixing affects the disk chemistry in the warm molecular layers, influencing the line emission from the disk and subsequently improving agreement with observations. We find that NH3, CH3OH, C2H2, and sulfur-containing species are greatly enhanced by the inclusion of turbulent mixing. We demonstrate that disk winds potentially affect the disk chemistry and the resulting molecular line emission in a manner similar to that found when mixing is included.

The Type Ic SN 2007gr: a census of the ejecta from late-time optical-infrared spectra

Nebular spectra of supernovae (SNe) offer an unimpeded view of the inner region of the ejecta, where most nucleosynthesis takes place. Optical spectra cover most, but not all, of the emitting elements and therefore offer only a partial view of the products of the explosion. Simultaneous optical-infrared spectra, on the other hand, contain emission lines of all important elements, from C and O through to the intermediate mass elements (IME) Mg, Si, S, Ca and to Fe and Ni. In particular, Si and S are best seen in the IR. The availability of IR data makes it possible to explore in greater detail the results of the explosion. SN 2007gr is the first Type Ic SN for which such data are available. Modelling the spectra with a non-local thermodynamic equilibrium (NLTE) code reveals that the inner ejecta contain similar to 1M(circle dot) of material within a velocity of approximate to 4500 km s(-1). The same mass of Ni-56 derived from the light-curve peak (0.076M(circle dot)) was used to power the spectrum, yielding consistent results. Oxygen is the dominant element, contributing similar to 0.8M(circle dot). The C/O ratio is