Local Thermodynamic Equilibrium Approximation Research Articles

Radiation hydrodynamical wind revisited: Nonrelativistic regime

Abstract We re-examine the radiatively-driven spherical wind under the diffusion and local thermodynamic equilibrium (LTE) approximations, while focusing our attention on the topological nature of critical points. We first consider the nonrelativistic case, where there is no radiation drag and advection luminosity. We find that under the diffusion approximation almost all critical points (loci) are of the nodal type, which is higher order singular points, which makes the solutions stiff. On the other hand, under the LTE approximation, where the diffusive terms do not exist in the source terms, the critical points are of the saddle type, and transonic solutions are not stiff. Although the loci of critical points are quite similar for both approximations in the nonrelativistic regime, the types of critical points are found to be quite different.

Unsteady three-dimensional model of electric arc. Part 1. Mathematical model and testing results

A non-stationary three-dimensional mathematical model of the electric arc of constant current in the approximation of a partial local thermodynamic equilibrium of plasma is presented. For the purpose of testing the model and computer code a computation of the isothermal laminar viscous fluid flow past a circular cylinder (the testing of the dynamic part of the system of equations) and a computation of the axisymmetric electric arc with a reduced anode attachment have been done. A fair agreement of numerical results with experimental data points overall to the correctness of the mathematical model and the numerical solution technique.

Spectral studies of nanosecond laser interaction with magnesium sulfate target in air

AbstractThe optical emission characterization of the plasma-assisted pulsed laser ablation of the magnesium sulfate target is discussed in this study. The emission spectrum produced by the magnesium sulfate plasma in the wavelength range 200–700 nm has been carefully investigated for different experimental conditions. The spectra analysis was performed by assuming the local thermodynamic equilibrium (LTE) approximation and calculating the plasma temperature with the Boltzmann plot method using neutral Mg spectral lines. The plasma temperature was obtained for different positions along the expansion axis, which allowed obtaining the electron population distribution as a function of the distance from the target. The plasma temperature along the expansion axis allowed evaluating the evolution of the excited states population when the plume expands. Moreover, the Stark broadening method has been employed for electron number density measurements. In this study, the Stark width of the Mg (I) spectral line at 285.21 nm was used. Besides, we have studied the variation of electron temperature (Te) and electron number density (Ne) as a function of laser irradiance.

Complex processing of interferograms of light-erosion gas-plasma streams in vacuum

A technique for automated processing of the results of interferometry of light-erosion gas-plasma flows using the local thermodynamic equilibrium approximation and data on the mass flow rate of the target substance was developed. The application of this technique allowed evaluation of the spatiotemporal distributions of the optical (refraction and absorption coefficients), thermophysical (temperature, density, and electron concentration), gas-dynamic (velocity distribution of particles, average-mass velocity, and pressure), and optomechanical (momentum coupling coefficient) characteristics of light-erosion gas-plasma flows. The features of application of frequency filters at various stages of automatic processing of measurement results are considered. Examples of processing the experimental results that were obtained under the impact of ultrashort laser pulses on condensed media are presented.

NON-LTE DETERMINATION OF THE SILICON ABUNDANCE USING A THREE-DIMENSIONAL HYDRODYNAMICAL MODEL OF THE SOLAR PHOTOSPHERE

Confrontations of spectroscopic observations with local thermodynamic equilibrium (LTE) spectral syntheses in a three-dimensional (3D) hydrodynamical model of the photosphere led to a downward revision of the photospheric and meteoritic silicon abundances. Here we derive the photospheric silicon abundance taking into account non-LTE (NLTE) effects in the same 3D model. We show that the above-mentioned downward revision of the silicon abundance is caused by using the LTE approximation in the context of 3D modeling, an experimental scale of oscillator strengths, and a small number of Si I lines. We demonstrate that no revision of the silicon abundance is required if NLTE effects are taken into account and one uses a solar oscillator strength scale and an extended list of Si I lines. The NLTE abundance value we find by fitting the equivalent widths of 65 Si I lines is A NLTE Si = 7.549 ± 0.016. This value agrees well with the silicon abundance that had been recommended earlier by Grevesse & Sauval and Lodders for the photosphere and CI chondrite meteorites.

Thermodynamic and SIMS analyses on the role of proton/water in oxygen reduction process and related degradations in solid oxide fuel cells

Roles of Secondary Ion Mass Spectrometry and the local thermodynamic equilibrium approximation are discussed in understanding high temperature electrochemical processes. Fundamental issues are first considered on metal dense electrode (Pt/Au) and oxide electrolyte (YSZ/GDC) systems; the so-called three phase boundary (TPB) mechanism is dominant for YSZ systems, whereas for the GDC systems, a new proton/water mechanism is dominant; protons play an important role in a such way that the cathodic reaction of protons to form water vapors takes place at TPBs, while evaporated water vapors are transported on the GDC surface; oxide ions are transported to the anode and protons are circulated to the TPBs of the cathode; another effect of water vapors is to enhance oxygen isotope exchange reactions over a whole area of surface and a resulting flow of 18O inside GDC masks the charge transfer process in the SIMS analyses. A local proton flow in the proton/water mechanism provides a drastic change in the distribution of chemical potential of water vapors under the dense electrodes, leading to the pore formation or the non-homogenized cation distribution. Concerning industrial issues, two degradation topics are analyzed on drastic changes in chemical potential distribution caused by electrode reactions or by non-uniform flows of oxide ions inside electrolyte.

Velocity and Temperature Response Functions of 77 Near-Infrared (800 – 1400 nm) Photospheric Lines – I

We present a new list of solar photospheric lines in the near-infrared (NIR) region obtained by synthesis under local thermodynamic equilibrium (LTE) approximation. We give novel velocity and temperature response functions (RFs) for 77 lines over the spectral range 800 – 1400 nm. Using these RFs, we are able to obtain for each line the core formation height and the range of atmospheric layers where thermodynamic perturbations are dominant. Moreover, by using the depth-integrated RFs, we give an indication of the dependence on the wavelength of the RFs and quantify their sensitivity to thermodynamic variations. The NIR region represents a significant source of interest for spectroscopic and polarimetric studies. Indeed, at these wavelengths we explore the deeper photospheric layers, and the Zeeman splitting is larger than in the visible range.

Numerical modelling of unsteady heating and melting of the anode by electric arc. Part 1. Mathematical model and computed characteristics of the arc column

The two-dimensional mathematical model in the approximation of a partial local thermodynamic equilibrium of plasma and the technique for numerical computation of the unsteady electric arc characteristics, including the conjugate heat exchange of the electric-arc plasma flow with the treated product (anode) are considered. The results of overall testing of the numerical algorithm point to the correctness of the model and computational technique. The results of the computation of the arc characteristics from the conventional ignition moment until the passage to stationary regime are presented. It is found that a single thermal torus, which scatters fairly quickly in the ambient medium, forms around the arc column.

Interstellar HOCN in the Galactic center region

Aims. Our aim is to confirm the interstellar detection of cyanic acid, HOCN, in the Galactic center clouds. It has previously been tentatively detected only in Sgr B2(OH). Methods. We used a complete line survey of the hot cores Sgr B2(N) and (M) in the 3 mm range, complemented by additional observations carried out with the IRAM 30 m telescope at selected frequencies in the 2 mm band and towards four additional positions in the Sgr B2 cloud complex in the 2 and 3 mm bands. The spectral survey was analysed in the local thermodynamical equilibrium approximation (LTE) by modeling the emission of all identified molecules simultaneously. This allowed us to distinguish weak features of HOCN from the rich line spectrum observed in Sgr B2(N) and (M). Lines of the more stable (by 1.1 eV) isomer isocyanic acid, HNCO, in these sources, as well as those of HOCN and HNCO towards the other positions, were analysed in the LTE approximation as well. Results. Four transitions of HOCN were detected in a quiescent molecular cloud in the Galactic center at a position offset in (R.A., decl.) by (20'',100'') from the hot core source Sgr B2(M), confirming its previous tentative interstellar detection. Up to four transitions were detected toward five other positions in the Sgr B2 complex, including the hot cores Sgr B2(M), (S), and (N). A fairly constant abundance ratio of ~ 0.3 - 0.8 % for HOCN relative to HNCO was derived for the extended gas components, suggesting a common formation process of these isomers.

Oxygen abundance in local disk and bulge: chemical evolution with a strictly universal IMF

This paper has two parts: one about observational constraints related to the empirical differential oxygen abundance distribution (EDOD), and the other about inhomogeneous models of chemical evolution, in particular the theoretical differential oxygen abundance distribution (TDOD). In the first part, the EDOD is deduced from subsamples related to two different samples involving (i) N=532 solar neighbourhood (SN) stars within the range, −1.5<[Fe/H]<0.5, for which the oxygen abundance has been determined both in presence and in absence of the local thermodynamical equilibrium (LTE) approximation (Ramirez et al. in Astron. Astrophys. 465:271, 2007); and (ii) N=64 SN thick disk, SN thin disk, and bulge K-giant stars within the range, −1.7<[Fe/H]<0.5, for which the oxygen abundance has been determined (Melendez et al. in Astron. Astrophys. 484:L21, 2008). A comparison is made with previous results implying use of [O/H]–[Fe/H] empirical relations (Caimmi in Astron. Nachr. 322:241, 2001b; New Astron. 12:289, 2007) related to (iii) 372 SN halo subdwarfs (Ryan and Norris in Astron. J. 101:1865, 1991); and (iv) 268 K-giant bulge stars (Sadler et al. in Astron. J. 112:171, 1996). The EDOD of the SN thick + thin disk is determined by weighting the mass, for assumed SN thick to thin disk mass ratio within the range, 0.1–0.9. In the second part, inhomogeneous models of chemical evolution for the SN thick disk, the SN thin disk, the SN thick + thin disk, the SN halo, and the bulge, are computed assuming the instantaneous recycling approximation. The EDOD data are fitted, to an acceptable extent, by their TDOD counterparts with the exception of the thin or thick + thin disk, where two additional restrictions are needed: (i) still undetected, low-oxygen abundance thin disk stars exist, and (ii) a single oxygen overabundant star is removed from a thin disk subsample. In any case, the (assumed power-law) stellar initial mass function (IMF) is universal but gas can be inhibited from, or enhanced in, forming stars at different rates with respect to a selected reference case. Models involving a strictly universal IMF (i.e. gas neither inhibited from, nor enhanced in, forming stars with respect to a selected reference case) can also reproduce the data to an acceptable extent. Our main conclusions are (1) different models are necessary to fit the (incomplete) halo sample, which is consistent with the idea of two distinct halo components: an inner, flattened halo in slow prograde rotation, and an outer, spherical halo in net retrograde rotation (Carollo et al. in Nature 450:1020, 2007); (2) the oxygen enrichment within the inner SN halo, the SN thick disk, and the bulge, was similar and coeval within the same metallicity range, as inferred from observations (Prochaska et al. in Astron. J. 120:2513, 2000); (3) the fit to thin disk data implies an oxygen abundance range similar to its thick disk counterpart, with the extension of conclusion (2) to the thin disk, and the evolution of the thick + thin disk as a whole (Haywood in Mon. Not. R. Astron. Soc. 388:1175, 2008) cannot be excluded; (4) leaving outside the outer halo, a fit to the data related to different environments is provided by models with a strictly universal IMF but different probabilities of a region being active, which implies different global efficiencies of the star formation rate; (5) a special case of stellar migration across the disk can be described by models with enhanced star formation, where a fraction of currently observed SN stars were born in situ and a comparable fraction is due to the net effect of stellar migration, according to recent results based on high-resolution N-body + smooth particle hydrodynamics simulations (Roškar et al. in Astrophys. J. Lett. 684:L79, 2008).

Dynamical opacity-sampling models of Mira variables - I. Modelling description and analysis of approximations

We describe the Cool Opacity-sampling Dynamic EXtended (codex) atmosphere models of Mira variable stars, and examine in detail the physical and numerical approximations that go in-to the model creation. The codex atmospheric models are obtained by computing the temperature and the chemical and radiative states of the atmospheric layers, assuming gas pressure and velocity profiles from Mira pulsation models, which extend from near the H-burning shell to the outer layers of the atmosphere. Although the code uses the approximation of Local Thermodynamic Equilibrium (LTE) and a grey approximation in the dynamical atmosphere code, many key observable quantities, such as infrared diameters and low-resolution spectra, are predicted robustly in spite of these approximations. We show that in visible light, radiation from Mira variables is dominated by fluorescence scattering processes, and that the LTE approximation likely underpredicts visible-band fluxes by a factor of 2.

The G-dwarf problem in the Galaxy

This paper has two parts: one about observational constraints, and the other about chemical evolution models. In the first part, the empirical differential metallicity distribution (EDMD) is deduced from three different samples involving (i) local thick disk stars derived from Gliese and scaled in situ samples within the range, - 1.20 ⩽ [ Fe / H ] ⩽ - 0.20 [Wyse, R.F.G., Gilmore, G., 1995. AJ 110, 2771]; (ii) 46 likely metal-weak thick disk stars within the range, - 2.20 ⩽ [ Fe / H ] ⩽ - 1.00 [Chiba, M., Beers, T.C., 2000. AJ 119, 2843]; (iii) 287 chemically selected G dwarfs within 25 pc from the Sun, with the corrections performed in order to take into account the stellar scale height [Rocha-Pinto, H.J., Maciel, W.J., 1996. MNRAS 279, 447]; in addition to previous results [Caimmi, R., 2001b. AN 322, 241; Caimmi, R., 2007. NewA 12, 289] related to (iv) 372 solar neighbourhood halo subdwarfs [Ryan, S.G., Norris, J.E., 1991. AJ 101, 1865]; and (v) 268 K-giant bulge stars [Sadler, E.M., Rich, R.M., Terndrup, D.M., 1996. AJ 112, 171]. The metal-poor and metal-rich EDMD related to the thick disk shows similarities with their halo and bulge counterparts, respectively. Then the thick disk is conceived as made of two distinct regions: the halo-like and the bulge-like thick disk, and the related EDMD is deduced. Under the assumption that each distribution is typical for the corresponding subsystem, the EDMD of the thick disk, the thick + thin disk, and the Galaxy, is determined by weighting the mass. In the second part, models of chemical evolution for the halo-like thick disk, the bulge-like thick disk, and the thin disk, are computed assuming the instantaneous recycling approximation. The EDMD data are fitted, to an acceptable extent, by simple models of chemical evolution implying both homogeneous and inhomogeneous star formation, provided that star formation is inhibited during thick disk formation, with respect to the thin disk. The initial mass function (IMF) is assumed to be a universal power law, which implies the same value of the true yield in different subsystems. The theoretical differential metallicity distribution (TDMD) is first determined for the halo-like thick disk, the bulge-like thick disk, and the thin disk separately, and then for the Galaxy by weighting the mass. An indicative comparison is performed between the EDMD deduced for the disk both in presence and in absence of [O/Fe] plateau, and its counterpart computed for (vi) N = 523 nearby stars within the range, - 1.5 < [ Fe / H ] < 0.5 , for which the oxygen abundance has been determined both in presence and in absence of the local thermodynamical equilibrium (LTE) approximation [Ramirez, I., Allende Prieto, C., Lambert, D.L., 2007. A&A 465, 271]. Both distributions are found to exhibit a similar trend, although systematic differences exist. In addition, the related empirical age-metallicity relation (EAMR) cannot be fitted by the theoretical age-metallicity relation (TAMR) predicted by the model, and the reasons for this discrepancy are explained.

Analysis of Radio Astronomical Data of the Negative Ion C 6 H - in IRC +10 216

Radio astronomical data of C6H- observed with the Nobeyama 45 m and IRAM 30 m telescopes have been analyzed by the local thermodynamic equilibrium approximation to give the column density of (6.1-8.0) × 1012 cm-2 and the excitation temperature of 32 ± 3 K, with an assumed source size of 30'' ± 3''. The abundance of C6H- was estimated to be 8.6% of C6H. The observed line shapes of C6H - and C6H indicate that the distribution of C 6H- is more present in the inner region than C6H. The production mechanism of C6H- is discussed.

Survey of the Star-Formation Regions Associated with Infrared Sources Observed in the J = 1−0 Line of the CO Molecule and Its Isotopes. Results of Observations Performed in the C18O(J = 1−0) Line

We present results of observations of 23 compact cores of molecular clouds associated with IRAS “ cold” infrared sources. The observations were performed in the J = 1−0 line of the C18O molecule on a 13.7-meter radio telescope of the Purple Mountain Observatory, China. The C18O (J = 1−0) line was detected in the emission of 21 objects. Column densities of the C18O and H2 molecules towards the maximum of integral intensity of the C18O emission were estimated in the approximation of local thermodynamic equilibrium and amounted to (2.5–10.4) · 1015cm−2 and (1.5–6.1) · 1022 cm−2, respectively. The kinetic temperatures determined for these maxima from the CO lines vary from 14 to 45 K. For six objects, whose mapping has been almost completed, the dimensions of the C18O emission regions are estimated to range from 0.5 to 1.2 pc. The masses of these objects lie in the range of (390–1750) M⊙ and are close to the estimates following from the virial theorem. The range of average densities of the objects is (0.3–1.4) · 104 cm−3.

Spectral simulation of laser ablated magnesium plasmas

We describe a collisional-radiative equilibrium model forpredicting the optical emission spectrum of low-temperature magnesium plasmas,specifically those created by laser ablation. In the model, levels arepopulated by a balance of collisional and radiative rates. We include Starkwidths of lines and trapping of radiation in the calculations. By use of thismodel we discuss various issues of importance in spectral analysis of laserablated plasma plumes, such as the partial local thermodynamic equilibriumapproximation, line trapping and time dependence.

Calculation of radiation characteristics of diatomic and some triatomic molecules

A mathematical model and a software package that permit calculation of the chemical composition of complex mixtures in a wide range of temperatures and densities are developed. A thermodynamic databank for a large number (about 300) of molecules and radicals up to pentatomic ones inclusive is set up. The chemical composition is determined in the approximation of local thermodynamic equilibrium. A mathematical model and a software package for calculating electron-vibration-rotation spectra of diatomic molecules are proposed. A databank of optical characteristics of molecules makes it possible to calculate spectra of about 50 of the most important molecules. The calculation is performed in the approximation of Morse potential—nonrigid rotator. A version for calculating spectra in the approximation of the Rydberg—Klein—Reese potential is also set up.

Non‐local thermodynamic equilibrium in general circulation models of the Martian atmosphere 1. Effects of the local thermodynamic equilibrium approximation on thermal cooling and solar heating

Calculations of CO2 thermal cooling and near‐IR solar heating rates under non‐local thermodynamic equilibrium (non‐LTE) situations have been performed to understand and evaluate the effects of non‐LTE on the energy balance of the upper atmosphere of Mars. We find that the 15‐μm cooling rates can be in error if LTE is assumed above 80 km. In general, the correct non‐LTE values are significantly smaller than the LTE values above about 85 km, but the magnitude and sign of the error depend on the temperature structure and the top altitude of the model and, to a lesser extent, on the collisions with atomic oxygen. A detailed analysis of the relevance of the upper boundary layer and a suggested buffer region are presented for both LTE and non‐LTE. Based on general considerations of the thermal profile in the mesosphere and lower thermosphere, recommendations for general circulation models (GCM) are presented as a first guide for minimizing the LTE cooling rates inaccuracies. The error of assuming LTE on the CO2 near‐IR solar heating rates is found to be about 20% at 85 km and increases strongly above this altitude. The dependences of this LTE‐non‐LTE difference on rate coefficients, thermal structure, surface pressure, and solar zenith angle (SZA) are studied. In contrast to the large effect of the SZA on the solar heating rate, we find it is not important for the LTE‐non‐LTE relative difference, which permits a simple tabulation of the non‐LTE effect as a function of pressure only. A table of LTE correction factors for the solar heating rate is included for its potential use as a fast yet accurate operative scheme within GCMs.

THEORETICAL STUDY OF SPECTRA OF 3-2 TRANSITION AND ITS SATELLITE LINES FOR Ne-LIKE ION OF La

Based on the calculated wavelengths and transition probabilities of n-3 to n-2 transitions for Ne-like, Na-like, Mg-like and Al-like ions of La, in the case of high temperature condition and local thermodynamic equilibrium approximation, we simulated the spectral structure of all the charged states by considering the broadening of individual line and overlapping of a large number of lines in plasma, presented the mean wavelengths and half width of the satellite peaks, interpreted the previous experimental spectral structures, and predicted some new satellite peaks in a larger wavelength region.

Nonparametric dynamical analysis of globular clusters: M15, 47 TUC, NGC 362, and NGC 3201

We use radial velocities of member stars and cluster surface brightness profiles to non-parametrically determine the mass density profiles and isotropic phase-space distribution functions $f(E)$ for the globular clusters M15 (NGC7078), 47~Tuc (NGC104), NGC~362, and NGC~3201. Assuming isotropy and using the velocity dispersion and surface brightness profiles, the Jeans equation uniquely determines the mass density profile. In the two centrally-concentrated clusters, M15 and 47~Tuc, we find that the mass-to-light ratios (M/L's) reach minima around 1\arcmin, and increase by more than a factor of four towards the cluster centers. For the two less centrally concentrated clusters, the M/L decreases monotonically all the way into the center. All four clusters exhibit an increase in the M/L's in their outer parts. If the variations in the M/L's are due to equipartition of energy between different mass stars, then we attribute the central increases to massive remnants and the outer increases to low-mass stars (m$<0.3$M$_\odot$). By applying the crude approximation of local thermodynamic equilibrium, we derive the present-day mass function for each cluster. In the central 2--3 parsecs, 0.7--1.5 M$_\odot$ objects provide the bulk of the cluster mass. The paper is in a uuencoded compressed tar file (260kb).

Density distributions in dark clouds

view Abstract Citations (100) References (41) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Density distributions in dark clouds. Arquilla, R. ; Goldsmith, P. F. Abstract The density distributions within seven dark cloud envelopes are investigated by using high-quality 12CO and 13CO J = 1→0 spectra to calculate 13CO and H2 column densities via the local thermodynamic equilibrium approximation. Column densities are analyzed by modeling cloud local density distributions as power laws of the form ρ(r) ∝ r-γ. Most of the clouds are found to be strongly centrally condensed. Using estimated cloud distances and the inferred density laws, local H2 number densities throughout the envelopes are calculated. Implications of the density and the temperature structure for cloud energetics, and for the interpretation of molecular spectral lines observed from dark clouds are considered. Publication: The Astrophysical Journal Pub Date: October 1985 DOI: 10.1086/163542 Bibcode: 1985ApJ...297..436A Keywords: Density Distribution; Interstellar Matter; Mass Distribution; Molecular Clouds; Nebulae; Carbon Monoxide; Monte Carlo Method; Stability; Thermodynamic Equilibrium; Astrophysics full text sources ADS | data products SIMBAD (6)