LTE Case Research Articles

COMBINED EFFECT OF LOCAL THERMAL NONEQUILIBRIUM AND GRAVITY MODULATION ON THERMAL INSTABILITY IN MICROPOLAR NANOFLUID SATURATED POROUS MEDIA

In the present paper an effect of gravity modulation in a horizontal parallel flat plate having micropolar nanofluid saturated by a porous medium is examined. Local thermal nonequilibrium (LTNE) has been observed for the problem, i.e., the fluid, particle, and solid matrix are at different temperatures. Onset of convection and heat and mass transfer for both the cases, i.e., linear stability and nonlinear stability, is analyzed. We conclude that rate of convection in the LTNE case is faster than in the LTE case. Effect of porosity is observed in the LTNE region, which is opposite to the effect observed in the LTE region. Increase in value of A, K<sub>1</sub>, and δ delay the rate of convection. Small value of frequency of gravity modulation forms a greater number of small periods which delay the rate of convection. On increasing the value, heat transfer increases. At higher frequency of modulation we obtain the case similar to unmodulated case.

Scandium Abundance in F–G–K Stars in a Wide Metallicity Range

A new Sc II model atom has been constructed using up-to-date atomic data. To test it, we have carried out nonlocal thermodynamic equilibrium (non-LTE) calculations for three stars with reliably determined atmospheric parameters: the Sun, HD 61421 (Procyon), and HD 84937. Allowance for the departures from LTE leads to a decrease in the root-mean-square abundance error compared to the LTE case and agreement, within the limits of this error, of the abundances deduced from different Sc II lines. The solar non-LTE abundance $$\log\varepsilon_{\textrm{Sun}}=3.12\pm 0.05$$ exceeds the meteoritic abundance recommended by Lodders (2021) by 0.08 dex. However, agreement within 0.02 dex with the meteoritic abundance has been obtained for Procyon. Based on high-resolution spectra, we have determined the LTE and non-LTE scandium abundances for 56 stars in a wide metallicity range, $${-}2.62\leq\textrm{[Fe/H]}\leq 0.24$$ . The dependence of [Sc/Fe] on [Fe/H] demonstrates a similarity with the behavior of the $$\alpha$$ -process elements: scandium is enhanced relative to iron ([Sc/Fe] $$\sim$$ 0.2) in stars with $$\textrm{[Fe/H]}<{-}1$$ , and [Sc/Fe] decreases with increasing [Fe/H] for a higher metallicity. The scandium abundance correlates with the titanium abundance. The results obtained are important for solving the problem of the origin of scandium.

Integration of water electrolysis for fossil-free steel production

This study investigates the integration of water electrolysis technologies in fossil-free steelmaking via the direct reduction of iron ore followed by processing in an electric arc furnace (EAF). Hydrogen (H2) production via low or high temperature electrolysis (LTE and HTE) is considered for the production of carbon-free direct reduced iron (DRI). The introduction of carbon into the DRI reduces the electricity demand of the EAF. Such carburization can be achieved by introducing carbon monoxide (CO) into the direct reduction process. Therefore, the production of mixtures of H2 and CO using either a combination of LTE coupled with a reverse water-gas shift reactor (rWGS-LTE) or high-temperature co-electrolysis (HTCE) was also investigated. The results show that HTE has the potential to reduce the specific electricity consumption (SEC) of liquid steel (LS) production by 21% compared to the LTE case. Nevertheless, due to the high investment cost of HTE units, both routes reach similar LS production costs of approximately 400 €/tonne LS. However, if future investment cost targets for HTE units are reached, a production cost of 301 €/tonne LS is attainable under the conditions given in this study. For the production of DRI containing carbon, a higher SEC is calculated for the LTE-rWGS system compared to HTCE (4.80 vs. 3.07 MWh/tonne LS). Although the use of HTCE or LTE-rWGS leads to similar LS production costs, future cost reduction of HTCE could result in a 10% reduction in LS production cost (418 vs. 375 €/tonne LS). We show that the use of HTE, either for the production of pure H2 or H2 and CO mixtures, may be advantageous compared to the use of LTE in H2-based steelmaking, although results are sensitive to electrolyzer investment costs, efficiencies, and electricity prices.

Non-local thermodynamic equilibrium line formation for Si i–ii–iii in A–B stars and the origin of Si ii emission lines in ι Her

ABSTRACT A comprehensive model atom was developed for Si i–ii–iii using the most up-to-date atomic data available so far. Based on non-local thermodynamic equilibrium (NLTE) line formation for Si i, Si ii and Si iii and high-resolution observed spectra, we determined the NLTE abundances for a sample of nine unevolved A9–B3 type stars with well-determined atmospheric parameters. For each star, NLTE reduces the line-to-line scatter for Si ii substantially compared with the LTE case and leads to consistent mean abundances from lines of different ionization stages. In the hottest star of our sample, ι Her, Si ii is subject to overionization that drives emission in the lines arising from the high-excitation doublet levels. Our NLTE calculations reproduced 10 emission lines of Si ii observed in ι Her. The same overionization effect leads to greatly weakened Si ii lines, which are observed in absorption in ι Her. Large positive NLTE abundance corrections (up to 0.98 dex for 5055 Å) were useful for achieving consistent mean abundances from lines of the two ionization stages, Si ii and Si iii. It was found that NLTE effects are overestimated for the Si ii 6347, 6371 Å doublet in ι Her, while the new model atom works well for cooler stars. At this stage, we failed to understand this problem. We computed a grid of the NLTE abundance corrections for lines of Si i, Si ii and Si iii in model atmospheres with effective temperatures and surface gravities characteristic of unevolved A–B type stars.

Impact of Thermal Non-equilibrium on Weak Nonlinear Rotating Porous Convection

The consequences of local thermal non-equilibrium (LTNE) on both stationary and oscillatory weak nonlinear stability of gravity-driven porous convection in an incompressible fluid-saturated rotating porous layer are investigated. A stability map is drawn in the Darcy–Taylor and scaled Vadasz number plane to demarcate the regions of stationary and oscillatory convection, and thereby, co-dimension-2 points are determined. It is found that the effect of increasing interphase heat transfer coefficient is to enhance the region of stationary convection and decrease the region of oscillatory convection. The complex Ginzburg–Landau equations are derived using the multi-scale method, and pitchfork and Hopf bifurcations occur at stationary and oscillatory critical Darcy–Rayleigh numbers, respectively. The linear and nonlinear oscillatory neutral curves are illustrated, and at the quartic point, the transition from supercritical to subcritical bifurcations is identified for the governing parameters. The impact of LTNE model is to enhance the region of forward bifurcation and post-transient amplitude compared to LTE case. Heat transfer is obtained in terms of Nusselt number for both stationary and oscillatory convection. The region of enhancement in heat flux for oscillatory convection in the smaller scaled Vadasz number domain with increasing Darcy–Taylor number increases with increasing interphase heat transfer coefficient and the porosity-modified conductivity ratio.

Influence of inelastic collisions with hydrogen atoms on the non-LTE modelling of Ca i and Ca ii lines in late-type stars

We perform the non-local thermodynamic equilibrium (NLTE) calculations for Ca I-II with the updated model atom that includes new quantum-mechanical rate coefficients for Ca I + H I collisions from two recent studies, that is, by Barklem and by Mitrushchenkov, Guitou, Belyaev, Yakovleva, Spielfiedel, and Feautrier, and investigate the accuracy of calcium abundance determinations using the Sun, Procyon, and five metal-poor (MP) stars with well-determined stellar parameters. We show that both collisional recipes lead to very similar NLTE results. When using the subordinate lines of Ca I and the high-excitation lines of Ca II, NLTE provides the smaller line-to-line scatter compared with the LTE case for each star. For Procyon, NLTE removes a steep trend with line strength among strong Ca I lines seen in LTE and leads to consistent [Ca/H] abundances from the two ionisation stages. In the MP stars, the NLTE abundance from Ca II 8498 A agrees well with that from the Ca I subordinate lines. NLTE largely removes abundance discrepancies between the high-excitation lines of Ca I and Ca II 8498 A obtained for our four [Fe/H] < -2 stars under the LTE assumption. We investigate the formation of the Ca I resonance line in the [Fe/H] < -2 stars. Consistent NLTE abundances from the Ca I resonance line and the Ca II lines are found for two hyper metal-poor stars HE0107-5240 and HE1327-2326. We provide the NLTE abundance corrections for 28 lines of Ca I in a grid of model atmospheres suitable for abundance analysis of FGK-type dwarfs and subgiants.

FORMATION OF SiC GRAINS IN PULSATION-ENHANCED DUST-DRIVEN WIND AROUND CARBON-RICH ASYMPTOTIC GIANT BRANCH STARS

We investigate the formation of silicon carbide (SiC) grains in the framework of dust-driven wind around pulsating carbon-rich Asymptotic Giant Branch (C-rich AGB) stars in order to reveal not only the amount but also the size distribution. Two cases are considered for the nucleation process; one is the LTE case where the vibration temperature of SiC clusters $T_{\rm v}$ is equal to the gas temperature as usual, and another is the non-LTE case in which $T_{\rm v}$ is assumed to be the same as the temperature of small SiC grains. The results of hydrodynamical calculations for a model with stellar parameters of mass $M_{\ast}$=1.0 $M_{\odot}$, luminosity $L_{\ast}$=10$^{4}$ $L_{\odot}$, effective temperature $T_{\rm eff}$=2600 K, C/O ratio=1.4, and pulsation period $P$=650 days show the followings: In the LTE case, SiC grains condense in accelerated outflowing gas after the formation of carbon grains and the resulting averaged mass ratio of SiC to carbon grains of $\sim$ 10$^{-8}$ is too small to reproduce the value of 0.01-0.3 inferred from the radiative transfer models. On the other hand, in the non-LTE case, the formation region of SiC grains is inner than and/or almost identical to that of carbon grains due to the so-called inverse greenhouse effect. The mass ratio of SiC to carbon grains averaged at the outer boundary ranges from 0.098 to 0.23 for the sticking probability $\alpha_{\rm s}$=0.1-1.0. The size distributions with the peak at $\sim$ 0.2-0.3 $\rm{\mu}$m in radius cover the range of size derived from the analysis of presolar SiC grains. Thus the difference between temperatures of small cluster and gas plays a crucial role in the formation process of SiC grains around C-rich AGB stars, and this aspect should be explored for the formation process of dust grains in astrophysical environments.

Non-LTE effects in Na I spectral lines in stellar atmospheres

The paper examines the statistical equilibrium of Na I in stellar atmospheres with a wide range of parameters: T eff=4000−12500 K, logg=0.0−4.5, and heavy element content [A] from 0.5 to −4.0. The effect of the “overrecombination” of Na I (i.e., excess relative to the equilibrium number density of Na I) is present over the entire range of parameters considered, and increases with T eff and luminosity. Na I lines are stronger than in the LTE case, so that non-LTE corrections to the sodium abundance, ΔNLTE, are negative. Eight Na I lines commonly employed in abundance analyses are used to construct the dependences of the non-LTE corrections on T eff, logg, and metallicity. The non-LTE corrections are small only for the Na I λλ615.4, 616.0 nm lines in main-sequence stars: |ΔNLTE| ≤0.08 dex. In all other cases, ΔNLTE depends strongly on T eff and logg, and a non-LTE treatment must be applied if the sodium abundance is to be determined with an accuracy no worse than 0.1 dex. The profiles of solar Na I lines are analyzed in order to empirically refine two types of atomic parameters required for the subsequent analysis of the stellar spectra. In the solar atmosphere, inelastic collisions with hydrogen atoms influence the statistical equilibrium of Na I only weakly, and the classical Unsold formula underestimates the van der Waals constant C 6. The empirical correction ΔlogC 6 is from 0.6 to 2 for various Na I lines. The sodium abundance in the solar atmosphere is determined based on line-profile analyses, yielding different results depending on whether the model atmospheres of Kurucz (logɛNa=6.20±0.02) or Holweger and Muller (logɛNa=6.28±0.03) are applied.

Non-LTE effects on the strength of the Lyman edge in quasar accretion disks

We have calculated UV/EUV (300 A which is less than or equal to lambda which is less than or equal to 1500 A) continuous energy distributions of accretion disks in the centers of active galactic nuclei (AGNs) for disk luminosities in the range 0.1 L(sub Edd) less than or equal to L(sub acc) less than 1.0 L(sub Edd) and central masses ranging from 10(exp 8) solar mass to 10(exp 9) solar mass. The vertical gas pressure structure of the disk and the disk height are obtained analytically; the temperature stratification and the resulting continuum radiation fields are calculated numerically. We have included non-Local Thermodynamic Equilibrium (LTE) effects of both the ionization equilibrium and the level populations of hydrogen and helium. We show that these non-LTE effects reduce the strength of the Lyman edge when comapred to the LTE case. In non-LTE we find that the edge can be weakly in emission or absorption for disks seen face-on, depending on the disk parameters.

Spectral Analysis of the Wolf-Rayet Star HD 50896

The helium spectrum of the WN5 star HD 50896 (EZ Canis Majoris, WR6) is studied. Our aim is to establish a technique which allows the determination of the parameters of a Wolf-Rayet star from a systematic analysis of its spectral lines. Since the method of “iteration with approximate Lambda operators” became available for application to expanding atmospheres (Hamann, 1986, 1987), we are now able to compare observed spectra to realistic model calculations (Hamann and Schmutz, 1987; Wessolowski et al., 1987).We consider the non-LTE spectral formation in a spherically expanding atmosphere. The velocity field v(r) is specified in its supersonic part by the usual analytical law with the parameters v∞ (final velocity) and the exponent ß=1. The temperature structure is derived from the assumption of radiative equilibrium, but only approximately evaluated for the grey LTE case. The atmosphere is assumed to consist of pure helium. The model atom has a total of 28 energy levels, among these 17 levels of He I. The line radiation transfer is treated in the “comoving frame”.

The effect of intermediate-scale motions on line formation

The problem of LTE and non-LTE line formation in the presence of nonthermal velocity fields with geometric scales between the microscopic and macroscopic limits is investigated in the cases of periodic sinusoidal and sawtooth waves. For a fixed source function (the LTE case), it is shown that time-averaged line profiles progress smoothly from the microscopic to the macroscopic limits as the geometric scale of the motions increases, that the sinusoidal motions produce symmetric time-averaged profiles, and that the sawtooth motions cause a redshift. In several idealized non-LTE cases, it is found that intermediate-scale velocity fields can significantly increase the surface source functions and line-core intensities. Calculations are made for a two-level atom in an isothermal atmosphere for a range of velocity scales and non-LTE coupling parameters and also for a two-level atom and a four-level representation of Na I line formation in the Harvard-Smithsonian Reference Atmosphere (1971) solar model. It is found that intermediate-scale velocity fields in the solar atmosphere could explain the central intensities of the Na I D lines and other strong absorption lines without invoking previously suggested high electron densities.

Non-Lte Model Atmospheres. I. Radiative Equilibrium Models with - Alpha

view Abstract Citations (45) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Non-Lte Model Atmospheres. I. Radiative Equilibrium Models with - Alpha Auer, L. H. ; Mihalas, Dimitri Abstract We present models of stellar atmospheres of pure hydrogen in hydrostatic, radiative, and statistical equilibrium, including for the first time Lyman-a as well as continua. Only by the direct inclusion of Ly-a may we properly evaluate the effect of this strong line on the structure of the atmosphere. A new temperature-correction scheme was used. It is of the constraint type, is capable of handling very large opacity variations, and guarantees vanishingly small flux derivatives. The model atom assumed the upper fourteen levels in LTE, but permitted non-LTE deviations in the lower two levels. This model was suffi- cient to show that: (a) non-LTE effects from the continua cause a temperature rise at the surface; (b) this rise is partially offset by the inclusion of Ly-a, which causes a temperature drop, the non-LTE drop being very much smaller than the LTE; (c) Ly-a is so optically thick that it does not affect the formation of even the Lyman continuum; and (d) there is essentially no back-warming due to Ly-a in either the LTE case or the non-LTE case Publication: The Astrophysical Journal Pub Date: April 1969 DOI: 10.1086/149955 Bibcode: 1969ApJ...156..157A full text sources ADS | Related Materials (6) Part 2: 1969ApJ...156..681A Part 3: 1969ApJ...158..641A Part 4: 1970ApJ...160..233A Part 5: 1970ApJ...160.1161M Part 6: 1970ApJ...161.1129M Part 7: 1972ApJS...24..193A