Local Equilibrium Research Articles

Steady state regimes in lid driven cavity flows of magnetic fluids in the presence of an external magnetic field

In this work, we study the flow of magnetic fluids in a square top lid driven cavity in the presence of an applied magnetic field. The magnetic field is generated by a steady electric current flowing through a wire placed underneath the cavity. The magnetization of the magnetic fluid is described by an evolution equation that combines magnetization relaxation, advection and interaction with the flow via the vorticity. The governing equations are solved via a vorticity-streamfunction formulation implemented in a finite difference scheme. The main governing physical parameters of the examined cavity flow are the Reynolds number, ranging from 50 to 500, the magnetic pressure coefficient, which measures the relative importance between magnetic and inertial forces, ranging from 0 to 1000, and Péclet number which is O(1) and measures the ratio between the magnetization relaxation time and the flow time scale. We have examined the different mechanisms which cause changes in the local fluid magnetization, i.e., flow vorticity and advection. In particular, we examine how vorticity of the flow intensifies deviations of the magnetization of the fluid with respect to the local equilibrium of magnetization. In addition, we identify a complex topological structure of the flow inside the cavity characterized by the magnetic effects that dominate the generation of secondary structures of vorticity induced by the effect of field gradient, orientation and a non-uniformity in the fluid magnetization inside the cavity.

A level set approach to modelling diffusional phase transformations under finite strains with application to the formation of [formula omitted]

This paper presents a sharp interface formulation for modelling diffusional phase transformations. Grain boundary motion is, in accordance with diffusional phase transformation kinetics, determined by the amount of flux towards the interface and is formulated in a level set framework. This approach enables a computational efficiency that can be expected to be higher than what can be achieved with conventional phase field methods. Compatibility of the interfaces is obtained through an interface reconstruction process, in which the locations of triple junction points are also determined. To ensure local equilibrium and a continuous chemical potential across the interfaces, the chemical composition is prescribed at the phase interfaces. The presented model is used to study the growth of the intermetallic compound (IMC) Cu6Sn5 for a system with Sn electroplated on a Cu substrate. A finite strain formulation is incorporated into the model to investigate the effects of the volume change resulting from the IMC formation. In this formulation, the Cu and Sn phases are allowed to deform plastically. The numerical simulations demonstrate IMC growth rates in agreement with experimental measurements. Moreover, the IMC evolves into a scallop-like morphology, consistent with experimental observations.

Disc novae: thermodynamics of gas-assisted binary black hole formation in AGN discs

ABSTRACT We investigate the thermodynamics of close encounters between stellar mass black holes (BHs) in the gaseous discs of active galactic nuclei (AGNs), during which binary black holes (BBHs) may form. We consider a suite of 2D viscous hydrodynamical simulations within a shearing box prescription using the Eulerian grid code athena++. We study formation scenarios where the fluid is either an isothermal gas or an adiabatic mixture of gas and radiation in local thermal equilibrium. We include the effects of viscous and shock heating, as well as optically thick cooling. We co-evolve the embedded BHs with the gas, keeping track of the energetic dissipation and torquing of the BBH by gas and inertial forces. We find that compared to the isothermal case, the minidiscs formed around each BH are significantly hotter and more diffuse, though BBH formation is still efficient. We observe massive blast waves arising from collisions between the radiative minidiscs during both the initial close encounter and subsequent periapsis periods for successfully bound BBHs. These ‘disc novae’ have a profound effect, depleting the BBH Hill sphere of gas and injecting energy into the surrounding medium. In analysing the thermal emission from these events, we observe periodic peaks in local luminosity associated with close encounters/periapses, with emission peaking in the optical/near-infrared (IR). In the AGN outskirts, these outbursts can reach 4 per cent of the AGN luminosity in the IR band, with flares rising over 0.5–1 yr. Collisions in different disc regions, or when treated in 3D with magnetism, may produce more prominent flares.

The Chemical Puzzle of Weak G-Band Stars: A Comprehensive Study of HD 54627, HD 105783, HD 198718, and HD 201557

Weak G-band stars (WGBs) are a unique class of objects characterized by weak CH molecular lines in the Fraunhofer G band, indicative of a deficiency in 12C. This peculiar spectral feature is often accompanied by significant enrichments in N and, occasionally, Li and Na abundances. Despite their rarity and recent discoveries of new WGB candidates, the underlying formation mechanism of these stars remains unknown. In this study, we present a comprehensive chemical analysis of four neglected WGBs: HD 54627, HD 105783, HD 198718, and HD 201557. These stars, though identified as WGBs, have been poorly studied to date. Our analysis utilizes high-resolution échelle spectra with a power resolution of R ≈ 48,000, complemented by photometric and astrometric data from the literature. Applying the local thermodynamic equilibrium (LTE) approximation we determine the chemical abundance and then we conduct posterior non-LTE (NLTE) corrections for specific chemical abundances, including Li, O, Na, and Mg. Additionally, we provide details on the projected rotational velocities ( vsini ) and conduct a thorough investigation of the kinematics and orbits of our sample, comparing them with other well-studied WGBs reported in the literature. Our findings indicate that these stars originate from the thin disk, as evidenced by the absence of alpha-element enrichment and kinematics. Notably, half of the WGBs in our sample exhibit Li-rich characteristics, and we identify no rapid rotators ( vsini> 8.0 km s−1) or infrared excess among our studied stars.

The updated BOSZ synthetic stellar spectral library

Context. The modeling of stellar spectra of flux standards observed by the Hubble and James Webb space telescopes requires a large synthetic spectral library that covers a wide atmospheric parameter range. Aims. The aim of this paper is to present and describe the calculation methods behind the updated version of the BOSZ synthetic spectral database, which was originally designed to fit the CALSPEC flux standards. These new local thermodynamic equilibrium (LTE) models incorporate both MARCS and ATLAS9 model atmospheres, updated continuous opacities, and 23 new molecular line lists. Methods. The new grid was calculated with Synspec using the LTE approximation and covers metallicities [M/H] from −2.5 to 0.75 dex, [α/M] from −0.25 to 0.5 dex, and [C/M] from −0.75 to 0.5 dex, providing spectra for 336 unique compositions. Calculations for stars between 2800 and 8000 K use MARCS model atmospheres, and ATLAS9 is used between 7500 and 16 000 K. Results. The new BOSZ grid includes 628 620 synthetic spectra from 50 nm to 32 µm with models for 495 Teff−log 𝑔 parameter pairs per composition and per microturbulent velocity. Each spectrum has eight different resolutions spanning a range from R = 500 to 50 000 as well as the original resolution of the synthesis. The microturbulent velocities are 0, 1, 2, and 4 km s−1. Conclusions. The new BOSZ grid extends the temperature range to cooler temperatures compared to the original grid because the updated molecular line lists make modeling possible for cooler stars. A publicly available and consistently calculated database of model spectra is important for many astrophysical analyses, for example spectroscopic surveys and the determination of stellar elemental compositions.

Interstellar Nitrogen Isotope Ratios: Measurements on Tracers of C14N and C15N

The nitrogen isotope ratio 14N/15N is a powerful tool to trace Galactic stellar nucleosynthesis and constrain Galactic chemical evolution. Previous observations have found lower 14N/15N ratios in the Galactic center and higher values in the Galactic disk. This is consistent with the inside-out formation scenario of our Milky Way. However, previous studies mostly utilized double isotope ratios also including 12C/13C, which introduces additional uncertainties. Here we present observations of C14N and its rare isotopologue, C15N, toward a sample of star-forming regions measured by the IRAM 30 m and/or the ARO 12 m telescope at λ ∼ 3 mm wavelength. For those 35 sources detected in both isotopologues, physical parameters are determined. Furthermore, we have obtained nitrogen isotope ratios using the strongest hyperfine components of CN and C15N. For those sources showing small deviations from local thermodynamical equilibrium and/or self-absorption, the weakest hyperfine component, likely free of the latter effect, was used to obtain reliable 14N/15N values. Our measured 14N/15N isotope ratios from C14N and C15N measurements are compatible with those from our earlier measurements of NH3 and 15NH3 (Paper I), i.e., increasing ratios to a Galactocentric distance of ∼9 kpc. The unweighted second-order polynomial fit yields C14NC15N=(−4.85±1.89)kpc−2×RGC2+(82.11±31.93)kpc−1×RGC−(28.12±126.62) . Toward the outer galaxy, the isotope ratio tends to decrease, supporting an earlier finding by H13CN/HC15N. Galactic chemical evolution models are consistent with our measurements of the 14N/15N isotope ratio, i.e., a rising trend from the Galactic center region to approximately 9 kpc, followed by a decreasing trend with increasing R GC toward the outer Galaxy.

3D non-local thermodynamic equilibrium magnesium abundances reveal a distinct halo population

Magnesium is one of the most important elements in stellar physics as an electron donor; in Galactic archaeology, magnesium serves to distinguish different stellar populations. However, previous studies of Mg I and Mg II lines in metal-poor benchmark stars indicate that magnesium abundances inferred from one-dimensional (1D), hydrostatic models of stellar atmospheres, both with and without the local thermodynamic equilibrium (LTE) approximation, can be problematic. Here, we present three-dimensional (3D) non-LTE calculations for magnesium in FG-type dwarfs and provide corrections for 1D-LTE abundances. 3D non-LTE corrections reduce the ionisation imbalances in the benchmark metal-poor stars HD84937 and HD140283 from −0.16 dex and −0.27 dex in 1D LTE to just −0.02 dex and −0.09 dex, respectively. We applied our abundance corrections to 1D LTE literature results for stars in the thin disc, thick disc, α-rich halo, and α-poor halo. We observed that 3D non-LTE results had a richer substructure in [Mg/Fe] − [Fe/H] in the α-poor halo, revealing two sub-populations at the metal-rich end. These two sub-populations also differ in kinematics, supporting the astro-physical origin of the separation. While the more magnesium-poor sub-population is likely to be debris from a massive accreted galaxy, Gaia-Enceladus, the other sub-population may be related to a previously identified group of stars, called Eos. The additional separation in [Mg/Fe] suggests that previous Mg abundance measurements may have been imprecise due to the 1D and LTE approximations, highlighting the importance of 3D non-LTE modelling.

Revisiting the statistical equilibrium of H- in stellar atmospheres

The negative hydrogen ion is, almost without exception, treated in local thermodynamic equilibrium (LTE) in the modelling of F, G, and K stars, where it is the dominant opacity source in the visual spectral region. This assumption rests in practice on a study from the 1960s. Since that work, knowledge of relevant atomic processes and theoretical calculations of stellar atmospheres and their spectra have advanced significantly, but this question has not been reexamined. We present calculations based on a slightly modified analytical model that includes H and together with modern atomic data and a grid of 1D LTE theoretical stellar atmosphere models with stellar parameters ranging from T$_ eff = 4000$ to 7000 K, $ g = 1$ to 5 cm/s$^2$, and Fe/H $=-3$ to 0. We find direct non-LTE effects on populations in spectrum-forming regions, continua, and spectral lines of about 1--2<!PCT!> in stars with higher T$_ eff $ and/or lower $ g$. Effects in models for solar parameters are smaller by a factor of 10, about 0.1--0.2<!PCT!>, and are practically absent in models with lower T$_ eff $ and/or higher $ g$. These departures from LTE found in our calculations originate from the radiative recombination of electrons with hydrogen to form exceeding photodetachment, that is, overrecombination. Modern atomic data are not a source of significant differences compared to the previous work, although detailed data for processes on resolved with vibrational and rotational states provide a more complete and complex picture of the role of in the equilibrium of In the context of modern studies of stellar spectra at the percent level, our results suggest that this question requires further attention, including a more extensive reaction network, and indirect effects due to non-LTE electron populations.

Spectral analysis of three hot subdwarf stars: EC 11481-2303, Feige 110, and PG 0909+276

Context. For the precise spectral analysis of hot stars, advanced stellar-atmosphere models that consider deviations from the local thermodynamic equilibrium are mandatory. This requires accurate atomic data to calculate all transition rates and occupation numbers for atomic levels in the considered model atoms, not only for a few prominent lines exhibited in an observation. The critical evaluation of atomic data is a challenge because it requires precise laboratory measurements. Ultraviolet spectroscopy of hot stars with high resolving power provide such “laboratory” spectra. Aims. We compare observed, isolated lines of the iron group (here calcium to nickel) with our synthetic line profiles to judge the accuracy of the respective oscillator strengths. This will verify them or yield individual correction values to improve the spectral analysis, that is the determination of, for example, effective temperature (Teff) and abundances. Methods. To minimize the error propagation from uncertainties in Teff, surface gravity (𝑔), and abundance determination, we start with a precise reanalysis of three hot subdwarf stars, namely EC 11481-2303, Feige 110, and PG0909+276. Then, we measure the abundances of the iron-group elements individually. Based on identified, isolated lines of these elements, we compare observation and models to measure their deviation in strength (equivalent width). Results. For EC 11481–2303 and Feige 110, we confirmed the previously determined Teff and log 𝑔 values within their error limits. For all three stars, we fine-tuned all metal abundances to achieve the best reproduction of the observation. For more than 450 isolated absorption lines of the iron group, we compared modeled and observed line strengths. Considering the uncertainty of the analysis and evaluation procedure, an upper limit for the uncertainty of the underlying atomic data was established. Conclusions. We selected strong, reliable isolated absorption lines, which we recommend to use as reference lines for abundance determinations in related objects.

Application of hydrostatic local thermodynamic equilibrium atmosphere models to interpretations of supersoft X-ray source spectra

Supersoft X-ray sources (SSSs) are accreting white dwarfs (WDs) with stable or recurrent thermonuclear burning on their surfaces. High-resolution X-ray spectra of such objects are rather complex, often consist of several components, and are difficult to interpret accurately. The main emission source is the hot surface of the WD and the emergent radiation can potentially be described by hot WD model atmospheres. We present a new set of such model atmosphere spectra computed in the effective temperature range from 100 kK to 1000 kK, for eight values of surface gravity and three different chemical compositions. These compositions correspond to the solar one as well as to the Large and Small Magellanic Clouds, with decreased heavy element abundances, at one-half and one-tenth of the solar value. The presented model grid covers a broad range of physical parameters and, thus, it can be applied to a wide range of objects. It is also publicly available in XSPEC format. As an illustration, we applied it here for the interpretation of Chandra and XMM grating spectra of two classical SSSs, namely, CAL 83 (RX J0543.5–6823) and RX J0513.9–6951. The obtained effective temperatures and surface gravities of Teff ≈ 560 kK, log g ≈ 8.6–8.7, and Teff ≈ 630 kK, log g ≈ 8.5–8.6, respectively, are in a good agreement with previous estimations for both sources. The derived WD mass estimations are within 1.1–1.4 M⊙ for CAL 83 and 1.15–1.4 M⊙ for RX J0513.9–6951. The mass of the WD in CAL 83 is consistent with the mass predicted from the respective model of recurrent thermonuclear burning.

First detection of the J−1 → (J − 1)0 − E methanol maser transitions at J = 7 and 10

Context. Class I methanol masers provide sensitive information about the shocked environment around star-forming regions. Among the brightest Class I methanol masers, we have those in the J−1 → (J − 1)0 − E line series, currently reported for the J = 4 − 9 transitions, with the only exception being the J = 7 one at 181.295 GHz, and never expanded to higher J transitions. Aims. We aim to search for population inversion in the 7−1 → 60 − E and 10−1 → 90 − E methanol transition lines at 181.295 and 326.961 GHz, respectively, and also extend the number of known low-mass star-forming sources harboring Class I methanol masers. Methods. We employed the Atacama Pathfinder Experiment (APEX) 12 m telescope to survey low-mass Galactic sources, focusing on methanol emission lines. We built rotation diagrams for all sources with detected J = 7 methanol line transitions, while employing radiative transfer modeling (both in and out of local thermodynamic equilibrium) to characterize methanol excitation conditions in detail for one specific source with detected masers. Results. We detected the 7−1 → 60 − E and 10−1 → 90 − E methanol transitions in 6 out of 19 sources. Among them, we firmly determined the 10−1 → 90 − E maser nature in CARMA 7, L1641N, NGC 2024, and Serpens FIRS, and we show evidence for the presence of inverted population emission in the 7−1 → 60 − E line toward CARMA 7 and L1641N. This represents the first report of methanol maser emission in these particular transitions. Our study supports previous works indicating that conditions for Class I methanol maser emission are satisfied in low-mass star-forming regions and expands the range of detectable frequencies toward higher values.

Impact of the numerical conversion to optical depth on the transfer of polarized radiation

Making the conversion from the geometrical spatial scale to the optical depth spatial scale is useful in obtaining numerical solutions for the radiative transfer equation. This is because it allows for the use of exponential integrators, while enforcing numerical stability. Such a conversion involves the integration of the total opacity of the medium along the considered ray path. This is usually approximated by applying a piecewise quadrature in each spatial cell of the discretized medium. However, a rigorous analysis of this numerical step is lacking. This work is aimed at clearly assessing the performance of different optical depth conversion schemes with respect to the solution of the radiative transfer problem for polarized radiation, out of the local thermodynamic equilibrium. We analyzed different optical depth conversion schemes and their combinations with common formal solvers, both in terms of the rate of convergence as a function of the number of spatial points and the accuracy of the emergent Stokes profiles. The analysis was performed in a 1D semi-empirical model of the solar atmosphere, both in the absence and in the presence of a magnetic field. We solved the transfer problem of polarized radiation in different settings: the continuum, the photospheric Sr i AA modeled under the assumption of complete frequency redistribution, and the chromospheric Ca i AA taking the partial frequency redistribution effects into account during the modeling. High-order conversion schemes generally outperform low-order methods when a sufficiently high number of spatial grid points is considered. In the synthesis of the emergent Stokes profiles, the convergence rate, as a function of the number of spatial points, is impacted by both the conversion scheme and formal solver. The use of low-order conversion schemes significantly reduces the accuracy of high-order formal solvers. In practical applications, the use of low-order optical depth conversion schemes introduces large numerical errors in the formal solution. To fully exploit high-order formal solvers and obtain accurate synthetic emergent Stokes profiles, it is necessary to use high-order optical depth conversion schemes.

Going beyond an old shockwave conjecture for improving upon Navier-Stokes.

Nonequilibrium molecular dynamics (NEMD) computer simulations of steady shockwaves in dense fluids and rarefied gases produce detailed shockwave profiles of mechanical and thermal properties. The Boltzmann equation, under the assumption of local thermodynamic equilibrium (LTE), leads to the first-order (linear) continuum theory of hydrodynamic flow: Navier-Stokes-Fourier (NSF). (Expansion of the LTE Boltzmann equationin higher powers of gradients yields so-called Burnett second-order terms, etc.) NEMD simulations of strong shockwaves with high gradients are not well modeled by NSF theory. Many years ago, a conjecture for going "beyond Navier-Stokes" was proposed, applying the empirical observation of anisotropic thermal enhancement in the shock front to the temperature dependence of the NSF transport coefficients, whose dissipation determines the slope at the center of the shock profile: for weak shocks, the actual coefficients in NEMD simulations appear to be smaller than in NSF predictions, leading to steeper gradients being observed, while for strong shocks, the NEMD coefficients appear to be larger, leading to less steep shock rises than predicted by NSF calculations. In this paper, we show that adding significant Burnett nonlinearity into an LTE continuum theory reproduces the early shock rise and slope of NEMD profiles, for both weak and strong shocks in dense fluids, as well as strong shockwaves in the ideal gas. Moreover, we show that "Holian's conjecture" incorporates significant Burnett nonlinearity, but like all the other LTE continuum theories, it fails to describe the slow NEMD return to equilibrium beyond the shock front. We show that Maxwell relaxation has to be applied to the hydrodynamic variables themselves (rather than attempting indirect relaxation of their gradients) in order to more accurately model the entire shockwave profile. Non-LTE Maxwell relaxation is the only way to bring the entire profile into agreement with NEMD, most noticeably for strong shockwaves.

Abundances of neutron-capture elements in selected solar-type stars

The primary objective of this study is to accurately determine the abundances of Cu, Sr, Y, Zr, Ba, La, and Ce in selected solar-type stars. This will allow us to establish observational abundance--metallicity and abundance--age relations and to explore the reasons for the excess of Ba compared to other $s$-elements in younger solar-type stars. The chosen $s$-process elements are critical diagnostics for understanding the chemical evolution of our Galaxy. We analysed HARPS spectra with a high resolution ($R$ = 115\,000) and high signal-to-noise ratio (close to 100) of main-sequence solar-type FGK stars with metallicities from $-0.15$ to +0.35 dex and ages from 2 to 14 Gyr using one-dimensional (1D) local thermodynamic equilibrium (LTE) synthesis and MARCS atmospheric models. In the procedure of fitting synthetic to observed line profiles, the free parameters included abundance and microturbulent and macroturbulent velocity. The macroturbulent velocity can substantially compensate for non-local thermodynamic equilibrium (NLTE) effects in the line core. The resulting elemental abundance X/H increases with metallicity and age for solar-type stars. The ratio of the abundances of $s$-process elements s/Fe increases with decreasing metallicity and age, while the Cu/Fe ratio increases with both metallicity and age. These observed trends agree well with published observational data and with predictions from Galactic chemical evolution (GCE) models. A small Ba/Fe enhancement of 0.08 ± 0.08 dex has been detected in seven younger stars with an average age of $2.8 0.6$ Gyr. Compared to the abundances of other $s$-process elements Ba/Fe is 0.07 and 0.08 dex higher than La and Ce on average, respectively. Furthermore, we find that the Ba/Fe ratio increases with increasing chromospheric activity. The average Ba/Fe for the three most active stars is $0.15 0.10$ dex higher than that of the other stars. Chromospheric activity, characterised by stronger magnetic fields found in active regions such as pores, spots, plages, and networks, can significantly alter the physical conditions in the formation layers of the Ba lines. Our primary conclusion is that to account for the observed excess of Ba/Fe abundance in younger stars, it is essential to use more complex atmospheric models that incorporate magnetic structures.

Emergence hour-by-hour of features in the kilonova AT2017gfo

The spectral features in the optical/near-infrared counterparts of neutron star mergers (kilonovae, KNe) evolve dramatically on hourly timescales. To examine the spectral evolution, we compiled a temporal series that was complete at all observed epochs from 0.5 to 9.4\,days of the best optical/near-infrared (NIR) spectra of the gravitational-wave detected kilonova AT2017gfo. Using our analysis of this spectral series, we show that the emergence times of spectral features place strong constraints on line identifications and ejecta properties, while their subsequent evolution probes the structure of the ejecta. We find that the most prominent spectral feature, the 1\ P Cygni line, appears suddenly, with the earliest detection at 1.17\,days. We find evidence in this earliest feature for the fastest yet discovered kilonova ejecta component at 0.40--0.45$c$. Across the observed epochs and wavelengths, the velocities of the line-forming regions span nearly an order of magnitude, down to as low as 0.04--0.07$c$. The time of emergence closely follows the predictions for because combines rapidly under local thermal equilibrium (LTE) conditions. The transition time between the doubly and singly ionised states provides the first direct measurement of the ionisation temperature. This temperature is highly consistent with the temperature of the emitted blackbody radiation field at a level of a few percent. Furthermore, we find the KN to be isotropic in temperature, that is, the polar and equatorial ejecta differ by less than a few hundred Kelvin or \( 5\)<!PCT!>, in the first few days post-merger based on measurements of the reverberation time-delay effect. This suggests that a model with very simple assumptions, with single-temperature LTE conditions, reproduces the early kilonova properties surprisingly well.

MINDS: The DR Tau disk. II. Probing the hot and cold H_2O reservoirs in the JWST-MIRI spectrum

The Medium Resolution Spectrometer (MRS) of the Mid-InfraRed Instrument (MIRI) on the James Webb Space Telescope (JWST) gives insights into the chemical richness and complexity of the inner regions of planet-forming disks. Several disks that are compact in the millimetre dust emission have been found by Spitzer to be particularly bright in H_2O which is thought to be caused by the inward drift of icy pebbles. Here, we analyse the H_2O -rich spectrum of the compact disk DR Tau using high-quality JWST-MIRI observations. We infer the H_2O column densities (in cm$^ $) using methods presented in previous works, as well as introducing a new method to fully characterise the pure rotational spectrum. We aim to further characterise the abundances of H_2O in the inner regions of this disk and its abundance relative to CO . We also search for emission of other molecular species, such as CH_4 NH_3 CS H_2 SO_2 and larger hydrocarbons; commonly detected species, such as CO CO_2 HCN and C_2H_2 have been investigated in our previous paper. We first use 0D local thermodynamic equilibrium (LTE) slab models to investigate the excitation properties observed in different wavelength regions across the entire spectrum, probing both the ro-vibrational and rotational transitions. To further analyse the pure rotational spectrum (geq 10 $ mu $m), we use the spectrum of a large, structured disk (CI Tau) as a template to search for differences with our compact disk. Finally, we fit multiple components to characterise the radial (and vertical) temperature gradient(s) present in the spectrum of DR Tau. The 0D slab models indicate a radial gradient in the disk, as the excitation temperature (emitting radius) decreases (increases) with increasing wavelength, which is confirmed by the analysis involving the large disk template. To explain the derived emitting radii, we need a larger inclination for the inner disk ($i agreeing with our previous analysis on CO . From our multi-component fit, we find that at least three temperature components ($T_1 K, $T_2 K, and $T_3 K) are required to reproduce the observed rotational spectrum of H_2O arising from the inner $R_ em au. By comparing line ratios, we derived an upper limit on the column densities (in $) for the first two components of $ (N) within sim 1.2 au. We note that the models with a pure temperature gradient provide as robust results as the more complex models, which include spatial line shielding. No robust detection of the isotopologue H_2 ^ O can be made and upper limits are provided for other molecular species. Our analysis confirms the presence of a pure radial temperature gradient present in the inner disk of DR Tau, which can be described by at least three components. This gradient scales roughly as $ R_ em $ in the emitting layers, in the inner 2 au. As the observed H_2O is mainly optically thick, a lower limit on the abundance ratio of H_2O CO sim 0.17 is derived, suggesting a potential depletion of H_2O . Similarly to previous work, we detect a cold H_2O component ($T K) originating from near the snowline, now with a multi-component analysis. Yet, we cannot conclude whether an enhancement of the H_2O reservoir is observed following radial drift. A consistent analysis of a larger sample is necessary to study the importance of drift in enhancing the H_2O abundances.

Rotational state-to-state transition rate coefficients for H2O + H2O collisions at nonequilibrium conditions

The goal is to develop a database of rate coefficients for rotational state-to-state transitions in H$_ $O + H$_ $O collisions that is suitable for the modeling of energy transfer in nonequilibrium conditions, in which the distribution of rotational states of H$_ $O deviates from local thermodynamic equilibrium. A two-temperature model was employed that assumed that although there is no equilibrium between all possible degrees of freedom in the system, the translational and rotational degrees of freedom can be expected to achieve their own equilibria independently, and that they can be approximately characterized by Boltzmann distributions at two different temperatures, $T_ kin $ and $T_ rot Upon introducing our new parameterization of the collisional rates, taking into account their dependence on both $T_ kin $ and $T_ rot $, we find a change of up to 20<!PCT!> in the H$_ $O rotational level populations for both ortho and para-H$_ $O for the part of the cometary coma where the nonequilibrium regime occurs.

Comprehensive accuracy analysis for large closed-loop deployable structures based on matrix structure analysis and linear-complementarity-based contact analysis of spatial joint clearances

The surface accuracy of the deployable structure is crucial in determining the electromagnetic performance of the large satellite antenna. This paper proposes a comprehensive accuracy analysis framework for deployable structures considering clearances of spatial joints, geometric deviations, elastic deformations, external loads, and preloads, all of which can affect surface accuracy during the assembly process. Surface accuracy is calculated by combining the global equilibrium analysis of the deployable structure with the local equilibrium analysis of clearance-affected joints. First, a global elastostatic equilibrium analysis of the deployable structure is performed based on a unified mathematical formulation that describes the elasticity of beams and joints. Then, the local equilibrium analysis for the clearance-affected joints is transformed into a quadratic optimization problem through a linear-complementarity-based method. This method avoids the necessity for a combinatorial search for several traditional discontinuous contact configurations. Considering both global and local equilibrium in iterative analysis, the surface accuracy of the antenna is calculated. This integration avoids prior artificial assumptions about contact configurations of the joints. Finally, the proposed method is validated by comparing it with simulations and experimental results.

Low-temperature phase stability in calc-alkaline granitic systems and significance for cold granites

Granite formation and evolution are influenced by various physical and chemical processes in magmatic systems, resulting in diverse textures and compositions. While the generation of granitic rock through dehydration melting of hydrous minerals, which requires higher temperatures, is widely accepted, the formation and evolution of cold granite remains a topic of considerable debate. Our experiments aim to understand how small changes in granitic magma composition influence late-stage crystallization, providing insights into the chemical and textural evolution of granitic rocks and determining the significance of these conditions in shaping the diversity observed in nature. We conducted crystallization experiments at 1 and 2 kbar, between 680 and 815 °C, using two granitic compositions: a natural I-type granitoid (MA) and a slightly more mafic, synthetic analogue (FC). In these relatively low-pressure and low-temperature experiments, orthopyroxene remains stable at 1 kbar regardless of the starting material. At 2 kbar, its stability is limited to the more mafic sample FC when containing 3.7 wt% water. Hornblende only crystallizes in the more mafic rock FC at 2 kbar across all temperatures tested when water concentration exceeds 4 wt%. Plagioclase spans a broad temperature range (700–815 °C) at both 1 and 2 kbar in the FC material, whereas in the MA material at 2 kbar, it appears only at temperatures ≤725 °C. At 2 kbar few crystals were observed in the MA run at 750 °C, indicating that the liquidus temperature was nearly reached, contrasting with the FC starting material. Additionally, temperature cycling proved more efficient in promoting crystal growth in FC samples. Under low-temperature conditions, only local equilibrium was achieved, highlighting the significant role of late-stage crystallization processes and kinetic limitations in shaping the diversity observed in cold granites. Our experiments demonstrate that even small changes in CaO and FeO content can markedly alter the solidus/liquidus temperature of melts, significantly influence phase stability, melt production, and texture in granitic systems. This study surmises the need to further pursue systematic investigations of the influence of major elements on crystallization sequences in granitic systems, and we compare our findings to previous observations made on the Gentio metagranitoids of the Mineiro belt, Brazil.

Microscopic state equation for oscillator chains

Systems allowing anomalous transport of mass, momentum energy, etc., such as low-dimensional particles systems or highly confining media, are hard to characterize thermodynamically. Indeed, local thermodynamic equilibrium may not be established and their behaviour often strongly depends on many microscopic parameters, including the symmetry of the interaction potentials. Thermodynamic state equations, on the other hand, involve a small set of observables, which are obtained averaging in time and over the large number of particles that populate mesoscopic cells in which local equilibrium can be realized. In this work we show that a linear relation discovered earlier, that connects the average distance between pairs of consecutive particles with their kinetic energy, applies to quite a large set of 1-dimensional particle systems known to produce anomalous transport. This relation is microscopic in nature, since the quantities involved are neither averaged over many particles, neither over very large times. Nevertheless, its robustness is under variations of the external parameters, and the limited set of quantities it involves qualify it as a state equation, analogously to thermodynamic relations. We provide conditions for which the relation can be violated within a limited range of parameters values, and we find that it can be extended to two-dimensional networks of coupled oscillators. The validity of this relation further shows that the states of aggregation of matter in low-dimensional systems are often different from standard macroscopic ones.