Local Thermodynamic Equilibrium Value Research Articles

Carbon monoxide cooling in radiative transfer modelling of supernovae

ABSTRACT Carbon monoxide (CO) emission has been observed in a number of core-collapse supernovae (SNe) and is known to be an important coolant at late times. We have implemented a chemical reaction network in the radiative-transfer code cmfgen to investigate the formation of CO and its impact on SN ejecta. We calculate two 1D SN models with and without CO: a BSG explosion model at one nebular epoch and a full time-sequence (50–300 d) for a red supergiant explosion. In both models, CO forms at nebular times in the dense, inner regions at velocities <2000 km s$^{-1}$ where line emission from CO can dominate the cooling and reduce the local temperature by as much as a factor of 2, weakening emission lines and causing the optical light curve to fade faster. That energy is instead emitted in CO bands, primarily the fundamental band at $\sim 4.5 \mathrm{\mu m}$, which accounts for up to 20 per cent of the total luminosity at late times. However, the non-monotonic nature of the CO cooling function can cause numerical difficulties and introduce multiple temperature solutions. This issue is compounded by the sensitivity of the CO abundance to a few reaction rates, many of which have large uncertainties or disparate values across literature sources. Our results also suggest that, in many SNe, CO-level populations are far from their local thermodynamic equilibrium values. Unfortunately, accurate collisional data, necessary to compute non-local thermodynamic equilibrium populations, are limited to a few transitions.

Protonated acetylene in the z = 0.89 molecular absorber toward PKS 1830-211

We report the first interstellar identification of protonated acetylene, C2H3+, a fundamental hydrocarbon, in the z = 0.89 molecular absorber toward the gravitationally lensed quasar PKS 1830–211. The molecular species is identified from clear absorption features corresponding to the 212–101 (rest frequency 494.034 GHz) and 111–000 (431.316 GHz) ground-state transitions of ortho and para forms of C2H3+, respectively, in ALMA spectra toward the southwestern image of PKS 1830-211, where numerous molecules, including other hydrocarbons, have already been detected. From the simple assumption of local thermodynamic equilibrium (LTE) with cosmic microwave background photons and an ortho-to-para ratio of three, we estimate a total C2H3+ column density of 2 × 1012 cm−2 and an abundance of 10−10 compared to H2. However, formation pumping could affect the population of metastable states, yielding a C2H3+ column density higher than the LTE value by a factor of a few. We explore possible routes to the formation of C2H3+, mainly connected to acetylene and methane, and find that the methane route is more likely in PDR environment. As one of the initial hydrocarbon building blocks, C2H3+ is thought to play an important role in astrochemistry, in particular in the formation of more complex organic molecules.

NLTE effects on kilonova expansion opacities

ABSTRACT A binary neutron star merger produces a rapidly evolving transient known as a kilonova (KN), which peaks a few days after merger. Modelling of KNe has often been approached assuming local thermodynamic equilibrium (LTE) conditions in the ejecta. We present the first analysis of non-local thermodynamic equilibrium (NLTE) level populations, using the spectral synthesis code sumo, and compare these to LTE values. We investigate the importance of the radiation field by conducting NLTE excitation calculations with and without radiative transfer. Level populations, in particular higher lying ones, start to show deviations from LTE several days after merger. Excitation is lower in NLTE for the majority of ions and states, and this tends to give lower expansion opacities. While the difference is small for the first few days, it grows to factors 2–10 after this. Our results are important both for demonstrating validity of LTE expansion opacities for an initial phase (less than a week), while highlighting the need for NLTE modelling during later phases. Considering also NLTE ionization, our results indicate that NLTE can give both higher or lower opacities, depending on composition and wavelength, sometimes by orders of magnitudes.

First extragalactic detection of a phosphorus-bearing molecule with ALCHEMI: Phosphorus nitride (PN)

Context. Phosphorus (P) is a crucial element for life given its central role in several biomolecules. P-bearing molecules have been discovered in different regions of the Milky Way, but not yet towards an extragalactic environment. Aims. We searched for P-bearing molecules outside the Milky Way towards the nearby starburst Galaxy NGC 253. Methods. Using observations from the ALMA Comprehensive High-resolution Extragalactic Molecular Inventory (ALCHEMI) project, we used the MAdrid Data CUBe Analysis package to model the emission of P-bearing molecules assuming local thermodynamic equilibrium (LTE) conditions. We also performed a non-LTE analysis using SpectralRadex. Results. We report the detection of a P-bearing molecule, phosphorus nitride (PN), for the first time in an extragalactic environment, towards two giant molecular clouds (GMCs) of NGC 253. The LTE analysis yields total PN beam-averaged column densities N = (1.20 ± 0.09) × 1013 cm−2 and N = (6.5 ± 1.6) × 1012 cm−2, which translate into abundances with respect to H2 of χ = (8.0 ± 1.0) × 10−12 and χ = (4.4 ± 1.2) × 10−12. We derived a low excitation temperature of Tex = (4.4 ± 1.3) K towards the GMC with the brightest PN emission, which indicates that PN is sub-thermally excited. The non-LTE analysis results in column densities consistent with the LTE values. We also searched for other P-bearing molecules (PO, PH3, CP, and CCP), and upper limits were derived. The derived PO/PN ratios are < 1.3 and < 1.7. The abundance ratio between PN and the shock-tracer SiO derived towards NGC 253 follows the same trend previously found towards Galactic sources. Conclusions. Comparison of the observations with chemical models indicates that the derived molecular abundances of PN in NGC 253 can be explained by shock-driven chemistry followed by cosmic-ray-driven photochemistry.

New detections of (sub)millimeter hydrogen radio recombination lines towards high-mass star-forming clumps

Aims. Previous radio recombination line (RRL) observations of dust clumps identified in the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) have led to the detection of a large number of RRLs in the 3 mm range. Here, we aim to study their excitation with shorter wavelength (sub)millimeter radio recombination line (submm-RRL) observations. Methods. We made observations of submm-RRLs with low principal quantum numbers (n ≤ 30) using the APEX 12 m telescope, toward 104 H II regions associated with massive dust clumps from ATLASGAL. The observations covered the H25α, H28α, and H35β transitions. Toward a small subsample the H26α, H27α, H29α, and H30α lines were observed to avoid contamination by molecular lines at adjacent frequencies. Results. We have detected submm-RRLs (signal-to-noise (S∕N)≥ 3 σ) from compact H II regions embedded within 93 clumps. The submm-RRLs are approximately a factor of two brighter than the mm-RRLs and consistent with optically thin emission in local thermodynamic equilibrium (LTE). The average ratio (0.31) of the measured H35β/H28α fluxes is close to the LTE value of 0.28. No indication of RRL maser emission has been found. The Lyman photon flux, bolometric, and submm-RRL luminosities toward the submm-RRL detected sources present significant correlations. The trends of dust temperature and the ratio of bolometric luminosity to clump mass, Lbol ∕Mclump, indicate that the H II regions are related to the most massive and luminous clumps. By estimating the production rate of ionizing photons, Q, from the submm-RRL flux, we find that the Q(H28α) measurements provide estimates of the Lyman continuum photon flux consistent with those determined from 5 GHz radio continuum emission. Six RRL sources show line profiles that are a combination of a narrow and a broad Gaussian feature. The broad features are likely associated with high-velocity ionized flows. Conclusions. We have detected submm-RRLs toward 93 ATLASGAL clumps. Six RRL sources have high-velocity RRL components likely driven by high-velocity ionized flows. Their observed properties are consistent with thermal emission that correlates well with the Lyman continuum flux of the H II regions. The sample of H II regions with mm/submm-RRL detections probes, in our Galaxy, luminous clumps (Lbol > 104 L⊙) with high Lbol∕Mclump. We also provide suitable candidates for further studies of the morphology and kinematics of embedded, compact H II regions with the Atacama Large Millimeter/submillimeter Array (ALMA).

Rotational non-LTE in HCN in the thermosphere of Titan: Implications for the radiative cooling

Context. The thermal structure of Titan’s thermosphere is determined by the balance between several heating and cooling processes. These processes must be accurately modeled to correctly interpret the available measurements and enhance our understanding of the formation and evolution of this atmosphere. One of the most important thermospheric cooling process for Titan is emission in the HCN rotational band.Aims. We aim to determine the validity of local thermodynamic equilibrium (LTE) for the HCN rotational distribution in the thermosphere of Titan and the impact of its breakdown on the HCN radiative cooling rate in the thermosphere.Methods. A general non-LTE radiative transfer code for rotational lines based on the accelerated lambda iteration (ALI) was used to calculate the excitation of HCN rotational levels in Titan’s atmosphere. These level populations were then used to calculate the associated cooling rate.Results. We show that the common assumption in the models of Titan’s thermospheric energy balance, namely the LTE distribution of rotational lines of HCN, is generally not valid above about 1100 km, or ~0.025 nbar, which will affect the derived thermospheric cooling rates. The effect of non-LTE is to reduce the cooling rate to 15% of the LTE value at around the exobase altitudes depending on the given density of HCN and collisional partners (N2 , CH4 , H2 , and electrons). Since collision state-to-state quenching rates of HCN rotational levels are poorly known, a sensitivity analysis of our results to these rates is also presented.

EXPERIMENTAL INVESTIGATION OF THE ORTHO/PARA RATIO OF NEWLY FORMED MOLECULAR HYDROGEN ON AMORPHOUS SOLID WATER

Several astronomical observations have shown that the ortho/para ratio (OPR) of H2 can differ from the expected statistical value of 3 or the local thermodynamic equilibrium (LTE) value at the gas or dust temperature. It is thus important to know the OPR of H2 newly formed on dust grain surfaces, in order to clarify the dependence of the observed OPR in space on the formation process. Using an experimental setup designed to mimic interstellar medium environments, we measured the OPR of H2 and D2 formed on the surface of porous amorphous water ice held at 10 K. We report for the first time the OPR value for newly formed D2, consistent with the expected LTE value at the high-temperature limit found by previous theoretical and experimental works on the determination of the OPR upon H2 formation on surfaces at low temperature.

Local thermodynamic equilibrium modeling of ionization of impurities in argon inductively coupled plasma

Essentially higher ionization degree of small concentrations of elements in inductively coupled plasma in comparison to the ionization of pure elements is emphasized. This conclusion is used to determine the relative dependence of the sensitivity of the inductively coupled plasma mass spectrometer on the atomic mass. The possibility of evaluation of the ionization temperature and electron density from mass spectrometric signals is proposed. Temperatures about 7000 K and 8000 K were obtained from the ionization ratio dependences on ionization potentials. Electron densities of the order of magnitude 10 15 cm − 3 , in excess to the local thermodynamic equilibrium values, follow from the application of the Saha equation to the measurement results and indicate the recombining character of the plasma in the mass spectrometer measurement region. Effects due to additional ionization from matrix were discussed. The effect is largest on minor abundant ionization state components. Matrix effect is restricted to some temperature interval, which depends on the whole matrix composition and the plasma state. The results show that the local thermodynamic equilibrium modeling, if adequately matching the sample composition, can be useful as a quantitative basis for both description of the plasma state and indication of the character of the nonequilibrium effects.

Non-LTE effects on [formula omitted] emission in the jovian upper atmosphere

Calculations of column intensities are performed for a number of infrared transitions of the H 3 + molecular ion, using a model atmosphere recently produced by Grodent et al. [2001. A self-consistent model of the jovian auroral thermal structure. J. Geophys. Res. 106, 12933–12952]. The line intensities integrated along the line of sight through the model atmosphere are first computed assuming that all of the emitting energy levels are in local thermodynamic equilibrium (LTE). These results are compared with those derived from a detailed balance calculation using a method recently proposed by Oka and Epp [2004. Non-thermal rotational distribution of H 3 + . Astrophys. J. In press]. It is shown that the population of excited vibrational levels starts to depart from that derived from LTE at altitudes higher than 500 km (above the jovian cloud tops). This effect has been noted previously by Kim et al. [1992. Densities and vibrational distribution of H 3 + in the jovian auroral atmosphere. J. Geophys. Res. 97, 6093–6101]. By 2000 km, all of the excited vibrational levels are populated at less than 10% of the expected LTE value. This has important implications for the jovian upper atmosphere. In particular, the H 3 + cooling effect will be greatly reduced high in the atmosphere. Modelled LTE line emission is greater than that derived from non-LTE modelling. Comparison of the non-LTE modelling with recent spectral measurements of the jovian auroral/polar regions in the L- and K-infrared windows shows that the Grodent et al. [2001. A self-consistent model of the jovian auroral thermal structure. J. Geophys. Res. 106, 12933–12952] profile overestimates the measured line intensity by ∼3. Allowing for this, the non-LTE modelling shows that the column densities derived from (quasi-)LTE treatment of the measured line intensities may underestimate the real H 3 + abundance by a factor of between 6 and 200. This means that attempts to derive important ionospheric properties, such as conductivity and related energy inputs due to magnetosphere–ionosphere coupling, from observed spectra will need to take this into account, if they are not to be seriously in error.

Magnetic Field Clumping in Massive Star–forming Regions as Determined from Excited‐State OH Absorption and Maser Emission

We have observed six high-mass-star-forming regions in the 2Π3/2, J = 7/2 lines of OH using the Green Bank Telescope (GBT) in order to investigate whether the magnetic field, and hence the density, measured in absorption differs from that implied by maser Zeeman splitting. We detect absorption in both the 13,441 and 13,434 MHz main lines in all six sources. Zeeman splitting in the F = 3+ → 3- absorption line in W3(OH) implies a line-of-sight magnetic field strength of 3.0 ± 0.3 mG. This is significantly less than full magnetic field strengths detected from OH maser Zeeman splitting, suggesting that OH maser regions may be denser than the nonmasing OH material by a factor of several. Zeeman splitting is not detected in other sources, but we are able to place upper limits on B∥ of 1.2 mG in G10.624-0.385 and 2.9 mG in K3-50. These results are consistent with a density enhancement of the masers, but other explanations for the lower magnetic field in absorption compared to maser emission are possible for these two sources. Absorption in one or both of the 13,442 and 13,433 MHz satellite lines is also seen in four sources. This is the very first detection of the 2Π3/2, J = 7/2 satellite lines. Ratios of satellite-line to main-line absorption suggest enhancement of the satellite lines from local thermodynamic equilibrium values. Masers are seen in the F = 4+ → 4- and 3+ → 3- transitions of W3(OH) and the 4+ → 4- transition of ON 1. A previously undetected 4+ → 4- maser is seen near -44.85 km s-1 in W3(OH).

Hyperfine structure of HCN J = 1-0 and implied physical information concerning NGC 7538 IRS1

The so-called intensity anomalies of hyperfine components of HCN(v = 0, J = 1-0) in the NGC 7538 molecular cloud are studied with a high resolution spectrometer. The measured intensity ratio R02 = T(a)*(F = 0-1)/T(a)*(F = 2-1) is clearly larger than the value 0.2, which is expected under the optically thin local thermodynamic equilibrium (LTE) condition, and the ratio R12= T(a)*(F = 1-1)/T(a)*(F = 2-1) smaller than the LTE value 0.6 at most of the observed positions. Radiative transfer calculations were performed using the large velocity gradient (LVG) model with a spherically symmetric velocity field. The line overlaps have also been taken into account. The analysis of the observational data shows that the three hyperfine components of the J = 1-0 transition are optically thick. While the optical depths of F = 2-1 and F = 1-1 are much larger than that of F = 0-1 hyperfine component, the scattering effect must be taken into account. The stronger two hyperfine components, F = 2-1, and F = 1-1, are formed in the envelope with the average hydrogen density 1.6 X 10(4) cm-3, but the thinner F = 0-1 hyperfine component in the core and in the envelope. The excitation temperatures of the three hyperfine components are different and the LTE assumption for the HCN hyperfine intensity ratio is unrealistic.

Semiconductor laser-based measurements of quench rates in an atmospheric pressure plasma by using saturated-fluorescence spectroscopy

Plasma diagnostics based on saturated fluorescence and absorption spectroscopy with a semiconductor (diode) laser are developed to probe the 4s(3)P(1) ? 4p(3)D(2) transition (8425 A) of argon in an atmospheric pressure plasma produced by an inductively coupled plasma torch. Spatially resolved measurements of saturation intensity, nonradiative collisional transfer (quench) rate, and fluorescence yield (Stern-Volmer factor) are inferred from variations of spectral profile characteristics (line shape, line-center value, and frequency-integrated signal) with laser intensity. The results obtained by using fluorescence and absorption spectroscopy are mutually consistent in the analytical region 10 mm above the induction coil. The measured quench rates compare favorably with computed rates from a multilevel collisional radiative model that assumes a suprathermal electron population relative to the local thermodynamic equilibrium value at the kinetic temperature.

Comparisons of computed and measured premixed charge engine combustion

Comparisons are presented of computed and measured cylinder pressure in a reciprocating engine with a pancake combustion chamber and premixed propane/air charges. Engine operating conditions range over volumetric efficiency of 30–60%; equivalence ratio of 0.87–1.1; and rpm of 1000–1500. The computations start from the actual spark times and simulate the growth of the flame kernel into a fully developed turbulent flame by taking into account the increasing influence of turbulent eddies on the growing flame kernel. A k-ϵ submodel is used for turbulence. The species conversion submodel assumes that the species (C 3H 8, O 2, H 2O, CO 2, CO, H 2, and N 2) concentrations approach their local thermodynamic equilibrium values with a characteristic conversion time that is a combination of a turbulent mixing time and a chemical conversion time in laminar propaneair flames. In all cases computed and measured cylinder pressure agree well in trends and magnitudes during the entire duration of combustion. The difference in magnitudes generally is much less than 8%. The main conclusion is that laminar flame processes must be explicitly accounted for in order to reproduce certain elements of premixed charge engine combustion.

Infrared Radiative Heating and Cooling in the Venusian Mesosphere.I: Global Mean Radiative Equilibrium

Abstract Global mean sources and sinks of radiative energy are calculated for the upper atmosphere of Venus. We especially consider the region between 90 and 130 km, where the equilibrium temperature is largely controlled through infrared absorption and emission by vibrational-rotational bands of CO2. Source functions for bands deviating from thermodynamic equilibrium are determined as part of the calculation. Radiative transfer in the region of non-overlapping lines is calculated by summing the contribution of individual Voigt lines. Many isotopic and hot bands contribute amounts to 15μ cooling or near-infrared heating at some levels comparable to the contributions by strong bands. The emission of the fundamental 15μ state of C120216 is maintained at near local thermodynamic equilibrium values by the radiation field to pressures three orders of magnitude less than would be expected in considering only relative values of radiative and vibrational relaxation rates. Conversion of near-infrared solar photon ...

Nonequilibrium in Confined-Arc Plasmas

The nonequilibrium behavior of argon and helium confined-arc plasmas at atmospheric pressure is analyzed in terms of a two-temperature ambipolar-diffusion model. Examination of spectroscopic data for the nonquilibrium arc shows that the free and bound electrons are mutually in equilibrium at a common electron temperature but not in equilibrium with the translational degrees of freedom of the heavy particles; the electron density in the outer portions of the arc may be as much as several orders of magnitude greater than its local thermodynamic-equilibrium value. Integration of the electron continuity equation and the electron and heavy-particle energy equations, with calculated transport properties and recombination coefficients, yields a satisfactory comparison with the measurements.

Theoretical model for a nonequilibrium helium arc plasma

A semiempirical model for a nonequilibrium helium arc plasma is used to interpret systematic deviations in existing spectroscopic data and to aid in computing nonequilibrium plasma transport properties. Two groups of bound electronic states are assumed to exist which follow Boltzmann distributions at T e (upper states) and T R ≠ T e (lower states). Under certain conditions, T R can be interpreted as a radiation temperature characterizing the optically thick part of the spectrum and can be calculated using a restricted Rosseland approximation. The nonequilibrium plasma is characterized by electron densities as much as several orders of magnitude greater than the local thermodynamic equilibrium value. The model reproduces the experimental data in detail once the electron temperature profile is given.