Kinetic Temperature Profile Research Articles

Configurational temperature profile in confined fluids. I. Atomic fluid

Two configurational expressions for the temperature are applied to the calculation of temperature profiles within a confined atomic fluid in a narrow slit pore. The configurational temperatures profiles so obtained are compared to the kinetic temperature, calculated from the equipartition principle, in equilibrium (EMD), and nonequilibrium molecular dynamics (NEMD) simulations of planar Poiseuille flow. We show that one of the configurational expressions exhibits a system-size dependence which prevents its application to the determination of high-resolution temperature profiles. The other expression yields good agreement with the kinetic temperature profile in both equilibrium and nonequilibrium systems.

Non‐LTE effects on retrieval of temperature from the CO2 laser bands using CIRRIS 1A data

It is well known that in the upper stratosphere and lower mesosphere, the CO2 laser band (00011–10001) transitions are populated by both local thermodynamic equilibrium (LTE) and non‐LTE mechanisms. Examination of infrared (IR) limb emission measurements from the Cryogenic Infrared Radiance Instrumentation for Shuttle (CIRRIS 1A) experiment clearly illustrates this effect. The presence of non‐LTE emissions, if left unaccounted for, will severely degrade the retrieval of kinetic temperature profiles. We have applied a non‐LTE compensation technique whereby the non‐LTE component is modeled and the resulting non‐LTE radiance is subtracted from the measured radiances. The kinetic temperature profile is then retrieved utilizing the modified data. As a means of validating this approach, we have compared the resulting temperature profiles to ones retrieved using the 792 cm−1 Q branch of CO2, the (11101–10002) transition, which is not significantly affected by non‐LTE excitation.

The Water Vapor Abundance in Circumstellar Envelopes

The maser emission of the para-H2O 313 → 220 line at 183 GHz in O-rich evolved stars has been modeled to account for the empirical characteristics of this line reported by González-Alfonso et al. Likewise, efforts have been made to derive water vapor abundance in these sources. The Sobolev or large velocity gradient (LVG) method has been employed to study the intensity of this line as a function of source properties and physical conditions (i.e., mass-loss rate, p-H2O abundance, velocity field, kinetic temperature profile, stellar luminosity, and the set of collisional rates adopted in the calculations). It has been found that the intensity of the 313 → 220 line is sensitive to the mass-loss rate, the p-H2O abundance, and the terminal velocity of the envelope, but it is rather insensitive to the rest of the parameters in stars with high mass-loss rates ( > 10-6 M☉ yr-1). The models reproduce the main spectral characteristics of the emission at 183 GHz in the latter sources. A global fit to the data proves that the observational luminosities can be explained by assuming an H2O abundance relative to H2 [x(H2O)] of 1-2 × 10-4. Detailed fitting to the line profile in five selected objects yields a similar value for x(H2O). The validity of the LVG approach has been verified by modeling the maser emission at 183 GHz through a nonlocal radiative transfer code. The model calculations with both methods lead to similar results. The pumping of the first bending mode of water vapor through absorption of photons emitted by the dust and the star has been also simulated. This effect is found to be important in the pumping of the H2O rotational levels. Hence, in order to recover LVG results, the water abundance must be increased by a factor of ≈2 for stars with high mass-loss rates. Consequently, x(H2O) has been estimated to be 3 × 10-4 within a factor ≃2. With this value for x(H2O), the expected near- and far-infrared spectra of the circumstellar envelopes of O-rich stars for several mass-loss rates have also been computed. Hence, it is possible to predict that, in some stars, the ro-vibrational lines of the 6 μm water vapor band with wavelengths longer that 6.3 μm—the P-branch—can be observed in emission, rather than in absorption.

Iterative method to improve the Mott-Smith shock-wave structure theory

In order to improve the Mott-Smith theory for shock-wave structures, an iterative method is introduced. The method is basically one of the family of iterative schemes constructed by Ikenberry and Truesdell [J. Rat. Mech. Anal. 5, 1 (1956)]. In the present work, the initial values for the iteration are calculated by using the Mott-Smith bimodal function [Phys. Rev. 82, 885 (1951)]; the equilibrium Maxwellian function is used in conventional Ikenberry-Truesdell--type approaches. The density profile in the first iterative step for monatomic Maxwellian molecular gases has been obtained in a closed form. Within the limitation of the lowest-order calculation, the results show asymmetric density profiles, the correct shock thickness limiting law at the weak limit, and nonmonotonic kinetic temperature profiles even for monatomic molecules.

On the location of a priori information to the solution of inverse problems of remote sensing of the non-LTE atmosphere in the infrared region by high-resolution spectral instruments

The optimal estimation method has been applied to the solution of the inverse problem of the retrieval of atmospheric composition, vibrational temperature profiles of gases under non-LTE (non-local thermodynamic equilibrium) conditions, and kinetic temperature profile from the limb measurements of atmospheric radiance and transmittance in the infrared region. The efficiency of the multi-parameter retrieval algorithm has been investigated in a number of numerical experiments simulating the MIPAS and ATMOS measurements. The influence of 4 types of a priori information on the retrieval accuracy is discussed: (1) “initial guess”; (2) a priori uncertainties and covarlances of unknown variables; (3) the knowledge of the altitude level of the breakdown of LTE for different vibrational transitions; (4) coupling of levels with close energies in accordance with LTE.

A non‐local thermodynamic equilibrium radiative transfer model for infrared emissions in the atmosphere of Mars: 1. Theoretical basis and nighttime populations of vibrational levels

A radiative transfer model to study the infrared (1–20 μm) emissions of the CO and CO2 molecules in the atmosphere of Mars has been developed. The model runs from the planet's surface up to 180 km and has been especially elaborated to study non‐local thermodynamic equilibrium (non‐LTE) situations. It includes the most important energy levels and vibration‐rotation bands able to give a significant atmospheric emission or produce a significant cooling/heating rate. Exchanges of energy in thermal and nonthermal (vibrational‐vibrational) collisions as well as by radiative processes have been included. An exhaustive review of the rate constants for vibrational‐thermal and vibrational‐vibrational collisional exchanges has been carried out. Radiative transfer processes have been treated by using a modified Curtis matrix formulation. The populations of the excited vibrational levels for nighttime conditions are presented along with a sensitivity study of their variations to the kinetic temperature profile and to collisional rate constants. The populations of the CO2(0,ν2,0) levels follow LTE up to about 85 km with the radiative transfer processes playing a very important role in maintaining this situation above the tropopause. This result is practically insensitive to plausible variations in the kinetic temperature of the troposphere. The uncertainties in the rate constants play an important role in determining the populations of the levels at thermospheric altitudes, but they are of little significance for the heights where they start departing from LTE. The CO2(0,0°,1) level breaks down from LTE at about 60 km, the laser bands at 10 μm giving a significant contribution to its population in the Martian mesosphere. The CO(1) level starts departing around 50 km and is noticeably enhanced in the upper thermosphere by absorption of upwelling flux from the planet's surface.

Non‐local thermodynamic equilibrium studies of the 15‐μm bands of CO2 for atmospheric remote sensing

A new line‐by‐line non‐local thermodynamic equilibrium (non‐LTE) radiance model based on the GENLN2 radiative transfer code is presented. This is capable of high resolution spectral radiance calculations for the upper atmosphere. We describe the non‐LTE model implementation and discuss the molecular state vibrational temperature input requirements for studies of the 15‐μm ν2 bands of CO2. Monochromatic and band‐integrated radiance calculations have been performed for atmospheric limb view tangent heights between 50 and 120 km for non‐LTE nighttime and daytime conditions. Two model atmospheres are considered, the U.S. 1976 Standard and a subarctic summer, which show, respectively, mean and large radiance differences from a reference LTE radiance calculation. Non‐LTE radiance considerations are shown to be important for the 15‐μm CO2 bands for tangent heights greater than 70 km, the magnitude of the divergence from LTE values and diurnal variation being dependent on the band and kinetic temperature profile. We show that the use of the Voigt line shape, rather than the Doppler, is important for tangent heights below 85 km, and that the inclusion of the effect of overlapping lines is a consideration for tangent heights below 75 km. We present calculations of synthetic radiance spectra showing the non‐LTE effect for two CO2 temperature sounding channels of instruments aboard the Upper Atmosphere Research Satellite as a demonstration of the model capability.

Non‐local‐thermodynamic‐equilibrium populations of the first vibrational excited state of CO in the middle atmosphere

A non‐LTE radiative transfer model for the population of the CO(1) vibrational state in the middle atmosphere is presented. Radiative transfer is treated by using the Curtis matrix method. The transmittances needed for the Curtis matrix have been computed by using the GENLN2 line‐by‐line radiance/transmittance code. A study of the radiative and collisional processes and atmospheric parameters that affect the population of CO(1) populations has been performed. We find that the tropospheric kinetic temperature and CO abundance profiles play an important role through radiative coupling in the population of mesospheric CO(1) at night‐time. During the day, the solar flux and the mesospheric CO abundance are the main factors determining the CO vibrational temperature in the mesosphere. Non‐thermal collisions with the atmospheric N2(1) are also shown to be important for the daytime population of CO(1) in that region. The consequences of these results for the retrieval of CO abundances from the remote sensing of radiance at 4.7 μm are discussed.

Analysis of the upper atmosphere CO2(v2) vibrational temperatures retrieved from ATMOS/Spacelab 3 observations

An analysis of the upper atmospheric (80–116 km) CO2(v2) vibrational temperatures retrieved from atmospheric trace molecule spectroscopy (ATMOS) experiment Spacelab 3 spectra by using a nonlocal thermodynamic equilibrium (non‐LTE) radiative transfer model is presented. Thermal collisions with atmospheric atomic oxygen keep this vibrational state very close to LTE up to around 100 km. Above this height the different deviations from LTE retrieved from ATMOS/Spacelab 3 spectra for the northern and southern hemispheres are explained in terms of this collisional process and in terms of the different kinetic temperature profiles measured at those locations. From these simultaneous observations of the kinetic and CO2(v2) vibrational temperatures a deactivation rate of CO2(v2) by O(3P) has been derived which, considering the available climatologies of the concentration of this compound, leads to a rate coefficient value between 3 and 6 × 10−12 cm3 s−1 and favors an independent or negative temperature dependence rate constant for the atmospheric temperature range. Cooling rates induced by the CO2 15‐μm fundamental band in the upper mesosphere and lower thermosphere (80–116 km) were derived from the simultaneous kinetic temperature, CO2(v2) vibrational temperature, and CO2 concentration, as measured by ATMOS/Spacelab 3, and found to be a factor of between 5 and 10 times larger than those generally accepted until very recently.

Upper atmospheric infrared radiance from CO2and NO observed during the SPIRIT 1 Rocket Experiment

Spectral limb radiance data on CO2ν2and NO 5.3‐μm emissions obtained in the Spectral Infrared Interferometric Telescope rocket experiment have been analyzed. The data cover auroral intensities from several kilorayleighs to over 100 kR at 391.4 nm, and tangent heights of ∼70–200 km at high latitudes (60°–65°N). Volumetric emission and kinetic temperature profiles have been obtained using linear least squares inversion procedures. The CO2ν2radiance profile is found to be similar to previous observations. The NO 5.3‐μm emission is somewhat weaker than that typically measured; this is ascribed mainly to below‐average thermospheric temperatures. Auroral enhancement of NO hot bands was not observable with the available sensitivity. An approximate thermospheric temperature profile derived from the NO band shape compares reasonably with the mass spectrometer/incoherent scatter 86 model.

Carbon dioxide 4.3‐μm emission in the Earth's atmosphere: A comparison between Nimbus 7 SAMS measurements and non‐local thermodynamic equilibrium radiative transfer calculations

A detailed analysis of CO2 4.3‐μm limb radiances measured by the Stratospheric and Mesospheric Sounder on Nimbus 7 has been conducted using a non‐local thermodynamic equilibrium (non‐LTE) radiative transfer model. The data display diurnal, latitudinal, and seasonal variations which are shown, after the latitudinal variation of the instrument's response has been taken into account, to be caused by different conditions of solar illumination and variations in the kinetic temperature profile. A study of the sensitivity of the populations and limb radiances to spectral, atmospheric, and collisional interactions parameters has been undertaken, and a limited range of values for some of these quantities has been derived. Among other findings, we conclude that the rate at which energy is exchanged (as ν3 quanta) between N2 and CO2 may be approximately twice the initial model value, which was inferred from laboratory data, and that the CO2 volume mixing ratio above 80 km may be significantly less than that predicted by photochemical models.

Infrared Spectroscopy of Cometary Parent Molecules

AbstractMost cometary parent molecules do not strongly fluoresce at ultraviolet and visible wavelengths, and some do not possess permanent electric dipole moments, preventing their study in the radio region as well. However, many of these molecules have strong ro-vibrational transitions in the near infrared (λ ∼ 2 – 5 μm). Since the solar flux at these wavelengths is quite strong, parent molecules in cometary comae can be probed directly via fluorescence in these infrared transitions. The feasibility of this approach was convincingly demonstrated by the detection of H2O in comet Halley (1986 III) from the Kuiper Airborne Observatory and by the detection of H2O, CO2, and H2CO using an infrared spectrometer (IKS) on VEGA. Tentative detections of near infrared lines of CH4 were also reported during ground-based and airborne observations of comets Halley and Wilson (1987 VII). High resolution spectroscopy of the infrared water transitions has yielded a wealth of new information on cometary physics: the absolute line intensities and spatial brightness profiles are used to determine water production rates and lifetimes, the relative line intensities probe the kinetic temperature profile in the coma, the line widths and line positions shed light on coma outflow dynamics, and the temporal variability in the lines provides information on the structure of the nucleus. These observations also allow the determination of the water ortho-to-para ratio, which may provide fundamental insight into the origin and/or evolutionary history of cometary nuclei. Similar observations of other molecules (those mentioned above plus others) will provide important complementary data and will also allow us to compile a volatile inventory for cometary nuclei, but such observations are extremely difficult due to the low abundances of these molecules (≤10% relative to water) and the limitations of present infrared facilities. Recent advances in infrared instrumentation promise to extend sensitivities for parent molecule searches to relative abundances well below 1%, especially if cooled, Earth-orbiting facilities are available.

Computerized analysis of glow curves from thermally activated processes

A method is presented to analyze complex glow curves composed of several, possibly overlapping, peaks from thermally stimulated processes of general kinetic order and is applicable when the process studied is activated using any arbitrary temperature profile. A theoretical analysis is given to determine the properties of a single glow curve peak. Several new results are presented, among which is an expression for the peak temperature for general kinetic order and temperature profile. From the theoretical analysis of the asymmetry of a glow peak a method is described to determine the kinetic order of a peak and to obtain an initial estimate of the peak parameters sufficiently accurate to start a least-squares minimization procedure to determine the actual parameters of all peaks present in the total glow curve. The method is demonstrated for a synthetic glow curve and for two measured glow curves from a thermoluminescence experiment and a thermal gas desorption experiment.

Vibrational and rotational excitation of CO in comets Nonequilibrium calculations

Ultraviolet observations of atomic carbon in cometary comae show that carbon-bearing compounds must comprise a significant fraction (approximately equal to or greater than 10 percent) of the volatiles. One likely source is CO. This compound is an important constituent of at least some cometary nuclei, even though it may not be the ultimate source of atomic carbon in all comets. Feldman (1983) has suggested that the relative abundance of CO may be one of the few fundamental characteristics which distinguish one comet from another. The present investigation is, therefore, concerned with the vibrational and rotational excitation of the CO molecule in cometary comae. Two previously neglected factors are taken into account in the study. The fractional populations of CO as solutions to time-dependent differential equations are derived, and a nonisothermal and cold kinetic temperature profile for the inner coma is considered.

The kinetic temperature and CH3CCH column density profiles in SGR B2, Orion, and DR 21

Kinetic temperatures, T(kin), are presently estimated by means of a technique employing the intensities of the adjacent rotational transitions of symmetric top molecules, under the assumptions that the metastable levels are thermalized, and that the excitation temperature connecting the upper level of the observed transition to the lowest level in the K ladder is the same for the both adjacent transitions. The method is applied to observations of the J = 5-4 and J = 6-5 transitions of CH3CCH obtained at 1-arcmin intervals along a NS-EW cross that centered on Orion KL, Sgr B2, and Dr 21. The technique's application to CH3CN lines from the central positions of Sgr B2 and Orion produces T(kin) values that are in good agreement with other determinations. The fact that these lines are broader than those of CH3CCH is interpreted in terms of a model in which CH3CN emission is confined to small and warm core region while CH3CCH emission is dominated by a more extensive, almost isothermal and cooler halo region in Orion KL and Sgr B2.

Thermal relaxation in a dense liquid under shock compression

We have studied by means of molecular dynamics the propagation of a planar shock wave in a dense, three-dimensional column of a simple modified Lennard-Jones liquid. The column is $49.37{\ensuremath{\sigma}}^{2}$ in cross section, and $238.5\ensuremath{\sigma}$ in length, where $\ensuremath{\sigma}$ is the length parameter in the potential. The column contains approximately 10 000 atoms. It is initially in equilibrium at a density of $0.85{\ensuremath{\sigma}}^{\ensuremath{-}3}$ and temperature of $\frac{1.16\ensuremath{\epsilon}}{k}$, where $\ensuremath{\epsilon}$ is the energy parameter in the potential. Shock compression is effected by causing the column to move in the longitudinal direction with a velocity of --- ${U}_{p}$ and to collide with its mirror image across a mirror located at the origin. From the motion of the atoms in response to this kind of excitation, we calculate the shock velocity and the shock-front structure in the liquid, as well as the profiles of mass density, stress distribution, and energy density behind the shock front. Our shock-front structure agrees well with that obtained from the Navier-Stokes equations, but we also find important differences between our shock profiles and those postulated or computed from the continuum theory. In particular, we find that in 4\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}11}$ s, the longest time of our calculations, the stress components did not relax to a hydrostatic condition, and the corresponding kinetic temperature profile showed a relaxation process similar to what we found earlier in a crystalline solid. We examine the atomistic mechanisms of the various relaxation processes, and discuss their implications on the shock compression of dense systems of solids and liquids as opposed to rarefield systems of gases.

Kinetic energy and temperature profiles of shockwaves in solids

Tsai and MacDonald (1973, 1978) published a critical analysis of the authors' molecular dynamic simulation of shockwave propagation. Most of their criticism was directed to the authors' definition of temperature and kinetic energy. It is shown that their analysis is incorrect and that the authors' calculation of kinetic energy is correct and the definition of temperature is reasonable. Most of the misunderstanding arose from the other not understanding that all the authors' calculations were performed in a stationary frame of reference. It is further shown that, when there is a variation in the planar velocity, the Tsai-MacDonald local kinetic temperature is neither equal to the local kinetic energy (expressed as temperature) nor does it have the characteristics of temperature.