Hot Atmosphere Research Articles

Hot Exoplanet Atmospheres Resolved with Transit Spectroscopy (HEARTS)

Context. High-resolution transmission spectroscopy has allowed for in-depth information on the composition and structure of exoplanetary atmospheres to be garnered in the last few years, especially in the visible and in the near-infrared. Many atomic and molecular species have been detected thanks to data gathered from state-of-the-art spectrographs installed on large ground-based telescopes. Nevertheless, the Earth daily cycle has been limiting observations to exoplanets with the shortest transits. Aims. The inflated sub-Saturn KELT-11 b has a hot atmosphere and orbits a bright evolved subgiant star, making it a prime choice for atmospheric characterization. The challenge lies in its transit duration – of more than 7 h – which can only be covered partially or without enough out-of-transit baselines when observed from the ground. Methods. To overcome this constraint, we observed KELT-11 b with the HARPS spectrograph in series of three consecutive nights, each focusing on a different phase of the planetary orbit: before, during, and after the transit. This allowed us to gather plenty of out-of-transit baseline spectra, which was critical to build a spectrum of the unocculted star with sufficient precision. Telluric absorption lines were corrected using the atmospheric transmission code MOLECFIT. Individual high-resolution transmission spectra were merged to obtain a high signal-to-noise transmission spectrum to search for sodium in KELT-11 b’s atmosphere through the ~5900 Å doublet. Results. Our results highlight the potential for independent observations of a long-transiting planet over consecutive nights. Our study reveals a sodium excess absorption of 0.28 ± 0.05% and 0.50 ± 0.06% in the Na D1 and D2 lines, respectively. This corresponds to 1.44 and 1.69 times the white-light planet radius in the line cores. Wind pattern modeling tends to prefer day-to-night side winds with no vertical winds, which is surprising considering the planet bloatedness. The modeling of the Rossiter-Mclaughlin effect yields a significantly misaligned orbit, with a projected spin-orbit angle of λ = −77.86−2.26+2.36∘. Conclusions. Belonging to the under-studied group of inflated sub-Saturns, the characteristics of KELT-11 b – notably its extreme scale height and long transit – make it an ideal and unique target for next-generation telescopes. Our results as well as recent findings from HST, TESS, and CHEOPS observations could make KELT-11 b a benchmark exoplanet in atmospheric characterization.

The Reactive Element Effect

Rationalizing the reactive element effect operative in alumina- and chromia-forming alloys upon oxidation under oxidizing hot gas atmospheres, referring to investigations on zirconium oxide-coated test samples for gas turbine alloys. This retrospective study uses the results of cyclic furnace lifetime tests conducted at 1100 °C on ZrO2-coated Ni-base alloys with Y− or Y+ Hf-doped bond coats and correlates them with the parabolic oxidation rate constant at 1100 °C of binary NiAl alloys doped with Y, Zr, or Hf. Parallel results at higher temperatures allow the respective oxidation processes during the cyclic lifetimes to be assigned to cation-dominated or anion-dominated transport processes. The correlations document the close interrelationship betweenthe refractory element content (Mo, Re, Ta, W) in the substrate alloythe total content of the two reactive elements Y and Zr in the mixed zone of the scale, representing a Me3+ iso-valence valueindividual relative lifetime parameters in pct for EBPVD thermal barrier coating systems associated with cation-dominated transport processes.

Hubble WFC3 Spectroscopy of the Rocky Planet L 98–59 b: No Evidence for a Cloud-free Primordial Atmosphere

We are using archived data from HST of transiting exoplanet L 98-59 b to place constraints on its potentially hot atmosphere. We analyze the data from five transit visits and extract the final combined transmission spectrum using Iraclis. Then we use the inverse atmospheric retrieval code TauREx to analyze the combined transmission spectrum. There is a weak absorption feature near 1.40 μm and 1.55 μm in the transmission spectrum, which can be modeled by a cloudy atmosphere with abundant hydrogen cyanide (HCN). However, the unrealistically high abundance of HCN derived cannot be explained by any equilibrium chemical model with reasonable assumptions. Thus, the likeliest scenario is that L 98-59 b has a flat, featureless transmission spectrum in the WFC3/G141 bandpass due to a thin atmosphere with high mean molecular weight, an atmosphere with an opaque aerosol layer, or no atmosphere, and it is very unlikely for L 98-59 b to have a clear hydrogen-dominated primary atmosphere. Due to the narrow wavelength coverage and low spectral resolution of HST/WFC3 G141 grism observation, we cannot tell these different scenarios apart. Our simulation shows future higher precision measurements over wider wavelengths from the James Webb Space Telescope can be used to better characterize the planetary atmosphere of L 98-59 b.

Constraints on dark matter self-interaction from the internal density profiles of X-COP galaxy clusters

The fundamental properties of the postulated dark matter (DM) affect the internal structure of gravitationally bound structures. In the cold dark matter paradigm, DM particles interact only via gravity. Their distribution is well represented by an Einasto profile with shape parameter α ≈ 0.18 in the smallest dwarf galaxies or the most massive galaxy clusters alike. Conversely, if DM particles self-interact via additional forces, we expect the mass density profiles of DM halos to flatten in their central regions, thereby increasing the Einasto shape parameter. We measured the structural properties of 12 massive galaxy clusters from observations of their hot gaseous atmosphere, using the X-ray observatory XMM-Newton, and of the Sunyaev-Zel’dovich effect using the Planck all-sky survey. After removing morphologically disturbed systems, we measured Einasto shape parameters with mean ⟨α⟩=0.19 ± 0.03 and intrinsic scatter σα = 0.06, which is in close agreement with the prediction of the cold dark matter paradigm. We used cosmological hydrodynamical simulations of cluster formation with self-interacting DM (BAHAMAS-SIDM) to determine how the Einasto shape parameter depends on the self-interaction cross section. We used the fitted relation to turn our measurements of α into constraints on the self-interaction cross section, which imply σ/m < 0.19 cm2 g−1 (95% confidence level) at collision velocity vDM − DM ∼ 1000 km s−1. This is lower than the interaction cross section required for DM self-interactions to solve the core-cusp problem in dwarf spheroidal galaxies, unless the cross section is a strong function of velocity.

Universal Scaling Laws for Solar and Stellar Atmospheric Heating: Catalog of Power-law Index between Solar Activity Proxies and Various Spectral Irradiances

The formation of extremely hot outer atmospheres is one of the most prominent manifestations of magnetic activity common to late-type dwarf stars, including the Sun. It is widely believed that these atmospheric layers, the corona, transition region, and chromosphere, are heated by the dissipation of energy transported upwards from the stellar surface by the magnetic field. This is signified by the spectral line fluxes at various wavelengths, scaled with power-law relationships against the surface magnetic flux over a wide range of formation temperatures, which are universal to the Sun and Sunlike stars of different ages and activity levels. This study describes a catalog of power-law indices between solar activity proxies and various spectral line fluxes. Compared to previous studies, we expanded the number of proxies, which now includes the total magnetic flux, total sunspot number, total sunspot area, and the F10.7 cm radio flux, and further enhanced the number of spectral lines by a factor of 2. This provides the data to study in detail the flux–flux scaling laws from the regions specified by the temperatures of the corona (log(T/K) = 6–7) to those of the chromosphere (log(T/K) ∼ 4), as well as the reconstruction of various spectral line fluxes of the Sun in the past, F-, G-, and K-type dwarfs, and the modeled stars.

The relation between accretion rate and jet power in early-type galaxies with thermally unstable hot atmospheres

ABSTRACT We use Chandra X-ray data and Very Large Array radio observations for a sample of 20 nearby, massive, X-ray bright, early-type galaxies to investigate the relation between the Bondi accretion rates and the mechanical jet powers. We find a strong correlation ($\rho = 0.96^{+0.03}_{-0.09}$; BF10 > 100) between the Bondi accretion power, PBondi, and the mechanical jet power, Pjet, for a subsample of 14 galaxies, which also host cool H α+[N ii] line emitting gas and thus likely have thermally unstable atmospheres. The relation between the Bondi accretion power and the mechanical jet power for this subsample is well described by a power-law model $\log \frac{P_{\mathrm{Bondi}}}{{10^{43} \, \mathrm{erg \, s^{-1}}}} = \alpha + \beta \log \frac{P_{\mathrm{jet}}}{{10^{43} \, \mathrm{erg \, s^{-1}}}}$, where α = 1.10 ± 0.25 and β = 1.10 ± 0.24 with an intrinsic scatter $\sigma = 0.08^{+0.14}_{-0.06}$ dex. The results indicate that in all galaxies with thermally unstable atmospheres the cooling atmospheric gas feeds the central black holes at a similar jet-to-Bondi power ratio. For the full sample of 20 galaxies, the correlation is weaker and in a subset of galaxies with no signs of H α+[N ii] emission, we see a hint for a systematically lower jet-to-Bondi power ratio. We also investigate the dependence of jet power on individual quantities in the Bondi formula such as the supermassive black hole mass (M•) and the specific entropy of the gas (K) at the Bondi radius. For the subsample of H α+[N ii] emitting galaxies, we find a very tight correlation of Pjet with M• ($\rho = 0.91^{+0.06}_{-0.11}$; BF10 > 100) and, although poorly constrained, a hint of an anticorrelation for Pjet and K ($\rho = -0.47^{+0.60}_{-0.37}$; BF10 = 1.1).

Molecular flows in contemporary active galaxies and the efficacy of radio-mechanical feedback

ABSTRACT Molecular gas flows are analysed in 14 cluster galaxies (BCGs) centred in cooling hot atmospheres. The BCGs contain $10^{9}\!-\!10^{11}~\rm M_\odot$ of molecular gas, much of which is being moved by radio jets and lobes. The molecular flows and radio jet powers are compared to molecular outflows in 45 active galaxies within z < 0.2. We seek to understand the relative efficacy of radio, quasar, and starburst feedback over a range of active galaxy types. Molecular flows powered by radio feedback in BCGs are ∼10–1000 times larger in extent compared to contemporary galaxies hosting quasar nuclei and starbursts. Radio feedback yields lower flow velocities but higher momenta compared to quasar nuclei, as the molecular gas flows in BCGs are usually ∼10–100 times more massive. The product of the molecular gas mass and lifting altitude divided by the AGN or starburst power – a parameter referred to as the lifting factor – exceeds starbursts and quasar nuclei by 2–3 orders of magnitude, respectively. When active, radio feedback is generally more effective at lifting gas in galaxies compared to quasars and starburst winds. The kinetic energy flux of molecular clouds generally lies below and often substantially below a few per cent of the driving power. We find tentatively that star formation is suppressed in BCGs relative to other active galaxies, perhaps because these systems rarely form molecular discs that are more impervious to feedback and are better able to promote star formation.

Simple semiclassical model of pressure-broadened infrared/microwave linewidths in the temperature range 200–3000 K

Abstract There is a need for line-broadening parameters for molecules found in exoplanetary atmospheres for a variety of broadeners and a range of temperatures. The use of an easily handled semiclassical theoretical expression is suggested for the calculation of pressure-broadened linewidths for (vib)rotational transitions over a large temperature range (200–3000 K) starting from a minimal set of input parameters: kinetic molecular properties and the character of the leading term in the intermolecular interaction potential. Applications to NO and OH colliding with rare-gas atoms and non-polar molecules demonstrate good consistency with available measurements over the full temperature range indicated. The procedure therefore can be expected to provide realistic estimates for line broadening of ‘exotic’ molecules and molecular ions present in hot planetary atmospheres.

Climate Change: Policy Support for National Adaptation Plans in Sub-Saharan African

The global climate has experienced tremendous change, notably since the industrial revolution. Beginning from 1880 all through to 2012, the average global temperature increased by 0.85°C. This subtle increase primarily from anthropogenic contribution has had devastating effects on crop (grains) yields. Specifically, between 1981 and 2002, major crops like wheat, and maize, among others, have suffered substantial yield declines of about forty megatons annually, due to a hotter atmosphere. With the oceans equally warming faster and snow and ice sheets on a dramatic decrease, global average sea levels climbed by 19 cm from 1901 to 2010. While climate change is a global phenomenon with varying degrees of consequential implications for different world regions, Africa South of the Sahara with a negligible contribution to global warming has seen a few of the worst impacts of climate change in recent years. Temperatures in Africa have risen by at least 0.5°C in the last 50 to 100 years. As IPPC 5th Assessment concluded, Africa is particularly vulnerable to climate change (Lisa 2020). Of about 2.1 billion people in the world that require access to drinking and safe water services that are well-managed, more than eleven million of this population live in Madagascar (World Health Organisation (WHO) 2017/Liberty supports WaterAid 2015). However, the precarious state of the global climate calls for serious and well-coordinated action from state and multilateral actors with the capacity to help the world’s poorest, specifically in Africa, to either mitigate or develop credible adaptation measures. This paper, therefore, provides a comprehensive literature review on UNDP Climate Change Adaptation policies for “Supporting Developing Countries to Advance National Adaptation Plans (NAPs)”, using Sub-Saharan Africa as a case study. The findings of the review suggest the adoption of an evidence-based policymaking approach as a way of influencing the adoption of NAPs by developing countries.

Novel methodology for systematically constructing global effective models from ab initio-based surfaces: A new insight into high-resolution molecular spectra analysis.

In this paper, a novel methodology is presented for the construction of ab initio effective rotation-vibration spectroscopic models from potential energy and dipole moment surfaces. Non-empirical effective Hamiltonians are obtained via the block-diagonalization of selected variationally computed eigenvector matrices. For the first time, the derivation of an effective dipole moment is carried out in a systematic way. This general approach can be implemented quite easily in most of the variational computer codes and turns out to be a clear alternative to the rather involved Van Vleck perturbation method. Symmetry is exploited at all stages to translate first-principles calculations into a set of spectroscopic parameters to be further refined on experiment. We demonstrate on H2CO, PH3, CH4, C2H4, and SF6 that the proposed effective model can provide crucial information to spectroscopists within a very short time compared to empirical spectroscopic models. This approach brings a new insight into high-resolution spectrum analysis of polyatomic molecules and will be also of great help in the modeling of hot atmospheres where completeness is important.

Imaging of the Quiet Sun in the Frequency Range of 20–80 MHz

Radio emission of the quiet Sun is considered to be due to thermal bremsstrahlung emission of the hot solar atmosphere. The properties of the quiet Sun in the microwave band have been well studied, and they can be well described by the spectrum of bremsstrahlung emission. In the meter-wave and decameter-wave bands, properties of the quiet Sun have rarely been studied due to the instrumental limitations. In this work, we use the LOw Frequency ARray telescope to perform high quality interferometric imaging spectroscopy observations of quiet Sun coronal emission at frequencies below 90 MHz. We present the brightness temperature spectrum and the size of the Sun in the frequency range of 20–80 MHz. We report on dark coronal regions with low brightness temperatures that persist with frequency. The brightness temperature spectrum of the quiet Sun is discussed and compared with the bremsstrahlung emission of a coronal model and previous quiet Sun observations.

Stack effects in tall building fires: a case study of Taiwan old apartment fire

Tainan, a city that prospered early in Taiwan, has a hot and humid atmosphere. Hence, the grilled doors in numerous old buildings for ventilation and lighting to conserve energy. This study analyzed a fire incident that occurred during the late night of March 17, 2019 in a 38-year-old dwelling, where three residents were severely covered with soot. The site investigation showed that eight staircases lead to the same basement, which apparently created a stack effect and a makeup air phenomenon. Numerical simulations have been performed in this study to reconstruct the fire scene, whose results were consistent with the actual fire scene. In particular, the results showed that some staircases in the fire were blackened by smoke, while others acted as makeup air inlets. The temperature at the households’ doors on all floors of Staircase 2, which was closest to the fire, exceeded 60 °C after four minutes. Furthermore, two immediately feasible improvement strategies according to the control volume theory of fluid mechanics were proposed in this study. Firstly, changing the grilled doors in the basement to a closed flat door style could effectively prevent smoke from flowing up in the staircases. Secondly, residents may consider closing the windows of the stairs at night to improve fire safety. The results showed that the chimney effect can be significantly reduced. These improvements could be a reference for other old dwellings to enhance their fire safety.

Detection of Stellar-like Abundance Anomalies in the Slow Solar Wind

The elemental composition of the Sun’s hot atmosphere, the corona, shows a distinctive pattern that is different from the underlying surface or photosphere. Elements that are easy to ionize in the chromosphere are enhanced in abundance in the corona compared to their photospheric values. A similar pattern of behavior is often observed in the slow-speed (<500 km s−1) solar wind and in solar-like stellar coronae, while a reversed effect is seen in M dwarfs. Studies of the inverse effect have been hampered in the past because only unresolved (point-source) spectroscopic data were available for these stellar targets. Here we report the discovery of several inverse events observed in situ in the slow solar wind using particle-counting techniques. These very rare events all occur during periods of high solar activity that mimic conditions more widespread on M dwarfs. The detections allow a new way of connecting the slow wind to its solar source and are broadly consistent with theoretical models of abundance variations due to chromospheric fast-mode waves with amplitudes of 8–10 km s−1, sufficient to accelerate the solar wind. The results imply that M-dwarf winds are dominated by plasma depleted in easily ionized elements and lend credence to previous spectroscopic measurements.

Corrosion Behavior of Multiphase Bainitic Rail Steels

Pearlitic steel experiences excessive corrosion in a hot and humid atmosphere. The multiphase bainitic/martensitic structure was developed for a better combination of strength and ductility, especially rolling contact fatigue, but little attention to corrosion has been investigated. Corrosion behaviors of multiphase steels obtained from bainitic-austempering (BAT) and bainitic-quenching and -partitioning (BQ&amp;P) processes were investigated via immersion and electrochemical tests in 3.5 wt.% NaCl solution. The corroded surface and rust after immersion and electrochemical tests were analyzed via electron microscopy, Fourier transform infrared spectra, and x-ray diffraction. The multiphase bainite + martensite/retained austenite island showed higher corrosion resistance than that of the pearlitic one. The acicular bainite obtained from the BQ&amp;P process showed slightly higher corrosion resistance than the granular bainite + martensite structure obtained from the BAT process.

Performance of the Plant in Treatment Cana indica of Waste Water by Vertical Flow Method for the Touggourt Region, Algeria

The effectiveness of the plant in treating waste water with a vertical flow system under dry and hot atmosphere was Canna indica studied. This study included a comparison between a basin planted with and a non-planted one (witness), with the study of the ability C. Indica of the plant to filter waste water. The study was carried out through an experimental model at the National Institute of Disinfection C. Indica (ONA) in Touggourt, Algeria. This model consists of circular basins with a capacity of 52L filled from bottom to top on a thickness of 18cm with gravel (25/15) mm. The process of supplying the basins with urban waste water after primary treatment (physical treatment) with 15L per day at a regular rate once every week and the water obtained after Its stay in the tank for 5 days is collected through a container placed under the sink. After the study that lasted for six months from December 2019 to May 2020, obtained the removal of pollutants, with percentages of DCO (83.95%), N-NO (81.81%), P-PO (90.49%), and bacteria (99.86%).These percentages comply with the recommended standards for 2 4 - -3 E. Coli the safe use of this water in the agricultural field.

The cycle of metals in the infalling elliptical galaxy NGC 1404

ABSTRACT Hot atmospheres pervading galaxy clusters, groups, and early-type galaxies are rich in metals, produced during epochs and diffused via processes that are still to be determined. While this enrichment has been routinely investigated in clusters, metals in lower mass systems are more challenging to probe with standard X-ray exposures and spectroscopy. In this paper, we focus on very deep XMM–Newton (∼350 ks) observations of NGC 1404, a massive elliptical galaxy experiencing ram-pressure stripping of its hot atmosphere while infalling towards the centre of the Fornax cluster, with the aim to derive abundances through its hot gas extent. Importantly, we report the existence of a new fitting bias – the ‘double Fe bias’ – leading to an underestimate of the Fe abundance when two thermal components cannot realistically model the complex temperature structure present in the outer atmosphere of the galaxy. Contrasting with the ‘metal conundrum’ seen in clusters, the Fe and Mg masses of NGC 1404 are measured 1–2 orders of magnitude below what stars and supernovae could have reasonably produced and released. In addition, we note the remarkable Solar abundance ratios of the galaxy’s halo, different from its stellar counterpart but similar to the chemical composition of the ICM of rich clusters. Completing the clusters regime, all these findings provide additional support towards a scenario of early enrichment, at play over two orders of magnitude in mass. A few peculiar and intriguing features, such as a possible double metal peak as well as an apparent ring of enhanced Si near the galaxy core, are also discussed.

Very Large Array Radio Study of a Sample of Nearby X-Ray and Optically Bright Early-type Galaxies

Abstract Many massive early-type galaxies host central radio sources and hot X-ray atmospheres indicating the presence of radio-mechanical active galactic nucleus (AGN) feedback. The duty cycle and detailed physics of the radio-mode AGN feedback is still a matter of debate. To address these questions, we present 1–2 GHz Karl G. Jansky Very Large Array radio observations of a sample of the 42 nearest optically and X-ray brightest early-type galaxies. We detect radio emission in 41/42 galaxies. However, the galaxy without a radio source, NGC 499, has recently been detected at lower frequencies by the Low-Frequency Array. Furthermore, 27/42 galaxies in our sample host extended radio structures and 34/42 sources show environmental interactions in the form of X-ray cavities. We find a significant correlation between the radio flux density and the largest linear size of the radio emission and between the radio power and the luminosity of the central X-ray point source. The central radio spectral indices of the galaxies span a wide range of values, with the majority of the systems having steep spectra and the rest flat spectra. These results are consistent with AGN activity, where the central radio sources are mostly switched on, thus the duty cycle is very high. Seven out of 14 galaxies with pointlike radio emission (Fanaroff–Riley Class 0; FR 0) also show X-ray cavities indicating that, despite the lack of extended radio structures at 1–2 GHz, these AGNs do launch jets capable of inflating lobes and cavities.

High Accuracy Molecular Line Lists for Studies of Exoplanets and Other Hot Atmospheres

The desire to characterize and model the atmospheres of the many extrasolar planets that have been discovered over the last three decades is a major driver of current astronomy. However, this goal is impacted by the lack of spectroscopic data on the molecules in question. As most atmospheres that can be studied are hot, some surprisingly so, this activity requires spectroscopic information not readily available from laboratory studies. This article will review the current status of available molecular spectroscopic data, usually presented as line lists, for studies of exoplanet atmospheres and, indeed, the atmospheres of other astronomical objects hotter than the Earth such as brown dwarfs, cool stars and even sunspots. Analysis of exoplanet transit spectra and the calculation of the relevant opacities often require huge datasets comprising billions of individual spectroscopic transitions. Conversely, the newly-developed high-resolution Doppler-shift spectroscopy technique has proved to be a powerful tool for detecting molecular species in exoplanet atmospheres, but relies on the use of smaller, highly accurate line lists. Methods of resolving issues arising from the competing demands of completeness versus accuracy for line lists are discussed.

Thermal and intermediates' effects of pre-injection on the auto-ignition of main-injection in cold-start conditions

• The pilot injection inhibits the ignition of main injection at Ta ≤ 722.5 K. • The effect of split-injection on IDT changes at turning point of Ta = 725 K. • The thermal effect of pilot injection is dominant. • Equivalence ratio of ignition position of split injection is reduced by pilot spray. Spray misfire is highly likely to happen when diesel engines are operated in extremely low-temperature or high-altitude conditions. In this study, single and split injections of n-dodecane spray are compared to identify the role of pilot injection in main spray autoignition near spray misfire. Two different effects of the pilot injection are identified, depending on the relative importance of cool flame and evaporation heat absorption: (1) when ambient temperature (T a ) is lower than 722.5 K, pilot spray inhibits the autoignition of the main spray because the heat release of the cool flame cannot overcome evaporation heat absorption; (2) when T a > 722.5 K, the cool flame reactions in the pilot spray create a hot atmosphere that is rich with cool-flame intermediates for the main spray. In such a case, the pilot spray could promote the autoignition of the main spray. When T a > 725 K, the benefits of split injection to ignition delay reduction are weakened because the cool flame of the pilot injection becomes more similar with increasing T a . Moreover, the effects of thermal and cool-flame intermediates on the main spray are investigated separately in kinetical analyses. It is found that the thermal effects of cool flame are dominant in promoting the autoignition of the main spray under cold- start conditions.

Stark broadening effect in hot DA white dwarfs: Ultraviolet lines of Fe V

AbstractStark widths and shifts have been calculated for 17 ultraviolet lines of Fe V of astrophysical interest. The calculations have been made using semiclassical perturbation approach. The work is motivated by the importance of ultraviolet lines for the study of hot white dwarf atmospheres specially for investigations of the variation of fine structure constant in strong gravitational field. Our Stark broadening parameters are presented for a range of temperature from 50,000 to 600,000 K. Our results are used to investigate the importance of electron impact broadening in plasma conditions of hot DA white dwarfs. Electron impact Stark width is compared to Doppler width as a function of atmospheric layer temperature and as a function of logarithm of Rosseland optical depth.