We present a formalism for a first-order estimation of the magnetosphere radius of exoplanets orbiting stars in the range from 0.08 to 1.3 Mo. With this radius, we estimate the atmospheric surface that is not protected from stellar winds. We have analyzed this unprotected surface for the most extreme environment for exoplanets: GKM-type and very low-mass stars at the two limits of the habitable zone. The estimated unprotected surface makes it possible to define a likelihood for an exoplanet to retain its atmosphere. This function can be incorporated into the new habitability index SEPHI. Using different formulations in the literature in addition to stellar and exoplanet physical characteristics, we estimated the stellar magnetic induction, the main characteristics of the stellar wind, and the different star-planet interaction regions (sub- and super-Alfvénic, sub- and supersonic). With this information, we can estimate the radius of the exoplanet magnetopause and thus the exoplanet unprotected surface. We have conducted a study of the auroral aperture angles for Earth-like exoplanets orbiting the habitable zone of its star, and found different behaviors depending on whether the star is in rotational saturated or unsaturated regimes, with angles of aperture of the auroral ring above or below 36^\circ, respectively, and with different slopes for the linear relation between the auroral aperture angle at the inner edge of the habitable zone versus the difference between auroral aperture angles at the two boundaries of the habitable zone. When the planet is tidally locked, the unprotected angle increases dramatically to values higher than 40^\circ with a low likelihood of keeping its atmosphere. When the impact of stellar wind is produced in the sub-Alfvénic regime, the likelihood of keeping the atmosphere is almost zero for exoplanets orbiting very close to their star.
We describe how the accurate characterization of exoplanetary atmospheres in the ELT and JWST era will inevitably require taking into consideration the stellar inhomogeneities caused by convection and magnetic fields. The existing evidence that demonstrates the mixture of stellar and planetary signatures in observed transiting spectra is presented. Finally, we discuss how to disentangle these two components through a multipronged approach that includes new solar reference spectra, improved MHD modeling, and synergistic collaborations between the communities involved, from solar to stellar and …
The lowest-mass stars, brown dwarfs and extrasolar planets present challenges and opportunities for understanding dynamics and cloud formation processes in low-temperature atmospheres. For brown dwarfs, the formation, variation and rapid depletion of photospheric clouds in L- and T-type dwarfs, and spectroscopic evidence for non-equilibrium chemistry associated with vertical mixing, all point to a fundamental role for dynamics in vertical abundance distributions and cloud/grain formation cycles. For exoplanets, azimuthal heat variations and the detection of stratospheric and exospheric layers …
The study of exoplanetary atmospheres is one of the most exciting and dynamic frontiers in astronomy. Over the past two decades ongoing surveys have revealed an astonishing diversity in the planetary masses, radii, temperatures, orbital parameters, and host stellar properties of exoplanetary systems. We are now moving into an era where we can begin to address fundamental questions concerning the diversity of exoplanetary compositions, atmospheric and interior processes, and formation histories, just as have been pursued for solar system planets over the past century. Exoplanetary atmospheres p…
This invited review for young researchers presents key ideas on cloud formation as key part for virtual laboratories for exoplanet atmospheres. The basic concepts are presented, followed by utilising a time-scale analysis to disentangle process hierarchies. The kinetic approach to cloud formation modelling is described in some detail to allow the discussion of cloud structures as prerequisite for future extrasolar weather forecasts.
Exoplanetary science is on the verge of an unprecedented revolution. The thousands of exoplanets discovered over the past decade have most recently been supplemented by discoveries of potentially habitable planets around nearby low-mass stars. Currently, the field is rapidly progressing towards detailed spectroscopic observations to characterise the atmospheres of these planets. While various surveys from space and ground are expected to detect numerous more exoplanets orbiting nearby stars, the imminent launch of JWST along with large ground-based facilities are expected to revolutionise exop…
Context: According to theory, high-energy emission from the coronae of cool stars can severely erode the atmospheres of orbiting planets. No observational tests of the long term effects of erosion have yet been made. Aims: To analyze the current distribution of planetary mass with X-ray irradiation of the atmospheres in order to make an observational assessment of the effects of erosion by coronal radiation. Methods: We study a large sample of planet-hosting stars with XMM-Newton, Chandra and ROSAT; make a careful identification of X-ray counterparts; and fit their spectra to make accurately m…
The atmospheres of highly irradiated exoplanets are observed to undergo hydrodynamic escape. However, due to strong pressures, stellar winds can confine planetary atmospheres, reducing their escape. Here, we investigate under which conditions atmospheric escape of close-in giants could be confined by the large pressure of their host star's winds. For that, we simulate escape in planets at a range of orbital distances ([0.04, 0.14] au), planetary gravities ([36%, 87%] of Jupiter's gravity), and ages ([1, 6.9] Gyr). For each of these simulations, we calculate the ram pressure of these escaping a…
We review several aspects of the calculation of exoplanet model atmospheres in the current era, with a focus on understanding the temperature-pressure profiles of atmospheres and their emitted spectra. Most of the focus is on gas giant planets, both under strong stellar irradiation and in isolation. The roles of stellar irradiation, metallicity, surface gravity, C/O ratio, interior fluxes, and cloud opacity are discussed. Connections are made to the well-studied atmospheres of brown dwarfs as well as sub-Neptunes and terrestrial planets, where appropriate. Illustrative examples of model atmosp…
Until recently, infrared observations of exoplanetary atmospheres have typically been interpreted using models that assumed solar elemental abundances. With the chemical composition fixed, attempts have been made to classify hot Jupiter atmospheres on the basis of stellar irradiation. However, recent observations have revealed deviations from predictions based on such classification schemes, and chemical compositions retrieved from some datasets have also indicated non-solar abundances. In hot hydrogen-dominated atmospheres, the C/O ratio critically influences the relative concentrations of se…
Characterizing the atmospheres of extrasolar planets is the new frontier in exoplanetary science. The last two decades of exoplanet discoveries have revealed that exoplanets are very common and extremely diverse in their orbital and bulk properties. We now enter a new era as we begin to investigate the chemical diversity of exoplanets, their atmospheric and interior processes, and their formation conditions. Recent developments in the field have led to unprecedented advancements in our understanding of atmospheric chemistry of exoplanets and the implications for their formation conditions. We …
We apply the picket fence treatment to model the effects brought about by spectral lines on the thermal structure of irradiated atmospheres. The lines may be due to purely absorption processes, purely coherent scattering processes or some combination of absorption and scattering. If the lines arise as a pure absorption process, the surface layers of the atmosphere are cooler whereas this surface cooling is completely absent if the lines are due to pure coherent isotropic scattering. The lines also lead to a warming of the deeper atmosphere. The warming of the deeper layers is, however, indepen…
Polarized scattering in planetary atmospheres is computed in the context of exoplanets. The problem of polarized radiative transfer is solved for a general case of absorption and scattering, while Rayleigh and Mie polarized scattering are considered as most relevant examples. We show that (1) relative contributions of single and multiple scattering depend on the stellar irradiation and opacities in the planetary atmosphere; (2) cloud (particle) physical parameters can be deduced from the wavelength-dependent measurements of the continuum polarization and from a differential analysis of molecul…
Transmission spectrum surveys have suggested the ubiquity of high-altitude clouds in exoplanetary atmospheres. Theoretical studies have investigated the formation processes of the high-altitude clouds; however, cloud particles have been commonly approximated as compact spheres, which is not always true for solid mineral particles that likely constitute exoplanetary clouds. Here, we investigate how the porosity of cloud particles evolve in exoplanetary atmospheres and influence the cloud vertical profiles. We first construct a porosity evolution model that takes into account the fractal aggrega…
Hot giant exoplanets are very exotic objects with no equivalent in the Solar System that allow us to study the behavior of atmospheres under extreme conditions. Their thermal and chemical day--night dichotomies associated with extreme wind dynamics make them intrinsically 3D objects. Thus, the common 1D assumption, relevant to study colder atmospheres, reaches its limits in order to be able to explain hot and ultra-hot atmospheres and their evolution in a consistent way. In this review, we highlight the importance of these 3D considerations and how they impact transit, eclipse and phase curve …
Spectroscopy of exoplanetary atmospheres has become a well established method for the characterisation of extrasolar planets. We here present a novel inverse retrieval code for exoplanetary atmospheres. TauRex (Tau Retrieval for Exoplanets) is a line-by-line radiative transfer fully Bayesian retrieval framework. TauRex includes the following features: 1) the optimised use of molecular line-lists from the Exomol project; 2) an unbiased atmospheric composition prior selection, through custom built pattern recognition software; 3) the use of two independent algorithms to fully sample the Bayesian…
We examine the mechanisms by which atmosphere can be eroded by giant impacts onto Earth-like planets with thin atmospheres, using 3D smoothed particle hydrodynamics simulations with sufficient resolution to directly model the fate of low-mass atmospheres. We present a simple scaling law to estimate the fraction lost for any impact angle and speed in this regime. In the canonical Moon-forming impact, only around 10% of the atmosphere would have been lost from the immediate effects of the collision. There is a gradual transition from removing almost none to almost all of the atmosphere for a gra…
Chemical compositions of exoplanets can provide key insights into their physical processes, and formation and evolutionary histories. Atmospheric spectroscopy provides a direct avenue to probe exoplanetary compositions. However, whether obtained in transit or thermal emission, spectroscopic observations probe limited pressure windows of planetary atmospheres and are directly sensitive to only a limited set of spectroscopically active species. It is therefore critical to have chemical models that can relate retrieved atmospheric compositions to an atmosphere's bulk physical and chemical state. …
We present a new scaling law to predict the loss of atmosphere from planetary collisions for any speed, angle, impactor mass, target mass, and body compositions, in the regime of giant impacts onto broadly terrestrial planets with relatively thin atmospheres. To this end, we examine the erosion caused by a wide range of impacts, using 3D smoothed particle hydrodynamics simulations with sufficiently high resolution to directly model the fate of low-mass atmospheres around 1% of the target's mass. Different collision scenarios lead to extremely different behaviours and consequences for the plane…
The polarization state of starlight reflected by a planetary atmosphere uniquely reveals coverage, particle size, and composition of aerosols as well as changing cloud patterns. It is not possible to obtain a comparable level of detailed from flux-only observations. Furthermore, polarization observations can probe the atmosphere of planets independently of the orbital geometry (i.e., transiting and non-transiting planets). We show that a high-resolution spectropolarimeter with a broad wavelength coverage, particularly if attached to a large space telescope, would enable simultaneous study of t…
We investigated the impact of selected cloud condensates in exoplanetary atmospheres on the polarization of scattered stellar radiation. We considered a selection of 25 cloud condensates that are expected to be present in extrasolar planetary atmospheres. Using the three-dimensional Monte Carlo radiative transfer code POLARIS and assuming Mie scattering theory, we calculated and studied the net polarization of scattered radiation as a function of planetary phase angle at optical to near-infrared wavelengths. In addition to the well-known characteristics in the state of polarization, such as th…
Spectroscopic observations of exoplanets are leading to unprecedented constraints on their atmospheric compositions. However, molecular abundances derived from spectra are degenerate with the absorption cross sections which form critical input data in atmospheric models. Therefore, it is important to quantify the uncertainties in molecular cross sections to reliably estimate the uncertainties in derived molecular abundances. However, converting line lists into cross sections via line broadening involves a series of prescriptions for which the uncertainties are not well understood. We investiga…
Knowing the bulk elemental abundances of an exoplanetary atmosphere is not an easy task, but it is crucial to understand the formation history of planets. The purpose of this work is to show that the observability of TiO features at optical wavelengths in the transmission spectra of hot Jupiter atmospheres is sensitive to the bulk chemical properties of the atmosphere. For that, we run a grid of chemical models which include TiO formation and destruction, for the ultra-hot Jupiter WASP-19b and an ultra-hot version of HD~209458b. We take into account non-equilibrium chemistry and changes in the…
An important source of opacity in exoplanet atmospheres at short visible and near-UV wavelengths is Rayleigh scattering of light on molecules. It is accompanied by a related, albeit weaker process -- Raman scattering. We analyze the signatures of Raman scattering imprinted in the reflected light and the geometric albedo of exoplanets, which could provide information about atmospheric properties. Raman scattering affects the geometric albedo spectra of planets in following ways. Firstly, it causes filling-in of strong absorption lines in the incident radiation, thus producing sharp peaks in the…
Supersonic flows are expected to exist in the atmospheres of irradiated exoplanets, but the question of whether shocks develop lingers. Specifically, it reduces to whether continuous flow in a closed loop may become supersonic and if some portions of the supersonic flow steepen into shocks. We first demonstrate that continuous, supersonic flow may exist in two flavors: isentropic and non-isentropic, with shocks being included in the latter class of solutions. Supersonic flow is a necessary but insufficient condition for shocks to develop. The development of a shock requires the characteristics…
The atmospheres of exoplanets reveal all their properties beyond mass, radius, and orbit. Based on bulk densities, we know that exoplanets larger than 1.5 Earth radii must have gaseous envelopes, hence atmospheres. We discuss contemporary techniques for characterization of exoplanetary atmospheres. The measurements are difficult, because - even in current favorable cases - the signals can be as small as 0.001-percent of the host star's flux. Consequently, some early results have been illusory, and not confirmed by subsequent investigations. Prominent illusions to date include polarized scatter…
We describe the recent updates to the ExoMol database regarding the molecular spectral line shapes. ExoMol provides comprehensive molecular line lists with a special emphasis on the applications involving characterization of atmospheres of exoplanets and cool stars. Among important requirements of such applications are (i) the broadening parameters for hydrogen and helium dominating atmospheres and (ii) very broad ranges of temperature and pressures. The current status of the available line shape data in the literature, demands from the exoplanetary community and their specific needs are discu…
A number of transiting exoplanets have featureless transmission spectra that might suggest the presence of clouds at high altitudes. A realistic cloud model is necessary to understand the atmospheric conditions under which such high-altitude clouds can form. In this study, we present a new cloud model that takes into account the microphysics of both condensation and coalescence. Our model provides the vertical profiles of the size and density of cloud and rain particles in an updraft for a given set of physical parameters, including the updraft velocity and the number density of cloud condensa…
We provide a new framework to model the day side and night side atmospheres of irradiated exoplanets using 1-D radiative transfer by incorporating a self-consistent heat flux carried by circulation currents (winds) between the two sides. The advantages of our model are its physical motivation and computational efficiency, which allows for an exploration of a wide range of atmospheric parameters. We use this forward model to explore the day and night side atmosphere of WASP-76~b, an ultra-hot Jupiter which shows evidence for a thermal inversion and Fe condensation, and WASP-43~b, comparing our …
We are entering the era of high-precision and high-resolution spectroscopy of exoplanets. Such observations herald the need for robust self-consistent spectral models of exoplanetary atmospheres to investigate intricate atmospheric processes and to make observable predictions. Spectral models of plane-parallel exoplanetary atmospheres exist, mostly adapted from other astrophysical applications, with different levels of sophistication and accuracy. There is a growing need for a new generation of models custom-built for exoplanets and incorporating state-of-the-art numerical methods and opacitie…
Atmospheric retrievals on exoplanets usually involve computationally intensive Bayesian sampling methods. Large parameter spaces and increasingly complex atmospheric models create a computational bottleneck forcing a trade-off between statistical sampling accuracy and model complexity. It is especially true for upcoming JWST and ARIEL observations. We introduce ExoGAN, the Exoplanet Generative Adversarial Network, a new deep learning algorithm able to recognise molecular features, atmospheric trace-gas abundances and planetary parameters using unsupervised learning. Once trained, ExoGAN is wid…
Context. Collecting a large variety of exoplanetary atmosphere measurements is crucial to improve our understanding of exoplanets. In this context, it is likely that the field would benefit from broad species surveys, particularly using transit spectroscopy, which is the most successful technique of exoplanetary atmosphere characterization so far. Aims: Our goal is to develop a model-unbiased technique using transit spectroscopy to analyze every qualified atomic spectral line in exoplanetary transit data, and search for relative absorption, that is, a decrease in the flux of the line when the …
Exoplanetary atmospheres retrieval via a quantum extreme learning machine
Università degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè（意大利帕尔马大学物理与化学系）；Dipartimento di Fisica e Astronomia “Galileo Galilei”, Università degli Studi di Padova（意大利帕多瓦大学伽利略·伽利莱物理与天文学系）；INAF Osservatorio Astronomico di Padova（意大利国家天体物理研究所帕多瓦天文台）
Transmission spectroscopy can be used to constrain the properties of exoplanetary atmospheres. During a transit, the light blocked from the atmosphere of the planet leaves an imprint in the light coming from the star. This has been shown for many exoplanets with different techniques, with both photometry and spectroscopy. We aim at testing chromatic line-profile tomography as a new tool to investigate exoplanetary atmospheres. The signal imprinted on the cross-correlation function (CCF) by a planet transiting its star is dependent on the planet-to-star radius ratio. We want to verify if the pr…
Transit observations in the helium triplet around 10830 Angstrom are a successful tool to study exoplanetary atmospheres and their mass loss. Forming those lines requires ionisation and recombination of helium in the exoplanetary atmosphere. This ionisation is caused by stellar photons at extreme ultra-violet (EUV) wavelengths; however, no currently active telescopes can observe this part of the stellar spectrum. The relevant part of the stellar EUV spectrum consists of individual emission lines, many of them being formed by iron at coronal temperatures. The stellar iron abundance in the coron…
Polarimetry is about to become a powerful tool for determining the atmospheric properties of exoplanets. To provide the basis for the interpretation of observational results and for predictive studies to guide future observations, sophisticated analysis tools are required. Our goal is to develop a radiative transfer tool that contains all the relevant continuum polarization mechanisms for the comprehensive analysis of the polarized flux resulting from the scattering in the atmosphere of, on the surface of, and in the local planetary environment (e.g., planetary rings, exomoons) of extra-solar …
This work presents theoretical studies which combine aspects of combustion and explosion theory with exoplanetary atmospheric science. Super Earths could possess a large amount of molecular hydrogen depending on disk, planetary and stellar properties. Super Earths orbiting pre-main sequence-M-dwarf stars have been suggested to possess large amounts of O2 produced abiotically via water photolysis followed by hydrogen escape . If these two constituents were present simultaneously, such large amounts of H2 and O2 can react via photochemistry to form up to about 10 Earth oceans. In cases where pho…
Sophisticated atmospheric retrieval algorithms, such as Nested Sampling, explore large parameter spaces by iterating over millions of radiative transfer (RT) calculations. Probability distribution functions for retrieved parameters are highly sensitive to assumptions made within the RT forward model. One key difference between RT models is the computation of the gaseous absorption throughout the atmosphere. We compare two methods of calculating gaseous absorption, cross-sections and correlated-$k$, by examining their resulting spectra of a number of typical \ce{H2}-He dominated exoplanetary an…
We present novel, analytical, equilibrium-chemistry formulae for the abundances of molecules in hot exoplanetary atmospheres that include the carbon, oxygen and nitrogen networks. Our hydrogen-dominated solutions involve acetylene (C$_2$H$_2$), ammonia (NH$_3$), carbon dioxide (CO$_2$), carbon monoxide (CO), ethylene (C$_2$H$_4$), hydrogen cyanide (HCN), methane (CH$_4$), molecular nitrogen (N$_2$) and water (H$_2$O). By considering only the gas phase, we prove that the mixing ratio of carbon monoxide is governed by a decic equation (polynomial equation of degree 10). We validate our solutions…
It has been posited that lunar eclipse observations may help predict the in-transit signature of Earth-like extrasolar planets. However, a comparative analysis of the two phenomena addressing in detail the transport of stellar light through the planet's atmosphere has not yet been presented. Here, we proceed with the investigation of both phenomena by making use of a common formulation. Our starting point is a set of previously unpublished near-infrared spectra collected at various phases during the August 2008 lunar eclipse. We then take the formulation to the limit of an infinitely distant o…
Within the context of exoplanetary atmospheres, we present a comprehensive linear analysis of forced, damped, magnetized shallow water systems, exploring the effects of dimensionality, geometry (Cartesian, pseudo-spherical and spherical), rotation, magnetic tension and hydrodynamic and magnetic sources of friction. Across a broad range of conditions, we find that the key governing equation for atmospheres and quantum harmonic oscillators are identical, even when forcing (stellar irradiation), sources of friction (molecular viscosity, Rayleigh drag and magnetic drag) and magnetic tension are in…
Thanks to the advances in modern instrumentation we have learned about many exoplanets that span a wide range of masses and composition. Studying their atmospheres provides insight into planetary origin, evolution, dynamics, and habitability. Present and future observing facilities will address these important topics in great detail by using more precise observations, high-resolution spectroscopy, and improved analysis methods. We investigate the feasibility of retrieving the vertical temperature distribution and molecular number densities from expected exoplanet spectra in the near-infrared. …
To understand the role that planet formation history has on the observable atmospheric carbon-to-oxygen ratio (C/O) we have produced a population of astrochemically evolving protoplanetary disks. Based on the parameters used in a pre-computed population of growing planets their combination allows us to trace the molecular abundances of the gas that is being collected into planetary atmospheres. We include atmospheric pollution of incoming (icy) planetesimals as well as the effect of refractory carbon erosion noted to exist in our own solar system. We find that the carbon and oxygen content of …
Transmission spectroscopy is an important technique to probe the atmospheres of exoplanets. With the advent of TESS and, in the future, of PLATO, more and more transiting planets around bright stars will be found and the observing time at large telescopes currently used to apply these techniques will not suffice. We demonstrate here that 2-m class telescopes equipped with spectrographs with high resolving power may be used for a certain number of potential targets. We obtained a time series of high-resolution FEROS spectra at the 2.2-m telescope at La Silla of the very hot Jupiter hosting plan…
We present an open-source and validated chemical kinetics code for studying hot exoplanetary atmospheres, which we name VULCAN. It is constructed for gaseous chemistry from 500 to 2500 K using a reduced C-H-O chemical network with about 300 reactions. It uses eddy diffusion to mimic atmospheric dynamics and excludes photochemistry. We have provided a full description of the rate coefficients and thermodynamic data used. We validate VULCAN by reproducing chemical equilibrium and by comparing its output versus the disequilibrium-chemistry calculations of Moses et al. and Rimmer & Helling. It rep…
The prevalence of clouds in currently observable exoplanetary atmospheres motivates the compilation and calculation of their optical properties. First, we present a new open-source Mie scattering code known as LX-MIE, which is able to consider large size parameters ($\sim 10^7$) using a single computational treatment. We validate LX-MIE against the classical MIEV0 code as well as previous studies. Second, we embark on an expanded survey of the published literature for both the real and imaginary components of the refractive indices of 32 condensate species. As much as possible, we rely on expe…
The atmospheres of the terrestrial planets are known to have been modified as a consequence of the impact degassing and atmospheric erosion during the late accretion. Despite the commonality of these processes, there are distinct gaps -- roughly two orders of magnitude -- between the abundances of noble gases and nitrogen in the present-day atmospheres on Venus, Earth, and Mars. The element partitioning on planetary surfaces is thought to be significantly different between the three planets ~4 Ga: the runaway greenhouse on Venus, the carbon-silicate cycle and ocean formation on Earth, and the …
We present a comprehensive study of the abundance of carbon dioxide in exoplanetary atmospheres in hot, hydrogen-dominated atmospheres. We construct novel analytical models of systems in chemical equilibrium that include carbon monoxide, carbon dioxide, water, methane and acetylene and relate the equilibrium constants of the chemical reactions to temperature and pressure via the tabulated Gibbs free energies. We prove that such chemical systems may be described by a quintic equation for the mixing ratio of methane. By examining the abundances of these molecules across a broad range of temperat…
Radiatively Controlled Thermal Stability of High-Altitude Clouds in Exoplanetary Atmospheres
Meikei Gakuen High School（明海学园高等学校）；Division of Science, National Astronomical Observatory of Japan（日本国立天文台科学部）；Graduate Institute for Advanced Studies, SOKENDAI（SOKENDAI高等研究院）
Optical phase curves have become one of the common probes of exoplanetary atmospheres, but the information they encode has not been fully elucidated. Building on a diverse body of work, we upgrade the Flexible Modeling System (FMS) to include scattering in the two-stream, dual-band approximation and generate plausible, three-dimensional structures of irradiated atmospheres to study the radiative effects of aerosols or condensates. In the optical, we treat the scattering of starlight using a generalisation of Beer's law that allows for a finite Bond albedo to be prescribed. In the infrared, we …
A major motivation of spectroscopic observations of giant exoplanets is to unveil planet formation processes from atmospheric compositions. Several recent studies suggested that atmospheric nitrogen, like carbon and oxygen, can provide important constrains on planetary formation environments. Since nitrogen chemistry can be far from thermochemical equilibrium in warm atmospheres, we extensively investigate under what conditions, and with what assumptions, the observable NH3 abundances can diagnose an atmosphere's bulk nitrogen abundance. In the first paper of this series, we investigate atmosp…
