Infrared Spectroscopy of Symmetric and Spherical Spindles for Space Observation 1. Pierre-Richard Dahoo

planetary missions.

      Moreover, the discovery in 1995 by Mayor and Quéloz (Nobel Prize in Physics 2019) of the first exoplanet, and the exponential number of discoveries of these celestial bodies ever since, opened the way for conducting the very first spectroscopic studies of their atmospheres. The coming new space instruments (JWST, ARIEL) will even be partially or entirely dedicated to the spectroscopic characterization of these extrasolar planets, the target being the research of biosignatures.

      However, using all these instruments and their large amounts of data requires significant upstream experimental and theoretical laboratory work, in order to record and model the spectra of many molecules. This may involve relatively complex organic molecules as well as simple molecules. Indeed, contrary to a preconceived idea, there is definitely still not enough modeling of the infrared spectrum of “small” molecules (CO₂, H₂O, CH₄, NH₃, etc.) in the current databases. In fact, the data needed by planetologists nowadays need to cover “extreme” conditions that were to a little extent, if at all, studied in the laboratory, that is: very high temperatures and pressures, molecules in confined environments, etc.

      The aim of this book is to review the theoretical knowledge required for understanding and modeling the spectra of two molecules that are essential in planetology, ammonia (NH₃) and methane (CH₄), and to provide the tools for their spectroscopic study in a confined environment, such as the clathrates.

      Vincent BOUDON

      Research Director (CNRS – French National Center for Scientific Research)

      Laboratoire interdisciplinaire Carnot de Bourgogne (ICB)

      January 2021

      Preface

      Infrared (IR) spectroscopic analysis is of fundamental interest for understanding the physics of the atmosphere and planets, as well as for the study of observable molecules in astrophysics. In the space field of space sciences or exploration, observations conducted by means of instruments at the ground level, or airborne by space probes or space telescopes, contribute to the discoveries that drive science forward or participate in observational sciences. The resulting database enables the confirmation or clarification of theoretical predictions that improve our understanding of the physical and chemical phenomena and processes in the surrounding environments. These observations are facilitated by technological advances and progresses both in the implementation of detection systems and in the analysis conducted by increasingly high-performance computers using ever better controlled statistical methods or theoretical models for the analysis of observational data. A recent example of black hole observation is worth mentioning:

      The Event Horizon Telescope (EHT) is a large telescope array consisting of a global network of radio telescopes and the EHT project combines data from several very-long-baseline interferometry (VLBI) stations around Earth with angular resolution sufficient to observe objects of the size of a supermassive black hole’s event horizon.

      The authors collaborating on the EHT project apply the methods that rely on the interference of electromagnetic waves using an array of instruments located at various sites on the Earth’s surface. The methods applied are increasingly sophisticated and require international collaborations for data collection, analysis and development in order to reveal the observed phenomenon.

      The diversity of discoveries contributes to advances in the field of astrophysics and cosmology, building a better understanding of the phenomena at the origin of the universe and addressing the nature and distribution of its constituents that are currently considered to be composed of below 5% visible matter, about 25% dark matter and 70% dark energy, which is responsible for a force that repels gravity and is believed to contribute to the expansion of the universe. Thanks to the analyzed data from space observations, astronomers and physicists have to improve the theoretical approaches, among which the following are worth mentioning: the cosmological model and Einstein’s equation in the general theory of relativity or the geometric theory of gravitation published in 1915 [EIN 15], and baryogenesis as an interpretation of the predominance of matter over antimatter [SAK 67]. Similarly, using automated and connected instruments, such as that of the Mars Perseverance Rover 2020 which was successfully launched on July 30, 2020, planetary exploration programs pave the way for observations and data analysis whose interpretation requires theoretical models adapted to various ranges of the electromagnetic spectrum, including IR spectroscopy, which is the focus of this volume.

      Theoretical and experimental spectroscopies contribute to the development of methods and devices for the observation and analysis of spectra corresponding to chemical species, molecules, radicals and ions in specific environments, as shown in Volumes 1 and 2 of the set Infrared Spectroscopy [DAH 17, DAH 19]. In the IR range, various types of instruments can be used for space observation, in order to detect molecules or chemical species (ions, radicals, macromolecules, nanocages, etc.) present in the atmosphere of planets, including the Earth, and their satellites, as well as in interstellar media, comets or exoplanets.

In molecular physics, the rovibrational energy levels of a molecule are calculated using the molecular Hamiltonian established by Wilson and Howard [WIL 36], reformulated by Darling and Dennison [DAR 40] and later simplified by Watson [WAT 68]. The contact transformation introduced by Van Vleck [VAN 29] is applied to determine the levels of vibration–rotation energy at different orders of approximation. The formalism of this method is described in Volumes 1 and 2, and its application is illustrated on diatomic and triatomic molecules. It was initially applied by Schaffer et al. [SCH 39a] and further improved by Nielsen, Amat and Goldsmith [AMA 57a, AMA 57b, AMA 58, GOL 56, GOL 57, NIE 51]. This method makes it possible to regroup the Hamiltonian in interacting polyads with the application of unit transformations, leading to a matrix form in blocks which is easier to diagonalize. Based on the method proposed by Watson [WAT 67, WAT 68b, WAT 68c] for the theoretical study of isolated states, Flaud and Camy-Peyret [FLA 81, FLA 90] showed that symmetry properties of nonlinear triatomic molecules (H₂O, O₃, etc.) can be used to build unitary transformations, leading to the transformation of the initial Hamiltonian into interacting blocks that could be linked to the experimental observations of interacting vibrational levels. Using similar methods developed in the field of IR spectroscopy, a study of ammonia and methane molecules in molecular physics was conducted by the research groups at the CNRS (French National Center for Scientific Research) laboratories in Paris and Dijon. The results obtained by these groups were shared in the PhD theses conducted in this field. The theses referred to in this volume are included in the references section. In particular, it is worth mentioning the theses of Moret-Bailly, Tarrago, Champion, Gherissi, Loëte, Coudert, Coquart, Boudon, Gabart and Permogorov [MOR 61,TAR 65, CHA 78, GHE 79, LOË 84, COU 86, COQ 94, BOU 95, GAB 96, PER 96], which are dedicated to the analysis of gas phase spectra and cover both cold and hot bands or combinations thereof. In this work, which is dedicated to the effects of an environment on the spectrum of an NH₃ or CH₄ molecule, as an example of symmetric or spherical tops, the cold bands are only addressed in situations where the degree of rotation is hindered either by a weak coupling (rotational motions limited to weak values of J) or a strong coupling (librational motions) depending on the type of environment, as studied in the theses of Abouaf-Marguin, Dubost, Gauthier, Boissel, Lakhlifi, Brosset and Dahoo [ABO 73, DUB 75, GAU 80, BOI 85, LAK 87, BRO 93, DAH 96].

      As mentioned in the preface to Volumes 1 and 2, the application of methods and tools of theoretical spectroscopy initially developed in molecular spectroscopy for the gas phase and adapted to environments in which the motion of the considered molecule is perturbed makes it possible to not only determine the structure of chemical species (in the gas, liquid or solid phase), but to also identify the species (atoms, molecules, molecular fragments, radicals, etc.) in various environments (nanocavities, media containing various species, ice surface, dust surface, etc.). The species themselves can be used as probes in order to characterize the environment (temperature, pressure, composition) and determine its nature based on theoretical models developed for the analysis