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date: 11 April 2021

# Hot Planetary Coronas

• Valery I. ShematovichValery I. ShematovichInstitute of Astronomy, Russian Academy of Sciences
•  and Dmitry V. BisikaloDmitry V. BisikaloInstitute of Astronomy, Russian Academy of Sciences

### Summary

The uppermost layers of a planetary atmosphere, where the density of neutral particles is vanishingly low, are commonly called exosphere or planetary corona. Since the atmosphere is not completely bound to the planet by the planetary gravitational field, light atoms, such as hydrogen and helium, with sufficiently large thermal velocities can escape from the upper atmosphere into interplanetary space. This process is commonly called Jeans escape and depends on the temperature of the ambient atmospheric gas at an altitude where the atmospheric gas is virtually collisionless. The heavier carbon, nitrogen, and oxygen atoms can populate the coronas and escape from the atmospheres of terrestrial planets only through nonthermal processes such as photo- and electron-impact energizing, charge exchange, atmospheric sputtering, and ion pickup.

The observations reveal that the planetary coronae contain both a fraction of thermal neutral particles with a mean kinetic energy corresponding to the exospheric temperature and a fraction of hot neutral particles with mean kinetic energy much higher than that expected for the exospheric temperature. These suprathermal (hot) atoms and molecules are the direct manifestation of the nonthermal processes taking place in the atmospheres. These hot particles populate the hot coronas, take a major part in the atmospheric escape, produce nonthermal emissions, and react with the ambient atmospheric gas, triggering the hot atom chemistry.

### Hot Planetary Corona: Description

Theories of planetary exospheres are based on ground-based and space observations of emission features such as the 121.6 nm Ly-$α$ and 102.6 nm Ly-$β$ hydrogen lines, the 58.4 nm helium line, and the 130.4 and 135.6 nm atomic oxygen lines. A hot atom corona is a part of the exosphere because the exosphere is populated by both thermal (with an origin from the high-energy tail of a Maxwellian distribution) and suprathermal (with an origin from nonthermal sources) atoms. The Mariner observations, for the first time, indicated the presence of hot hydrogen at Venus (see Figure 1; Anderson, 1976), whereas the Pioneer Venus UV spectrometer data established the presence of hot oxygen and carbon atoms there (Nagy, Cravens, Yee, & Stewart, 1981). Similar observations, together with in situ mass spectrometer measurements at Titan, allow reconstructing the density and temperature height profiles of the exospheric components there (De La Haye et al., 2007).

One of the brightest manifestations of the hot planetary corona is the formation of a hot oxygen corona around terrestrial planets. Oxygen atoms with excess kinetic energies are efficiently produced in the dissociative recombination of molecular oxygen ions, which are the most abundant in the upper layers of terrestrial thermospheres, so atomic oxygen is a preferable species to form the corona. Another important aspect related to oxygen is that it produces a lot of observational evidence. The transport of suprathermal oxygen atoms to exospheric heights leads to the formation of hot oxygen coronae around the terrestrial planets of Venus, Earth, and Mars (Johnson et al., 2008; Marov, Shematovich, & Bisikalo, 1996; Nagy et al., 1981; Shematovich, 2019; Shematovich & Marov, 2018; Shizgal & Arkos, 1996; Yee, Meriwether, & Hays, 1980). It has been well established by both observations and theoretical calculations that hot oxygen is an important constituent in the transition region between the upper thermosphere and the exosphere at the terrestrial planets.

The study of planetary coronas is based on direct observations and numerical simulations. The material there is present in a rarefied gas; therefore, production and transport of suprathermal particles into the corona requires solving a Boltzmann equation or a kinetic Monte Carlo simulation. The stochastic, kinetic Monte Carlo simulations have been widely used to investigate the formation, kinetics, and transport of suprathermal particles in the hot planetary coronae. This approach was first used to study the formation of the hot oxygen geocorona, taking into account the exothermic chemistry and the precipitation of magnetospheric protons and high-energy O+ ions from the planetary ring current region. It was found that only atmospheric sputtering results in the formation of an escaping flux of energetic oxygen atoms, which provides an important source of heavy atoms for the magnetosphere and geospace. A stochastic modeling approach was also applied to study the escape of hot oxygen atoms from the upper atmosphere of Mars and Venus; the kinetics and transport of suprathermal atoms and molecules in the hot oxygen corona at the Jovian satellite Europa (Shematovich, Johnson, Cooper, & Wong, 2005b), which is an example of a highly non-equilibrium near-surface atmosphere; and the hot extended corona at the Saturnian satellite Titan (Shematovich, Johnson, Michael, & Luhmann, 2003), which was directly measured by the spacecraft Cassini (De La Haye et al., 2007).

These observations and models required a different description of the uppermost atmospheric layers than that provided by the thermal, collisionless models of planetary exospheres (Chamberlain & Hunten, 1987). The presence of a hot atom component confirms the importance of nonthermal processes in planetary and satellite atmospheres (Johnson et al., 2008; Marov et al., 1996; Shematovich, 2019; Shematovich & Marov, 2018).

#### Suprathermal (Hot) Atoms and Molecules as a Source of Hot Corona

Suprathermal (or hot) atoms and molecules are generally considered to be particles with kinetic energies above 5–10 kT, where T is the temperature of an ambient atmospheric gas. Such energetic particles are produced in various physical and chemical processes whose products have an excess kinetic energy. In particular, they are produced by solar UV photon absorption and by electron impact collisions as well as in the exothermic chemical reactions induced by these external sources. If the production rate of these particles populating the range of suprathermal energies is high enough compared to the rate of their thermalization in elastic and inelastic collisions, then a stable fraction of these particles is formed. As it could be seen in Figure 2, this fraction can significantly perturb the local Maxwellian thermal energy distribution of the ambient atmospheric gas.

The main sources of suprathermal particles in the rarefied gas of planetary atmospheres are as follows: (a) the charge exchange between high-energy magnetospheric ions and neutral atmospheric gas components; (b) the dissociative recombination of molecular ions with ionospheric electrons; (c) the dissociation and dissociative ionization by UV solar radiation and high-energy electrons and ions of the magnetospheric plasma; (d) the exothermic chemical reactions; and (e) the sputtering (or knock-on) of the atmospheric gas by magnetospheric plasma.

The dissociative recombination, the dissociation by solar UV photons and energetic electrons, as well as the exothermic chemical reactions

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are accompanied by the release of energy of the order of several electronvolts (eVs). Part of this energy can be stored as the internal excitation of the reactions’ products. Although these external sources are the main carriers of the deposited energy, direct collisional transfer of energy to atmospheric gas is usually small compared to the indirect heating by exothermic chemical and ion–molecular reactions. These reactions result in the conversion of the original photon and electron energy into kinetic energy of the reaction products. Besides, because the suprathermal products of these exothermic reactions are chemically active, they induce subsequent atmospheric reactions with activation energies, thus heating the ambient atmospheric gas by elastic collisions (Johnson et al., 2008; Marov et al., 1996).

The charge exchange of high-energy ions and the sputtering of the atmospheric gas by high-energy ions of the magnetospheric plasma and ionospheric pickup ions can result in much higher energy, producing hot particles with energies up to several hundred eVs (Johnson, 1994):

$Display mathematics$(2)

The processes (Equation 2) are often the main sources of the escaping fluxes of neutrals from the planetary atmospheres, especially for Venus and the Earth.

The importance of understanding the role of suprathermal particles in the physics and chemistry of planetary and satellite upper atmospheres has grown significantly in the past decades (Johnson et al., 2008; Shematovich & Marov, 2018; Marov et al., 1996; Shematovich & Shematovich, 2019; Shizgal & Arkos, 1996; Wayne, 1993). In particular, hot particles produced in the upper atmospheric layers have been shown to play an important role in the chemistry and energetics of this region. Specifically, they do the following: (a) lead to local changes in chemical composition because the non-equilibrium rate coefficients of the chemical reactions (particularly with high activation energies) between suprathermal particles and an ambient atmospheric gas are much larger than those at thermal energies (Logan & McElroy, 1979; Shematovich, Bisikalo, & Gérard, 1994; Shizgal & Lindenfeld, 1979). Characteristic examples are the odd-nitrogen (see, e.g., Balakrishnan & Dalgarno [1999, 2003]) and odd-oxygen (see, e.g., Shematovich, Gérard, Bisikalo, & Hubert [1999]; Wayne [1993]) chemistries in the Earth’s atmosphere; (b) produce nonthermal atmospheric emission features (Gladstone et al., 2004; Hubert, Gerard, Cotton, Bisikalo, & Shematovich, 1999; 2015; Whipple, Van Zandt, & Love, 1975); and (c) form hot planetary coronas (Groeller, Lichtenegger, Lammer, & Shematovich, 2014; Nagy, Kim, & Cravens, 1990; Nagy & Cravens, 1988; Shematovich et al., 1994, 2003, 2005b) and enhance nonthermal atmospheric losses (Johnson et al., 2008; Shizgal & Arkos, 1996).

The produced suprathermal particles lose their excess kinetic energy in elastic and inelastic collisions with the ambient atmospheric gas: $Ath+Bhot(E)→Ahot(E′≤E)+Bhot(E″≤E−E′)$. If the hot particle density is small and they differ chemically from the ambient atmospheric gas, then thermalization can be treated in the linear approximation where it is assumed that the surrounding gas is in thermal equilibrium and that the perturbation of its state by suprathermal particles is small. However, if the production rate of hot particles is high, then a nonlinear kinetic model is needed. Collisional cooling is also essentially a nonlinear effect provided that fresh hot particles have the same chemical nature as the ambient atmospheric gas, because the incident and secondary particles cannot be separated. Subsequent collisions with the surrounding gas lead to a cascade of new hot particles, thus resulting in substantial perturbations of the thermal state of the atmospheric gas. The kinetics of hot particles can be described rigorously only at the microscopic level using the Boltzmann kinetic equation.

#### Kinetic Description of Suprathermal Particles

Let us assume the rarefied gas of a planetary upper atmosphere be composed of $αi,i=1,…,S$ atoms and molecules in a physical volume V. Each particle of the component $αi$ (an atom, a molecule, and/or their ion) has its own mass $mi$, position $ri∈V$, velocity $ci$, and set of quantum numbers $zi$ for each of the possible internal excitation levels. These chemically distinct components collisionally interact through $m=1,…,M>1$ chemical reactions in accordance with the dynamic schemes

$Display mathematics$(3)

For the generality of describing this chemically reactive system, the reactions (Equation 3) are considered as a collisional process that includes both elastic ($αi=αk$ and $αj=αl$), and inelastic ($αi=αk$, $αj=αl$, but $zi≠zk$ and/or $zj≠zl$) and chemically reactive ($αi≠αk$ and/or $αj≠αl$) collisions. The probabilities of reactions (Equation 3) are specified by the scattering functions $gijdσm=|ci−cj|σm(|ci−cj|,Ω)dΩ,$ where $σm$ are the differential scattering cross sections for reactions (Equation 3), $gij=|ci−cj|$ is the relative velocity, and $Ω$ is the solid angle of the scattering. Each channel of the collisional process (Equation 3) has the corresponding (elastic $σm(el)$, inelastic $σm(in)$, and chemically reactive $σm(r)$) scattering cross sections, with $σm=σm(el)+σm(in)+σm(r).$ The velocities $c′k$, $c′l$ of the product particles from reaction m can be determined from the laws of conservation of mass, momentum, and total energy of the interacting molecules, and their direction is determined by the probability density $dσm/σm,$ (Johnson, 1994).

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The evolution of a chemically reactive system at the microscopic level of description is defined by the system of Boltzmann kinetic equations together with the initial and boundary conditions for the atmospheric gas in the considered volume V subjected to the external force fields Y of the planet, and under the physical conditions that admit the validity of the assumptions of the gas rarefaction and finite or rapidly decreasing particle interaction radii in collisions (Marov et al., 1996; Shematovich, 2004, 2008). Here, the state of the gas is microscopically described by using the velocity and internal excitation state distribution functions for the gas particles $Fαi(t,r,c)=nαi(t,r,z)fαi(t,r,c)$, where $nαi(t,r,z)$ is the number density of the particles in the state z, and $fαi(t,r,c)$ is the single-particle velocity distribution function normalized to unity. The source functions $Qαi(t,r,c)$ specify the suprathermal particle production rates in the collisional processes (Equations 1 and 2). The collision integrals $Jmα$ on the right-hand sides of the kinetic equations describe the change in gas state due to the chemical reactions (Equation 3) and are written in the standard form (Marov et al., 1996; Shematovich, 2004, 2008).

The chemical kinetics of a rarefied atmospheric gas at the microscopic level of description is completely determined by means of the dynamical and probabilistic characteristics of atomic and molecular collisions (e.g., by the scattering functions and the distributions of the colliding particles in translational and internal degrees of freedom). The chemical evolution of the atmospheric gas with the production of suprathermal particles has a complex hierarchy of the kinetic rates of translational and internal energy exchange. The following characteristic cases can be distinguished (Shematovich, 2004, 2008):

a.

a mixed kinetic system with chemistry of suprathermal (hot) particlesa situation where suprathermal particles (hot subsystem) are a small admixture that weakly perturbs a thermal state of the ambient atmospheric gas (thermal subsystem); that is, the source functions in Equation 4 are much smaller than collision integrals. Thus, the thermal and hot subsystems are described by using the balance gasdynamic equations for the thermal components and the kinetic equations (Equation 4) for the suprathermal components, which contain the partially averaged collision integrals between particles of the different subsystems.

b.

a completely kinetic system with microscopic non-equilibrium kinetics—a situation where the characteristic microscopic and macroscopic timescales of the change in parameters for all gas components are comparable. In this case, the state of the gas is determined by the solution of the basic system (Equation 4) of nonlinear kinetic equations, and, accordingly, the distribution functions depend explicitly on time.

The state of gas in a planetary atmosphere is most faithfully described either by a mixed kinetic system, where the perturbations of the thermal state of the ambient atmospheric gas by suprathermal particles are small, or by a completely kinetic system (Equation 4) of Boltzmann equations, where these perturbations are significant. A very efficient approach to investigate such kinetic systems is the development of discrete mathematical models that use the probabilistic interpretation of collisions in an ensemble of model particles. The Direct Simulation Monte Carlo (DSMC) method (Bird, 1994) and its modification for studying kinetics of suprathermal atoms and molecules in the rarefied gas of planetary atmospheres (Marov et al., 1996; Shematovich, 2004, 2008) belong to this class of approaches.

#### Kinetic Monte Carlo Model for Suprathermal Particles

The following numerical approaches have been used to simulate nonthermal losses from planetary atmospheres (see, e.g., Johnson et al., 2008; Shizgal & Arkos, 1996):

a.

a two-stream method (Nagy & Cravens, 1988), where the phase space of escaping particles is divided into intervals in energy and direction of motion and the corresponding system of coupled algebraic equations for the fluxes of escaping particles is solved; this approach is commonly used only for systems with a weakly perturbed thermal state of the atmospheric gas,

b.

finite-difference methods that directly solve the Boltzmann kinetic equations for suprathermal particles (Kabin & Shizgal, 2002; Lie-Svendsen, Rees, Stamnes, & Whipple, 1991; Shizgal & Arkos, 1996); this approach is used only to analyze the local kinetics of the suprathermal particles,

c.

a test-particle Monte-Carlo method (Fox & Hac, 1997; Hodges, 2000; Ip, 1988; Lammer & Bauer, 1991); this approach is best suited also to the investigation of systems in which suprathermal particles perturb the thermal state of the gas only weakly, and

d.

a kinetic Monte Carlo simulation method (Marconi, Dagum, & Smyth, 1996; Shematovich, 2004; Shematovich et al., 1994), which modifies the Direct Simulation Monte Carlo (DSMC) method (Bird, 1994).

The kinetic Monte Carlo simulation method had been used to investigate the formation, kinetics, and transport of suprathermal particles for the hot planetary and satellite coronas by Shematovich et al. (1994, 1999, 2003, 2005a, 2005b). This approach was first used to study the formation of the hot oxygen geocorona (Bisikalo et al., 1995; Shematovich et al., 1994, 1999, 2005a), taking into account the exothermic chemistry (Gerard, Richards, Shematovich, & Bisikalo, 1995) and the precipitation of magnetospheric protons and high-energy O+ ions from the ring current. A kinetic modeling approach was also applied to study the hot hydrogen corona at Jupiter (Bisikalo et al., 1996) formed by electron precipitation and induced exothermic chemistry. These studies were extended to considering the formation of the hot oxygen corona at Europa (Shematovich et al., 2005b) and the hot nitrogen corona at Titan (Michael et al., 2005; Shematovich et al., 2003), created by atmospheric sputtering by the planetary magnetospheric and pickup ions.

##### A Numerical Kinetic Model for the Formation of a Hot Planetary Corona

A very promising approach is the development of discrete mathematical models that use the probabilistic interpretation of collisions in an ensemble of modeling particles. The DSMC method and its modification for studying non-equilibrium processes in the planetary atmospheres (Shematovich et al., 1994; Shematovich, Bisikalo, & Ionov, 2015) belong to this class of approaches. A stochastic discrete model to investigate the formation, kinetics, and transport of suprathermal particles in a planetary corona takes into account the following peculiarities of the atmospheric gas flow:

a.

the local mean free time and path for suprathermal particles gas should be taken as the characteristic time and space scales at the molecular level of describing the gas state in the planetary corona,

b.

the parameters of the atmospheric gas change strongly in a hot planetary corona from the collision-dominated regime of gas flow in the dense thermosphere to the virtually collisionless (free molecule) regime of flow in the exosphere, and

c.

significant differences between the densities of the suprathermal particles produced in the chemical and magnetospheric plasma sputtering processes and the density of the ambient atmospheric gas are commonly observed.

Therefore, the following approaches must be used in constructing a numerical model of hot planetary coronae: (a) the splitting of the solution of the basic kinetic system (Equation 1) in physical processes into the simulation steps for the suprathermal particle sources, the collisional thermalization of these particles, and the collisionless transport of suprathermal particles in the planetary corona on a discrete time scale; (b) the stochastic simulation of the formation of suprathermal particles and their local kinetics by using analog Monte Carlo algorithms with statistical weights; and (c) the calculation of the collisionless paths of suprathermal particles in the planetary corona by using finite-difference algorithms.

##### The Stochastic Kinetic Equation for Suprathermal Particles

Based on the theory of random processes, the evolution of the suprathermal particles in the atmospheric gas can be described by the following stochastic kinetic equation (Marov et al., 1996; Shematovich, 2004, 2008):

$Display mathematics$(5)

This equation is linear with respect to the probability density distribution $ϕ(X,t)$ for state $X$ of the gas at time $t$ and is called the stochastic (or master) kinetic equation for the chemical kinetics of a rarefied gas. Equation 5 describes the evolution of a homogeneous jump-like Markovian process (Marov et al., 1996; Shematovich, 2004, 2008).

##### The Analog Monte Carlo Method of Solving the Stochastic Kinetic Equation

The direct methods of solving the stochastic (master) kinetic equation consist in setting up and solving a system of equations for the probabilities of all possible paths of the state of a chemically reactive rarefied gas. Unfortunately, this direct procedure can be performed only for a few very simple chemical systems (Van Kampen, 1984) and involves enormous computational difficulties for real systems of chemical reactions. The Monte Carlo method, which consists of generating a sample of paths for the state of a chemically reactive gas, is an efficient tool for studying complex chemical systems in the stochastic approximation. The path generation procedure is much simpler: a sequence of transitions between the states of a chemically reactive gas and transition-separating times should be drawn based on the proper probability distributions. Such a procedure is an analog Monte Carlo algorithm for solving the stochastic kinetic equation (Equation 5). In the numerical realizations of the stochastic model, the following developments in the theory and practice of DSMC method were used:

a.

an effective approximation of the collision probabilities by the majorant frequency for choosing the next transition is used (Ivanov & Rogazinskij, 1988) when the collision probability for the selected pair is estimated from the maximum possible frequencies,

b.

the multichannel nature of the selected reaction is taken into account; the selected transition is treated as the simultaneous drawing of all possible (elastic, inelastic, and chemically reactive) channels, for each of which the corresponding weight, which is proportional to the ratio of the partial cross section for a given channel to the total cross section of the collisional process, is transferred, and

c.

since the algorithmic steps of including the suprathermal particles in accordance with the source functions, and drawing the collisional transitions are accompanied by the formation of new modeling particles, it is necessary to control the total number of modeling particles in the numerical model. An efficient method for this control is the so-called clustering of modeling particles (Rjasanow, Schreiber, & Wagner, 1998), where groups of modeling particles with similar parameters are combined into a single particle with accumulated weight. This procedure allows for control of the total number of modeling particles during the realization of the stochastic model.

### Progress in Modeling of Hot Coronas

The formation and loss to space of hot hydrogen, carbon, nitrogen, and oxygen atoms at terrestrial planets are mainly due to exothermic photochemistry. The photo- and electron-impact dissociation of molecules, as well as the dissociative recombination of the molecular ions, result in substantial densities of suprathermal H, C, N, and O atoms in the upper atmospheres of the terrestrial planets. These hot atoms, in turn, react with the ambient atmospheric gas, triggering hot atom chemistry such as odd-nitrogen and odd-oxygen chemistries in the Earth’s upper atmosphere (Balakrishnan & Dalgarno, 1999, 2003; Gerard, Bisikalo, Shematovich, & Duff, 1997; Kharchenko, Dalgarno, & Fox, 2005; Shematovich et al., 1999). Subsequently, the transport of suprathermal atoms to exospheric heights leads to the formation of hot atomic coronas around Venus, Earth, and Mars. It has been well established by both observations and theoretical calculations (see reviews by Johnson et al., 2008; Nagy et al., 1990; Shizgal & Arkos, 1996; and references within) that hot atoms are an important constituent in the transition region between the upper thermosphere and the exosphere at terrestrial planets.

A number of theoretical model calculations (Johnson et al., 2008) of hot hydrogen, carbon, nitrogen, and oxygen populations have appeared to compare with direct observations of hot oxygen. The presence of an extended neutral corona plays an important role in mass loading and slowing down the solar wind at Venus and Mars. The numerical analysis of the processes of formation, collisional kinetics, and transport of suprathermal atoms in the transition region of the upper atmosphere of the terrestrial planet is based on the solution of the Boltzmann kinetic equation (Shematovich et al., 1994, 1999, 2005b). In such models, it is important to use the differential cross sections because these molecular data are critical parameters in the calculations of the thermalization rate of suprathermal atoms in collisions with the ambient atmospheric gas. It is known that the calculated differential cross sections for elastic collisions of hot atoms with the main atmospheric constituents (O, N2, O2) are characterized by a strong peak at small scattering angles for energies below 5 eV. Consequently, it was found (Groeller et al., 2010; Krestyanikova & Shematovich, 2005, 2006) that such scattering angle distributions resulted in a lower rate of energy loss by the suprathermal oxygen atoms, and consequently, in higher escape rates as compared with the models utilizing an isotropic distribution of scattering angle in a hard sphere model of elastic collisions. This effect was also discussed in detail in the articles by Fox and Hac (2009, 2014).

#### Model for the O(1D) Distribution Function in the Earth’s Upper Atmosphere

Suprathermal metastable O(1D) atoms are produced in the Earth’s thermosphere as a result of photochemical exothermic processes in two ways: (a) photo- and electron impact dissociation of O2 molecules

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with a continuous kinetic energy spectrum up to energies of a few eV, and (b) as a dissociative recombination of O2+ ions (Kella, Johnson, Pedersen, Vejby-Christensen, & Andersen, 1997)

$Display mathematics$(7)

The second type of dissociation dominates in the nighttime thermosphere where it is believed also to be the main source of 630 nm of nightglow emission at the altitudes between 200 and 300 km. The presence of hot O(1D) is potentially detectable through the line profile of the O(3P)- O(1D) 630 nm emission. Indeed, a population of nonthermal O(1D) atoms will cause the departures from the Gaussian line profile associated with the Maxwellian distribution of the thermal atoms. Measurements of the Doppler width of the 630 nm airglow emission line have been extensively used to determine the thermospheric temperature (Hubert et al., 2001; Sipler & Biondi, 2003). This technique is based on the assumption that the bulk of the emitting O(1D) atoms are thermalized in the region of the airglow source (200–300 km). Therefore, the degree of thermalization of O(1D) in the daytime and nighttime airglow is a key issue, since the 630 nm emission is still extensively used to probe and map atmospheric temperatures and neutral winds from the ground or from space.

Hot O(1D) atoms formed in the processes (Equations 6 and 7) with the excess kinetic energies can either lose their energies gradually or be chemically quenched by collisions with the ambient thermal atmospheric gas. Note that hot atoms are continuously produced and suprathermal particles are present in the system at all characteristic times so that the steady-state energy distribution function of O(1D) atoms will be non-Maxwellian. In such an atmospheric system with continuous sources of translationally excited particles, the energy distribution functions are strongly disturbed, even in the local approximation (Shizgal & Lindenfeld, 1979). Since the O(1D) atoms have a long radiative lifetime ($A1D−1≈110s$), transport of these atoms in the thermosphere can be very important, especially at high altitudes. It leads to additional perturbations of the local thermal state. The thermalization rate of the hot O(1D) atoms is therefore determined by (a) the energy spectrum of the primary O(1D) atoms produced in the processes (Equations 6 and 7), (b) the collisional frequency with the ambient thermospheric gas, and (c) the chemical and radiative lifetimes. The thermalization rate is strongly dependent on the cross sections of the elastic, quenching, and excitation transfer processes. Collisions with thermal O(3P) atoms dominate the excitation transfer and thermalization of the hot O(1D) atoms. A complete analysis of the O(1D) kinetic energy distribution is quite a complex task and requires the use of the Boltzmann equation (Shematovich et al., 1999). This equation takes into account both the local kinetics and the transport of the thermal and hot O(1D) components:

$Display mathematics$(8)

where $F1D(c)$, and $Fi(c)$ are the distribution functions for O(1D) and the components of the ambient gas, respectively. In the right-hand part of Equation 8, the $Q1D(hot),Q1D(th)$ terms describe the sources of hot and thermal O(1D) atoms. The elastic, quenching, and excitation transfer collision terms, Jm , and the term of the spontaneous radiative decay with an Einstein coefficient, A1D, describe the sinks of O(1D) atoms. The atmospheric background gas consisting of O, N2, and O2 is characterized by local Maxwellian velocity distribution functions. The solution of Equation 8 with the kinetic Monte Carlo model (Shematovich et al., 1999) provided the energy distribution functions of O(1D) atoms resulting from the thermalization of suprathermal oxygen atoms formed in the processes of Equations 6 and 7 and the set of exothermic ion–molecular reactions. The calculated energy distribution functions shown in Figure 3 demonstrate that the O(1D) atoms are not fully thermalized in the region of the 630 nm emission excitation. It was found (Hubert et al., 2001; Shematovich et al., 1999) that O(1D) temperature deviates

from the background gas temperature not only in the upper thermosphere (above 300 km) but also in the region of the bulk 630 nm emission. At 300 km for low solar activity conditions, the model predicts an excess O(1D) temperature of 180 K during daytime and 950 K at night. The temperature deviation persists at lower altitudes as a result of the major contribution of the O2+ ion dissociative recombination source of hot O(1D) atoms. Experimental evidence based on the Fabry-Perot interferometer measurements on board the Dynamics Explorer satellite confirms the existence of an O(1D) temperature excess over the mass spectrometer and incoherent scatter (MSIS) value (Hubert et al., 2001; Sipler & Biondi, 2003). It was found that the temperatures deduced from the 630 nm airglow line profile width may significantly exceed the ambient gas temperature in a way depending on solar activity, local time, and observation geometry.

In the study by Kharchenko et al. (2005), the detailed calculations of the sources of suprathermal metastable O(1D) atoms in the atmosphere at altitudes between 80 km and 200 km were carried out, and the corresponding energy distribution functions were derived taking into account the energy transfer and quenching in collisions of the metastable atoms with the ambient atmospheric gas constituents. It was found that the suprathermal O(1D) atoms comprise 4–6% of the whole O population, and their effective temperatures are larger by 25–46% than the local temperatures of the ambient gas.

#### Common Features of Hot Oxygen Coronas at Terrestrial Planets

The upper atmospheres of the terrestrial planets (Venus, Mars, and the Earth) are very different in composition and extent as well as the amount of interaction they experience with the solar UV radiation and plasma of the solar wind. To illustrate the studies of suprathermal particle’s role in the aeronomy of planetary atmospheres, the kinetics of atomic oxygen was considered, which is the main constituent of the upper layers of the terrestrial planet atmospheres. It has been well established by both observations (Nagy et al., 1981; Yee et al., 1980) and theoretical calculations (see reviews by Johnson et al., 2008; Nagy et al., 1990; Shizgal, & Arkos, 1996; and references within) that hot oxygen is an important constituent in the transition region between the upper thermosphere and the exosphere at terrestrial planets.

An investigation of the chemically produced hot oxygen coronae at Venus, Earth, and Mars was conducted using a stochastic modification of the DSMC method (see, e.g., reviews by Fox & Hac, 2014; Marov et al., 1996; Shematovich & Marov, 2018; Shizgal & Arkos, 1996) to analyze the processes of formation, collisional kinetics, and transport of suprathermal oxygen atoms formed in the dissociative recombination of O2+ ions in the transition region of the terrestrial upper atmospheres. In studies (Fox & Hac, 1997, 2014; Groeller et al., 2010, 2014; Krestyanikova & Shematovich, 2005, 2006; Shematovich, 2013, 2017; Shematovich, Bisikalo, & Gérard, 2005a), the energy distributions of hot O in the upper atmospheres of terrestrial planets were recalculated using realistic differential cross sections (Kharchenko et al., 2000). Results are presented in Figure 4 showing, for example, that Venusian corona contains a significant hot O component. These hot O atoms populate the hot corona but do not escape from the Venusian atmosphere.

The hot oxygen corona (Shematovich et al., 1994; Shizgal & Arkos, 1996) at Earth is a source region of energetic neutral atoms (ENA). It contributes to the maintenance of the nighttime ionosphere, plays a role in the formation of the escape flux of neutral atoms, and controls the energetic ion populations in the thermosphere. The role of the auroral sources induced by electron and proton precipitation in the formation of the hot oxygen corona was studied for the Earth’s polar upper atmosphere by Shematovich, Bisikalo, and Gérard (2005a, 2006) and for the Martian atmosphere by Shematovich (2017).

The process of precipitation of auroral electrons results in the excitation, dissociation, and ionization of the atmospheric species, and has been added to the main set (Equations 6 and 7) of exothermic chemistry. Interactions of precipitating energetic protons of magnetospheric origin with the main atmospheric constituents include momentum and energy transfer in elastic and inelastic collisions, ionization of target atmospheric molecules and atoms, charge transfer, and electron capture collisions. Energetic H atoms produced by proton impact further collide with the main atmosphere constituents, transferring their momentum and kinetic energy to atmospheric particles by elastic and inelastic collisions, ionization, and stripping processes. Consequently, the interaction of the precipitating protons with the main neutral thermospheric constituents must be considered as a cascade process producing a growing set of translationally and internally excited particles of the ambient atmospheric gas. This process is known as ion-induced atmospheric sputtering (Johnson, 1994). To analyze the penetration of energetic H+/H into the auroral atmospheric gas, the kinetic Boltzmann equations are used (Gerard, Hubert, Bisikalo, & Shematovich, 2000). These coupled equations take into account both scattering and transport of the high-energy H+/H flux in elastic, inelastic, ionization, and charge transfer collisions with the ambient atmospheric gas. One of the consequences of the penetration of a high-energy H+/H flux into the upper atmosphere is the production of suprathermal oxygen atoms, $Oh$, by momentum transfer via elastic and inelastic collisions between the penetrating H+/H beam and atmospheric thermal oxygen $Oth:H+(H)+Oth→H+(H)+Oh$. Upward-moving hot oxygen atoms populate the corona and the fraction of their population with energies higher than the escape energy forms the nonthermal escape flux.

In the studies by Shematovich et al. (2005a, 2006), it was found that both electron precipitation through exothermic chemistry and proton precipitation through atmospheric sputtering significantly contribute to the population of the hot oxygen geocorona. The energy distribution functions for suprathermal oxygen atoms at 700 km for the daytime cusp in the polar upper atmosphere of the Earth are shown in Figure 5. From these calculations, it is seen that the energetic O atoms from the suprathermal tail of the local Maxwellian distribution mainly populate the hot oxygen corona at exobase altitudes. For the energies higher than several eV, nonthermal processes (exothermic chemistry and atmospheric sputtering) become dominant sources of hot atoms. It is important that only atmospheric sputtering results in the formation of the escape flux (with the kinetic energies higher than 10 eV) of energetic oxygen atoms, providing an important source of heavy atoms for the magnetosphere.

The exothermic chemistry induced by electron precipitation and by absorption of solar UV radiation is operating continuously in the polar upper atmosphere. It results in a steady-state populating of a very near-Earth environment by suprathermal oxygen atoms with energies below a few eVs. In contrast, atmospheric sputtering by the magnetospheric protons provides a more variable contribution, strongly coupled with the cusp region. It produces more energetic oxygen atoms that populate the external regions of the hot oxygen geocorona. The results of model calculations are in good agreement with the analysis (Moore & Horwitz, 2007; Wilson & Moore, 2005) of the low-latitude perigee LENA (Low Energy Neutral Atom) instrument images on board the IMAGE spacecraft, showing that the instrument signal is produced by the low- to medium-energy (5–30 eV) oxygen atoms generated in and near the cusp region. The more energetic

(> 30 eV) fraction of suprathermal oxygen atoms produced by ion-induced atmospheric sputtering could be responsible for the energetic neutrals observed by the instrument far away from the cusp or oval regions. The total escape flux of oxygen atoms associated with atmospheric sputtering by protons is found to be about 8 × 1023 s−1; therefore, this mechanism may provide a substantial contribution to the magnetospheric oxygen population (Seki, Elphic, Hirahara, Terasawa, & Mukai, 2001).

The common features of hot oxygen coronas at Venus and Earth are the following: Coronas are populated due to exothermic chemistry induced by photon and electron impact, but neutral oxygen loss to space is mainly due to sputtering (Johnson, 1994; Johnson et al., 2008). However, for Mars, both the photochemistry and sputtering are responsible for the hot oxygen corona population and escape from the atmosphere (Jakosky et al., 2018; Johnson et al., 2008).

#### Hot Oxygen Corona at Mars

It has been known for decades that atmospheric escape is important for the evolution of terrestrial planets in the solar system, although how atmospheric escape changes their atmospheres is still under investigation and discussion. The dissipation timescales of protoatmospheres, which were captured from the protosolar nebula during formation, are short for all terrestrial planets (Massol et al., 2016). After the loss of protoatmospheres, terrestrial planets underwent different evolutionary paths. The evolution of planetary atmospheres can only be understood if one considers that the radiation and the particle environment of the Sun have changed during their lifetimes. Present-day satellite observations and theoretical studies show that enhanced solar EUV radiation and plasma flows (e.g., winds and coronal mass ejections [CMEs]) result in a continuous forcing of the upper layers of planetary atmospheres, which can be ionized, heated, expanded, chemically modified, and eroded during an early phase of a planetary lifetime.

An important aspect of solar forcing on unmagnetized planets is their atmospheric evolution. The history of Mars’ atmosphere is important for understanding the geological evolution and potential habitability of the planet (Brain, Bagenal, Ma, Nilsson, & Stenberg Wieser, 2017; Jakosky et al., 2018). Mineralogical evidence suggests that liquid water was abundant on early Mars, and geological evidence reveals that it was present at the surface for sufficiently long periods of time to change the presently observed terrain. The present Martian atmosphere lacks sufficient greenhouse warming to support liquid water at the surface because the atmosphere has undergone fundamental change over the past several billion years. Gases are currently being lost from Mars’ atmosphere to space (Johnson et al., 2008; Shizgal & Arcos, 1996), potentially in quantities sufficient to change the planet’s climate (Chassefiиre & Leblanc, 2004; Lillis et al., 2015, 2017).

The NASA Mars Atmosphere and Volatile Evolution (MAVEN) mission orbiting Mars quantifies the amount of gas lost to space over time (Jakosky et al., 2015a; Lillis et al., 2015). Processes that strip gas to space preferentially remove the lighter isotopes, leaving the remaining atmosphere enriched in the heavier isotopes (Chamberlain & Hanten, 1987). The amount of gas lost to space through time was estimated using MAVEN measurements of the upper atmosphere structure, which allowed the derivation of the distribution structure of the isotope pair 38Ar/36Ar ratio between the homopause and exobase altitudes (Jakosky et al., 2017). Fractionation of argon occurs as a result of the loss of gas to space by the pickup-ion sputtering mechanism, which preferentially removes the lighter isotope. The measurements require that 66% of atmospheric argon has been lost to space (Jakosky et al., 2017). Thus, a large fraction of Mars’ atmospheric gas has been lost to space, contributing to the transition in climate from an early, warm, wet environment to today’s cold, dry atmosphere. The MAVEN observations suggest that a large fraction of the Martian volatile inventory has been lost to space, and this was an important process for the evolution of the Martian atmosphere through time (Jakosky et al., 2018). Altogether, the Martian hot C, N, and O coronas are the important regions where the escaping fluxes of atomic carbon, nitrogen, and oxygen are formed (Johnson et al., 2008).

##### Neutral and Plasma Environments of Mars

The neutral and plasma environments of Mars are strongly coupled (Bougher, Cravens, Grebowsky, & Luhmann, 2015). The Martian upper atmosphere, at altitudes ranging from the dense thermosphere to the collisionless exosphere, which is the main reservoir for hot atom formation, is coupled with both (a) the lower atmosphere (due to gravity waves, planetary waves, and dust storms) and (b) the solar wind via the ionosphere (due to ion sputtering and volatile escape) (see, e.g., Lillis et al. [2015] and references therein). Consequently, the dynamics and chemistry of lower layers strongly influence the vertical structure and the chemical composition of the thermosphere and, therefore, the hot atom distribution. On the topside, at the solar wind interface, various processes of energy, momentum, and mass exchange are at work. Escape occurs by thermal (Jeans escape for hydrogen) and nonthermal (photochemical escape, sputtering, and ion loss) mechanisms.

The Mars Global Surveyor mission added new, fundamental elements to the understanding of the Mars system. The discovery of the crustal magnetic field (Acuña et al., 1998) shows that at the beginning of its history, Mars developed an intrinsic magnetic field, but the primitive dynamo rapidly vanished about 3.7 Gyr ago. An important implication of the early vanishing of the Martian dynamo is the collapse of its magnetosphere, which certainly favored escape of its atmosphere by sputtering processes or by ion outflows resulting from a direct interaction with the solar wind. Plausibly, the terrestrial magnetosphere, which protects Earth’s atmosphere and hydrosphere from the erosive effect of the solar wind, has played a major role in the retention of volatiles and, therefore, in the development and maintaining of climate and life on Earth. In contrast, the Mars atmosphere directly interacts with the solar wind, which results in intense erosion.

The Martian atmosphere and exosphere alter the incoming energetic solar wind plasma by (a) mass loading the solar wind with newly created ions, produced mainly by photoionization, and solar wind electron impact ionization of the atmospheric gases, and (b) undergoing charge exchange collisions with solar wind ions. Charge exchange between an energetic ion and a cold atmospheric atom produces an energetic neutral atom (with energy E >> 1 eV) and an ionized thermal gas particle. The charge exchange processes result in creation of fast hydrogen and oxygen energetic atoms. Thus, such energetic atoms carry information about the properties of ions at the site where they were formed. From the ESA Mars Express and NASA MAVEN (Mars Atmosphere and Volatile EvolutioN) observations of energetic neutrals (Jakosky et al., 2015b; Lundin et al., 2004), it was established that solar wind plasma penetrates fairly deep into the Mars ionosphere and atmosphere, occasionally down to altitudes of ~270 km. Therefore, acceleration processes responsible for the loss of ionospheric ions may go deep into the ionosphere, with the planetary wind from the dayside region sweeping tailward at altitudes as low as 270 km. Accelerated or outflowing heavy ions (mainly O+) with an energy of several keV were found at 300 km in altitude. The observed planetary wind also comprises molecular species, mainly heavy molecular ions of CO2+ and O2+. This is consistent with the ionospheric ion energetization processes that reach low altitudes. The origin of escaping molecular and atomic ions is related with the photochemistry of the Martian upper atmosphere and in the hot oxygen corona, respectively. Moreover, an indirect signature of the Martian hot oxygen corona was fixed for the first time by the ALICE/ROSETTA instrument (Feldman et al., 2011) and confirmed by the Imaging Ultraviolet Spectrograph (IUVS)/MAVEN (Deighan et al., 2015).

##### Photochemical Sources

McElroy (1972) suggested that a hot oxygen population is likely to be present at Mars. The hot O atoms are produced primarily by the dissociative recombination of the molecular ions O2+ (Equation 7). This process is thought to determine the current loss rate of neutral oxygen to space (Fox & Hac, 1997; Groeller et al., 2014; Hodges, 2000; Krestyanikova & Shematovich, 2005, 2006; Lammer & Bauer, 1991; McElroy, 1972; Nagy et al., 1990). Oxygen atoms are produced in states 3P, 1D, and 1S, and the excess energy yields of the reactions (Equation 8) change in the range of 0.84–6.99 eV. In the current advanced models of the ionosphere and thermosphere of Mars (Bougher et al., 2015; Fox & Hac, 2009; Krasnopolsky, 2002), the ionospheric chemistry is calculated by taking into account the solar radiation model that was extended to include the recently measured soft X-rays (K. Tobiska S2K v1.24 model). Coupled ionosphere and thermosphere models of Mars provide important input parameters, allowing the calculation of the distribution of hot C, N, and O atoms in the upper atmosphere and the estimation of the implications for photochemical escape of atomic species from the atmosphere.

Lammer and Bauer (1991) used a test-particle Monte Carlo method to calculate the distribution of hot O in the Mars corona. After new data on the probabilities and yields of possible channels of O2+ dissociative recombination became available (Kella et al., 1997), Kim, Nagy, Fox, and Cravens (1998) recalculated the radial one-dimensional distribution of hot oxygen in the Mars upper atmosphere using a two-stream model. Hodges (2000) used a test-particle Monte Carlo approach to calculate a three-dimensional global distribution of hot oxygen at Mars. In both calculations of a hot oxygen corona at Mars, a hard sphere model of elastic collisions was used, and heating of the ambient atmospheric gas by hot atoms was not considered. The recently initiated investigation by Krestyanikova and Shematovich (2005, 2006) of the chemically produced hot oxygen corona at Mars uses a spherically symmetric (one-dimensional) approach in order to reduce the shortcomings of previous models. The numerical analysis of the processes of formation, collisional kinetics, and transport of suprathermal oxygen atoms formed in the dissociative recombination of O2+ ions in the transition region of the upper atmosphere of Mars is based on the solution of the Boltzmann kinetic equation (Shematovich et al., 1994, 1999, 2003). Since the Boltzmann kinetic equation for suprathermal atoms is a complex integro-differential equation, instead of solving it directly, a stochastic modeling approach for kinetic systems (Shematovich, 2004) was used. In this method, the flow of suprathermal particles in the transition region of the upper atmosphere of Mars is represented by a system of model particles. Since the state of the gas in the planetary corona is examined at the microscopic level, the collisional mean free-path for suprathermal particles near the lower boundary of the transition region is considered as a characteristic scale. Since the temperature of the Martian exosphere ranges from 200 to 360 K, depending on the solar activity level (Krasnopolsky, 2002), atoms with kinetic energies above 0.08–0.1 eV were treated as suprathermal. The region of interest covers the altitudes from 90 to 1000 km in the Mars atmosphere. As a lower boundary, an altitude of the relatively dense thermosphere where suprathermal particles quickly lose their excessive kinetic energy via collisions with thermal molecules of carbon dioxide and oxygen. An upper boundary is chosen to be well above the exobase (~ 200 km). Model O atoms are born in each cell in accordance with the local rate of dissociative recombination of O2+ ions. These fresh suprathermal O atoms move in the gravitational field of Mars and lose their energy via collisions with the atmospheric gas, producing secondary suprathermal atoms and molecules.

Of special interest are the differential cross sections because these values are critical parameters in the calculations of the thermalization rate of suprathermal oxygen atoms in collisions with the ambient atmospheric gas. The calculated differential cross sections for Ohot—O, N2, and O2 collisions (Balakrishnan, Kharchenko, & Dalgarno, 1998; Kharchenko et al., 2000) are used, and their energy-dependent distributions are characterized by a strong peak at small scattering angles for the energies below 5 eV. It was found that such scattering angle distributions result in a lower rate of energy loss by the suprathermal oxygen atoms, and consequently, in the higher escape rate (Fox & Hac, 2009, 2014; Krestyanikova & Shematovich, 2005) as compared with the models utilizing an isotropic distribution of scattering angle under the hard sphere approximation of elastic collisions (Hodges, 2000; Kim et al., 1998; Lammer & Bauer, 1991).

It is worth noting here that the modeling, which is implemented at the molecular level, leads to the accumulation of detailed statistics regarding the velocity (kinetic energy) distribution of suprathermal particles. Figure 6 convincingly shows that the dissociative recombination of O2+ ions results in a substantial population of suprathermal O atoms, which is located between two vertical lines in Figure 6. This energy range is populated by oxygen atoms with energies just below the escape energy (~ 2 eV for Mars, right vertical line), which move on parabolic and elliptic trajectories and constitute the hot oxygen corona at Mars.

The calculated density distribution in the corona is shown in the upper panel of Figure 7. One can see that the main fraction of the hot corona at heights below the exobase (~200 km) is represented by atmospheric oxygen atoms from the suprathermal energy range of the local Maxwellian distributions. At the same time, above the exobase, the main input is from the nonthermal hot O atoms, that are formed by the dissociative recombination and reach exospheric heights. The total distribution of hot oxygen in the corona is shown by the solid line in Figure 7(upper panel) and indicates a much greater scale height than the ambient atmospheric gas. A comparison with earlier models (Nagy & Cravens, 1988; N&C88 in Figure 7) and (Lammer & Bauer, 1991; L&B91 in Figure 7) of the Martian hot oxygen corona is given in the bottom panel of Figure 7. It is seen that the calculation in the Krestyanikova and Shematovich (2005, 2006) distribution differs from the earlier models by exhibiting a greater scale height. This is a direct consequence of using updated and more realistic differential cross sections with small scattering angle distributions for elastic and inelastic collisions between suprathermal oxygen and atmospheric species. The hot oxygen distribution is also characterized by higher kinetic energies.

It is currently accepted that photochemical escape of atomic oxygen is one of the dominant channels for Martian atmospheric loss, and it plays a potentially major role in the climate evolution of the planet (Jakosky et al., 2015b; Lillis et al., 2015; McElroy, 1972). In recent studies (Cravens et al., 2017; Leblanc et al., 2017; Lillis et al., 2017), the measurements by three MAVEN instruments—Langmuir Probe and Waves, Neutral Gas and Ion Mass Spectrometer, and SupraThermal and Thermal Ion Composition—were utilized to calculate the photochemical escape fluxes of atomic oxygen. The average dayside hot O escape rates in the range from 1.2 to 5.5 × 1025 s−1, depending on a season and the EUV flux, were derived from these MAVEN measurements. These estimates are generally consistent with several pre-MAVEN predictions (Fox & Hac, 2009, 2014; Groeller et al., 2014; Valeille, Bougher, Tenishev, Combi, & Nagy, 2010a; Valeille, Combi, Tenishev, Bougher, & Nagy, 2010b). Hot O escape fluxes do not vary significantly with the dayside solar zenith angle or crustal magnetic field strength but depend on CO2 photoionization frequency with a power law whose exponent is an unexpectedly high value of 2.6 ± 0.6, which may be partially due to seasonal and geographic sampling (Cravens et al., 2017; Lillis et al., 2017). From this dependence and historical EUV measurements over 70 years, a modern-era average escape rate of 4.3 × 1025 s−1 was estimated. Extrapolating this dependence to early solar system EUV conditions give (Lillis et al., 2017) the total losses of 13, 49, 189, and 483 mbar of oxygen over 1–3 and 3.5 Gyr, respectively, with the uncertainties significantly increasing with time in the past.

##### Atmospheric Sputtering

Precipitating oxygen ions can cause massive sputtering of the Martian atmosphere (Johnson & Luhmann, 1998; Luhmann & Kozyra, 1991; Luhmann, Johnson, & Zhang, 1992). These O+ ions of exospheric origin are accelerated by the solar wind and the interplanetary magnetic field. Pickup ions follow helical trajectories along the interplanetary magnetic field lines draped across Mars and can either be swept away or reimpact the atmosphere with significant amounts of energy (up to 1 keV). Through momentum transfer collisions they can excite other atmospheric atoms and molecules, thus enhancing the escape and population of the hot corona (Johnson, 1994). Sputtering differs from the dissociative recombination, as it is nonselective and can, in principle, eject all particles that are present at the Martian exobase, that is, C, O, CO, N, N2, and CO2 (Kass & Yung, 1999; Leblanc & Johnson, 2002). Solar wind and solar energetic particle sputtering have been shown to be small compared with pickup ion sputtering (Leblanc et al., 2002, 2017). In the present epoch, the loss rate of O and CO2 sputtered by O+ ions has been estimated to reach up to 5.0 × 1024 atoms (Chassefiиre & Leblanc, 2004; Leblanc et al., 2017), which is smaller than the photochemical escape of the hot oxygen atmospheric component.

The most recent models of atmospheric sputtering were developed by Leblanc, Luhmann, Johnson, and Chassefiere (2002), Leblanc et al. (2017), and Chaufray et al. (2007). They took into account the three-dimensional effects of pickup ion sputtering at Mars, but the atmosphere was represented there solely by atomic oxygen. To account for the atmospheric molecular species—CO, CO2—a one-dimensional test-particle Monte Carlo model was used together with a molecular dynamics model of collisions involving molecules (Leblanc & Johnson, 2002). There are several sources of uncertainty in the estimates of the sputtering effect on the Martian atmosphere such as the energy spectra of ionospheric pickup ions and the energy dependences of differential cross sections for the collisions of high-energy ions with atmospheric species. Furthermore, Johnson and Luhmann (1998) described the importance of feedback in determining escape and in modeling the oxygen corona; that is, an inflated corona which can, in principle, lead to greater loss rates and higher pickup ion production, but those are mitigated by the fact that the solar wind plasma will be deflected at larger distances from the Martian exobase, reducing coronal heating and expansion. This feedback process may be critical for quantifying the loss of atmosphere in earlier epochs.

##### Ion Escape and Ionospheric Outflow

Massive plasma escape through the magnetotail region of Mars, which was detected from the plasma instruments aboard the Phobos 2 spacecraft (Lundin et al., 1989), is a very important loss mechanism at Mars and is the only flux of escaping material ever measured there. Without shielding by the planetary magnetic field, the solar wind plasma transfers momentum to atoms and ions on high ballistic trajectories, and they can be swept away from the planet by the solar wind. There are two main sources for the pickup of new ions by the solar wind. The first source is ionization of neutral particles inside the corona by UV photons, electron impact, or charge exchange (Luhmann & Kozyra, 1991; Luhmann et al., 1992). Such a flux is composed mainly of O+, H+, and C+. The second source is the ionospheric planetary wind; that is, the outflow of ions produced above the photochemical equilibrium region and below the ionopause (Kar et al., 1996; Rahmati et al., 2014). Coupled ionosphere and thermosphere models of Mars (Bougher et al., 2015; Krasnopolsky, 2002) place constraints on atmospheric loss through ion outflow because the relative rates of ion loss are determined by ion-neutral chemistry. The inclusion of exothermic chemistry results in the production of hot atoms through the processes that involve ions, such as the dissociative recombination of O2+, N2+, CO+, and NO+, which yields fragments of various energies, often exceeding the escape energy for Mars. Ions other than N2+ are formed mostly or partially by ion–molecule reactions. Except for NO+, the ions may also be destroyed by ion–molecule reactions. Since many ions react with H2, its density profile is important in determining the photochemical escape of heavy ions (Lillis et al., 2017; Rahmati et al., 2017). A recent three-dimensional MHD model (Ma, Nagy, Sokolov, & Hansen, 2004; Ma et al., 2015), which incorporated both ion sources, shows that the escape flux is mainly composed of O+2, with only 10–25% of O+ probably originating from the corona. The loss rate of oxygen due to the ionospheric escape is estimated to be up to 2.8 × 1024 s−1 (Ma et al., 2004). Other ions like CO+2, CO+, and C+ are also expected to escape through ionospheric outflow (Ma et al., 2004, 2015). Moreover, the solar wind interaction with the Martian upper atmosphere during the March 8, 2015 interplanetary coronal mass ejection (ICME) was studied in Dong et al. (2015) by using a global multifluid MHD model (Ma et al., 2015). The total ion escape rate was found to increase by an order of magnitude, from 2.05 × 1024 s−1 (pre-ICME phase) to 2.25 × 1025 s−1 (ICME sheath phase), during this time period. Two major ion escape channels were inferred: the accelerated pickup ion loss through the dayside plume and ionospheric ion loss through the nightside plasma wake region (Jakosky et al., 2015b). Interestingly, both simulation and observational results indicate that there is no significant variation in the Martian ionosphere (at altitudes ≲ 200 km; i.e., in the photochemical region) during this event.

### Conclusion

A short review of modern (to date of this article) theoretical models describing hot planetary coronas for the solar system planets is presented here. The article does not pretend to be complete because the problem is very wide and still remains under extensive research by many scientific groups while the new observational data are coming. The main goal of the article is to outline most of the important physical processes and present most of the advanced models of hot planetary coronas. The main focus is on the theoretical side of the problem in order to give the reader a picture of the complicated nature of these objects, hidden under limited astronomical data. The hot oxygen corona at Mars was considered as a Rosetta Stone for such models.

The Martian thermosphere, exosphere, and ionosphere form the tenuous upper boundary—hot planetary corona—the region through which all energy and matter from the Sun that encounters Mars must either pass or be deflected. The Martian neutral corona, ionosphere, and crustal magnetic fields interact directly with the incident solar wind plasma, forming a highly dynamic induced magnetosphere that influences the structure and variability of the upper atmosphere and results in a bunch of plasma processes. Further, the energy input to the atmosphere from the Sun and solar wind energizes atmospheric particles, giving some of them sufficient energy to escape the planet. The close proximity of the solar wind to the Martian ionosphere, as well as the considerable extent of the exosphere relative to the size of the planet, leads to a number of atmospheric escape processes for both neutral and ionized particles. Neutral particles may have sufficient energy to escape on their own by virtue of their thermal distribution (Jeans escape). They may receive the energy necessary to escape from the sunlight and subsequent chemical reactions (photochemical escape) or from collisions with particles entering the atmosphere from above (e.g., by sputtering and/or precipitation). Escape rates of neutral particles have been indirectly estimated using a combination of measurements of the atmospheric reservoirs for escape and models. The total atmospheric escape from both ions and neutrals varies with the same drivers observed to modify the solar wind interaction region. This variation can be extrapolated to estimate the total atmospheric loss over the Martian history using the scaling arguments or by tuning simulations to match present-day variation.

The authors hope that the paradigm of the hot planetary corona presented in this article will not be strongly changed with the coming new observational data on the hot planetary coronas and accompanying atmospheric escape from upper atmospheres of planets in the solar and extrasolar planetary systems.

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