Stochastic Models of Hot Planetary and Satellite Coronas

 

The uppermost layers of a planetary (satellite) atmosphere where the density of neutral particles is infinitely low are commonly called the exosphere or the planetary (satellite) corona. Since the atmosphere is not completely bound to the planet (or satellite) by the planetary gravitational field, such light atoms as hydrogen and helium in the uppermost atmospheric layers can have velocities that exceed the escape velocity from this planet and can escape into interplanetary space. This process is commonly called thermal escape; the thermal escape flux depends on the temperature of the ambient atmospheric gas, while the flux itself is formed at heights where the flow of atmospheric gas is virtually collisionless (Chamberlain and Hunten, 1987). These heights correspond to the transition region between the underlying collision-dominated atmospheric layers and the free-molecule exospheric gas. The concept of exobase, the lower boundary of the exosphere, is introduced as a height at which the atmospheric particle mean free path is equal to the density scale height (Chamberlain and Hunten, 1987). For example, in the Earth's upper atmosphere, the exobase is at a height of about 500 km, and the exosphere here is populated mainly by atomic oxygen with small admixtures of hydrogen and helium. The heavier carbon, nitrogen, and oxygen atoms can escape from the atmospheres of the terrestrial planets only through the collisional processes that determine such nonthermal escape mechanisms as photodissociation, charge exchange and sputtering by magnetospheric plasma, and ion capture by the solar wind (Chamberlain and Hunten, 1987; Johnson, 1990; Hunten, 2002; Johnson, 2002).

 

The current theories of planetary coronas are based mainly on ground-based and space observations of such exospheric emission features as the 1026 A and 1216 A hydrogen lines, the 584 A helium line, and the 1304 and 1356 A oxygen lines. These observations, together with in-situ mass-spectrometer measurements, have allowed the density and temperature height profiles of the exospheric components to be constructed. These measurements have revealed that the planetary coronas contain both a thermal fraction of neutral particles with the mean particle kinetic energy corresponding to the exospheric temperature and a hot fraction of neutral particles with the mean kinetic energy corresponding to a manifold higher exospheric temperature ( Hunten, 2002; Johnson, 2002). The hot fraction is produced by the nonthermal processes that form both the nonthermal escape fluxes proper and the hot corona itself. These nonthermal collisional processes are triggered under the external effects of solar extreme ultraviolet radiation and magnetospheric plasma and are accompanied by intense energy exchange between the various degrees of freedom of the atmospheric particles as well as by a significant thermal effect of the photochemical reactions. A manifestation of the non-equilibrium behavior of planetary and satellite atmospheres is the formation of translationally excited (hot) particles with kinetic energies much higher than thermal energy of the ambient atmospheric gas. These hot particles are products of the photolytic and collisional dissociation and ionization of the molecular atmospheric components as well as several exothermic chemical reactions.

 

In recent years, interest in investigating the role of suprathermal (energetically active) particles in the physics and chemistry of the upper planetary and satellite atmospheres has increased (Johnson, 1990; Wayne, 1991; Shizgal and Arkos, 1996; Marov et al., 1997). In particular, the energetically active particles produced in the upper atmospheric layers have been shown to play an important role in the chemistry and energetics of the upper atmosphere or, more specifically,

 

• They lead to local changes in chemical composition, because the non-equilibrium rate coefficients of the chemical reactions (particularly with high activation energies) between the suprathermal particles and the ambient atmospheric gas are much larger than those for the chemical reactions at thermal energies. This is because the particle densities in the range of suprathermal kinetic energies are higher than those for local equilibrium distributions.

 

• They produce nonthermal atmospheric emission features.

 

• They form hot planetary coronas (Nagy and Cravens, 1988; Hedin, 1989) and enhance the nonthermal atmospheric losses (Shizgal and Arkos, 1996; Hunten, 2002).

 

 

The following numerical approaches are mainly used to simulate the nonthermal losses of planetary atmospheres in practice (see, e.g., Shizgal and Arkos, 1996; Hunten, 2002):

 

• The multi-stream method (Nagy and Cravens, 1988), where the phase space of the escaping particles is broken down into intervals in energies and directions 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, i.e., corresponds to the solution of linearized kinetic equations.

 

• The finite-difference methods of directly solving the Boltzmann kinetic equations for suprathermal particles (Shizgal and Arkos, 1996). This approach is currently used only to analyze the local kinetics of the suprathermal particles that weakly perturb the thermal state of the atmospheric gas, i.e., for the local linear systems of kinetic equations.

 

• The test-particle Monte-Carlo method (Ip, 1988). This approach is also best suited to studying systems in which suprathermal particles perturb the thermal state of the gas only weakly.

 

• The stochastic simulation method (Shematovich et al., 1994), which is a modification of the direct statistical simulation Monte-Carlo method (Bird, 1976).

 

In general, the stochastic simulation method consists in constructing a physical-probabilistic analogue of discrete media with collisional physical-chemical processes and is used to simulate chemically reacting multi-component gases (dsmc.html). This approach has been further developed to investigate the formation, kinetics, and transport of suprathermal particles for the linear and nonlinear formation of hot planetary and satellite coronas (Shematovich et al., 1994; Shematovich 2004).

 

The numerical stochastic models to study both the local formation and kinetics of suprathermal particles and their transport in the transition region between the collision-dominated and free molecular layers of planetary and satellite atmospheres were developed for different planets and satellites in our Solar System. Moreover, these numerical models are suitable for investigating the flows of atmospheric gas being weakly and strongly perturbed by suprathermal particles, i.e., for studying the formation of hot planetary and satellite coronas in a proper way.

 

 

Bird, G.A. Molecular Gas Dynamics, Oxford: Clarendon Press, 1976.

Chamberlain, J.W. and Hunten, D. Theory of Planetary Atmospheres. An Introduction to Their Physics and Chemistry, New York: Academic, 1987.

Ferziger, J. and Kaper, H. Mathematical Theory of Transport Processes in Gases, Amsterdam: North-Holland, 1972.

Hunten, D.M. Exospheres and Planetary Escape, Atmospheres in the Solar System, Mendillo, M., Nagy, A., and Waite, J.H., Eds., Washington: AGU, Geophysical Monograph 130, 2002. pp. 191-202.

Ip, W.-H. On a Hot Oxygen Corona of Mars, Icarus, 1988, vol. 76, pp. 135-145.

Johnson, R.E., Energetic Charged Particle Interactions with Atmospheres and Surfaces, Berlin: Springer, 1990.

Johnson, R.E. Surface Boundary Layer Atmospheres, Atmospheres in the Solar System, Mendillo, M., Nagy, A., and Waite, J.H., Eds., Washington: AGU, Geophysical Monograph 130, 2002, pp. 203-219.

Marov, M.Ya., Shematovich, V.I., Bisikalo, D.V., and Gerard, J.-C. Nonequilibrium Processes in the Planetary and Cometary Atmospheres: Theory and Applications, Dordrecht: Kluwer Academic, 1997.

Nagy, A.F. and Cravens, T.E. Hot Oxygen Atoms in the Upper Atmospheres of Venus and Mars, Geophys. Res. Lett., 1988, vol. 15, pp. 433-435.

Shematovich, V.I., Bisikalo, D.V., and Gerard, J.-C. A Kinetic Model of the Formation of the Hot Oxygen Geocorona. I. Quiet Geomagnetic Conditions, J. Geophys. Res., 1994b, vol. 99, pp. 217-226.

Shizgal, B.D. and Arkos, G.G. Nonthermal Escape of the Atmospheres of Venus, Earth, and Mars, Rev. Geophys., 1996, vol. 34, pp. 483-505.

Wayne, R.P., Chemistry of Atmospheres, Oxford: Clarendon 1991.

Whipple, E.C., Van Zandt, T.E., and Love, C.H. Kinetic Theory of Warm Atoms - Non-Maxwellian Velocity Distributions and Resulting Doppler-Broadened Emission-Line Profiles, J. Chem. Phys., 1975, vol. 62, pp. 3024-3030.

I. Hot hydrogen coronae:

EARTH:

- hydrogen emissions in the proton and electron auroras in the Earth's upper atmosphere:

• Gerard J.-C., Hubert B., Bisikalo D.V., and Shematovich V.I.

Ly-alpha emission in the proton aurora (abstract).

J. Geophys. Res., 2000, 105, No. A7, 15795-15806.

 

• Hubert B., Gerard J.-C., Bisikalo D.V., Shematovich V.I., and Solomon S.C.

The role of proton precipitation in the excitation of auroral FUV emissions (abstract</