Molecular Kinetic Simulations Research Articles

Molecular Kinetic Simulations of Transient and Steady Wave Propagation into a Planet’s Exosphere

The vertical propagation of wave energy into a planet’s exosphere, a process that affects atmospheric evolution, is calculated here using 1D molecular kinetic simulations. Effects sensitive to molecular interactions are examined by comparing simulation results to solutions of linear fluid models for steady wave activity using parameters associated with Mars’ upper atmosphere. In addition to correctly describing the wave behavior in the exobase region, these simulations directly yield nonlinear effects such as atmospheric heating. They also readily include the transient behavior due to the onset and decay of waves propagating into the rarefied region of a planet’s atmosphere. This is a first step in understanding the effects of variable wave activity in the region where the atmosphere evolves from collisional to collisionless.

The influence of upper boundary conditions on molecular kinetic atmospheric escape simulations

Molecular kinetic simulations are typically used to accurately describe the tenuous regions of the upper atmospheres on planetary bodies. These simulations track the motion of particles representing real atmospheric atoms and/or molecules subject to collisions, the object's gravity, and external influences. Because particles can end up in very large ballistic orbits, upper boundary conditions (UBC) are typically used to limit the domain size thereby reducing the time for the atmosphere to reach steady-state. In the absence of a clear altitude at which all molecules are removed, such as a Hill sphere, an often used condition is to choose an altitude at which collisions become infrequent so that particles on escape trajectories are removed. The remainder are then either specularly reflected back into the simulation domain or their ballistic trajectories are calculated analytically or explicitly tracked so they eventually re-enter the domain. Here we examine the effect of the choice of the UBC on the escape rate and the structure of the atmosphere near the nominal exobase in the convenient and frequently used 1D spherically symmetric approximation. Using Callisto as the example body, we show that the commonly used specular reflection UBC can lead to significant uncertainties when simulating a species with a lifetime comparable to or longer than a dynamical time scale, such as an overestimation of escape rates and an inflated exosphere. Therefore, although specular reflection is convenient, the molecular lifetimes and body's dynamical time scales need to be considered even when implementing the convenient 1D spherically symmetric simulations in order to accurately estimate the escape rate and the density and temperature structure in the transition regime.

Molecular kinetic simulations of transient perturbations in a planet's upper atmosphere

The upper atmospheres of planetary bodies can exhibit significant density perturbations as indicated by in situ spacecraft and remote sensing observations. As density vs. altitude data are often used to extract vertical temperature profiles, we examine their validity when such perturbations occur in the region where the atmosphere transitions from collision dominated and to nearly collisionless. Since an accurate temperature profile is critical for describing the chemistry and physics of the upper atmosphere, we use molecular kinetic simulations to examine the vertical propagation of transient perturbations. We find that in an atmosphere's transition region, the standard methods for extracting a 1D temperature profile can be unreliable and examine how the composition vs. altitude is transiently modified by simulating an atmosphere with Mars-like properties. These results suggest that molecular kinetic simulations, calibrated to observed density profiles, could be needed to fully understand the energy transfer and heating in this region of a planet's atmosphere.

Diffusion in sphere and spherical-cavity arrays with interacting gas and surface phases

Three-dimensional computations of coupled gas and surface diffusion in periodic arrays of solid spheres and spherical cavities are undertaken to assess the role of pore size, void fraction, and pore geometry on permeability. With nano-dimensioned pores, gas-phase diffusion is hindered by the small mean-free path, so the overall permeability hinges on surface diffusion. We prescribe the intrinsic gas-phase diffusivity to be self-consistent with the Knudsen diffusivity obtained from molecular-kinetic simulations reported in the literature. The continuum model of Albaalbaki and Hill then couples the gas and surface phases via an equilibrium adsorption isotherm and kinetic-exchange parameters. Solving these equations in complex pore-scale geometries provides new insights into the coupling. To interpret the results, we decompose the net flux into (i) gas and surface contributions that can be calculated without knowledge of the concentration perturbations to equilibrium, but which depend on the pore geometry, and (ii) counterparts that must be evaluated from integrals of the concentration perturbations to equilibrium. These measures are directly related to the familiar, but less precise, gas and surface tortuosity parameters, which are often used to interpret experiments. The results highlight (i) discontinuous variations in the fluxes when passing through void and solid percolation thresholds, (ii) how the surface flux depends on the specific surface area, and (iii) the pore sizes at which surface transport compares with void transport.

VOLATILE LOSS AND CLASSIFICATION OF KUIPER BELT OBJECTS

Observations indicate that some of the largest Kuiper Belt Objects (KBOs) have retained volatiles in the gas phase, which implies the presence of an atmosphere that can affect their reflectance spectra and thermal balance. Volatile escape rates driven by solar heating of the surface were estimated by Schaller and Brown (2007) (SB) and Levi and Podolak (2009)(LP) using Jeans escape from the surface and a hydrodynamic model respectively. Based on recent molecular kinetic simulations these rates can be hugely in error (e.g., a factor of $\sim 10^{16}$ for the SB estimate for Pluto). In this paper we estimate the loss of primordial N$_2$ for several large KBOs guided by recent molecular kinetic simulations of escape due to solar heating of the surface and due to UV/EUV heating of the upper atmosphere. For the latter we extrapolate simulations of escape from Pluto (Erwin et al. 2013) using the energy limited escape model recently validated for the KBOs of interest by molecular kinetic simulations (Johnson et al. 2013). Unless the N$_2$ atmosphere is thin ($\lesssim 10^{18}$ N$_2$/cm$^2$) and/or the radius small ($\lesssim 200-300$ km), we find that escape is primarily driven by the UV/EUV radiation absorbed in the upper atmosphere rather than the solar heating of the surface. This affects the previous interpretations of the relationship between atmospheric loss and the observed surface properties. The long-term goal is to connect detailed atmospheric loss simulations with a model for volatile transport (e.g., Young, 2014) for individual KBOs.

MOLECULAR-KINETIC SIMULATIONS OF ESCAPE FROM THE EX-PLANET AND EXOPLANETS: CRITERION FOR TRANSONIC FLOW

The equations of gas dynamics are extensively used to describe atmospheric loss from solar system bodies and exoplanets even though the boundary conditions at infinity are not uniquely defined. Using molecular-kinetic simulations that correctly treat the transition from the continuum to the rarefied region, we confirm that the energy-limited escape approximation is valid when adiabatic expansion is the dominant cooling process. However, this does not imply that the outflow goes sonic. In fact in the sonic regime, the energy limited approximation can significantly under estimate the escape rate. Rather large escape rates and concomitant adiabatic cooling can produce atmospheres with subsonic flow that are highly extended. Since this affects the heating rate of the upper atmosphere and the interaction with external fields and plasmas, we give a criterion for estimating when the outflow goes transonic in the continuum region. This is applied to early terrestrial atmospheres, exoplanet atmospheres, and the atmosphere of the ex-planet, Pluto, all of which have large escape rates. The paper and its erratum, combined here, are published: ApJL 768, L4 (2013); ApJ, 779, L30 (2013).