S. S. Davis

Condensation Front Migration in a Protoplanetary Nebula

Condensation-front dynamics is investigated in the solar nebula. A quasi-steady model of the evolving nebula is combined with equilibrium vapor pressure curves to determine evolutionary sublimation fronts for water and ammonia. A simple one-dimensional model includes local viscous and luminescent heating, allowing analytical solutions. The study is extended to two-dimensional protoplanetary disks including grain heating in the disk photosphere and vertical radiative transfer. Both approaches show the fronts migrating inward from the far nebula to final positions in the inner nebula during a period of 107 yr. The center-plane sublimation fronts are shown to evolve in a similar manner, but the two-dimensional model predicts a more complex two-branched structure. One branch forms an elongated gaseous region below the density scale height, and the second branch places a sublimation front in the low-density region near the disk photosphere. Along the center plane, the fronts initially propagate much faster than the nebular viscous accretion velocity, but eventually the accreting gas and dust overtake the slowing condensation front.

The Surface Density Distribution in the Solar Nebula

The commonly used minimum-mass power-law representation of the early solar nebula is reanalyzed using a new cumulative mass model. This model is a first integral of the planetary data and predicts a smoother surface density approximation compared with methods based on direct computation of surface density. The density is quantified using two independent analytical formulations. First, a best-fit transcendental function is applied directly to the basic planetary data. Next, a solution to the time-dependent disk evolution equation is parametrically adapted to the solar nebula data. The latter model is shown to be a good approximation to the finite-size early solar nebula and, by extension, to extrasolar protoplanetary disks.

UTILITARIAN OPACITY MODEL FOR AGGREGATE PARTICLES IN PROTOPLANETARY NEBULAE AND EXOPLANET ATMOSPHERES

As small solid grains grow into larger ones in protoplanetary nebulae, or in the cloudy atmospheres of exoplanets, they generally form porous aggregates rather than solid spheres. A number of previous studies have used highly sophisticated schemes to calculate opacity models for irregular, porous particles with size much smaller than a wavelength. However, mere growth itself can affect the opacity of the medium in far more significant ways than the detailed compositional and/or structural differences between grain constituents once aggregate particle sizes exceed the relevant wavelengths. This physics is not new; our goal here is to provide a model that provides physical insight and is simple to use in the increasing number of protoplanetary nebula evolution, and exoplanet atmosphere, models appearing in recent years, yet quantitatively captures the main radiative properties of mixtures of particles of arbitrary size, porosity, and composition. The model is a simple combination of effective medium theory with small-particle closed-form expressions, combined with suitably chosen transitions to geometric optics behavior. Calculations of wavelength-dependent emission and Rosseland mean opacity are shown and compared with Mie theory. The models fidelity is very good in all comparisons we have made, except in cases involving pure metal particles or monochromatic opacities for solid particles with size comparable to the wavelength.

On the Persistence of Small Regions of Vorticity in the Protoplanetary Nebula

The fate of small regions of vorticity in a barotropic model of the protoplanetary nebula is investigated over thousands of years using a finite difference model. It is found that the coherence time for a small island of vorticity depends on its size, strength, orientation, and radial location in the nebula. Anticyclonic vorticity retains its coherence for longer times than cyclonic vorticity due to favorable interactions with the Keplerian shear flow. Rossby waves are generated as a result of mean vorticity gradients across the disk. The two-dimensional nebula evolves from discrete vortices into an axisymmetric flow consisting of small-amplitude vortex sheets at the radial locations of the initial vorticity. These vortex sheets induce an additional small, potential flow velocity superimposed on the Keplerian rotation curve.

A Simplified Model for an Evolving Protoplanetary Nebula

The dynamic evolution of a protoplanetary nebula is investigated using analytical solutions of the surface density transport equations. Constant- and so-called β-viscosity turbulence models are compared with a functional analytical model and the well-known α-viscosity formulation. The model presented here is related to a number of simplified disk evolution models but is also associated with β-viscosity models based on hydrodynamic generation of turbulence. The β-viscosity model, heretofore used for steady state disks, is shown to be a useful approximation for disk evolution problems.

Unsteady facilitated transport of oxygen in hemoglobin-containing membranes and red cells

Abstract The unsteady transport of a reacting permeant diffusing through thin membranes and modeled red cells is investigated with a new nonlinear analysis of the reaction-diffusion equations. Implicit finite difference methods and a matrix formulation are used to study the deviation from equilibrium-based theories and the transient behavior of facilitated oxygen transport. The loading and unloading of oxygen from an erythrocyte model is computed and contrasted with the diffusion of oxygen across hemoglobin-saturated membranes.

Ice Formation in Radiated Accretion Disks

Gas to solid phase changes of abundant species in a viscous, irradiated protoplanetary disk are investigated using a new formulation for the freezeout effect. The method is based on a procedure using species-dependent phase diagrams while following the chemical evolution of water and carbon monoxide gas until their partial pressures are sufficient to de-sublimate vapor into ice. It is found that water ice is dominant throughout the nebula while a significant amount of water vapor coexists with the ice in the cooler parts of the inner nebula. Volatile CO molecules de-sublimate only in the colder outer regions of the nebula near the center plane. Computed column densities for CO gas are compared with similar calculations using an adsorption/desorption model by Aikawa and Herbst and are shown to predict similar distributions.

A note on transition, turbulent length scales and transport in differentially rotating flows

In this note we address the issue of hydrodynamical instabilities in Astrophysical rotating shear flows in the light of recent publications focused on the possibility for differential rotation to trigger and sustain turbulence in the absence of a magnetic field. We wish to present in a synthetic form the major arguments in favor of this thesis along with a simple schematic scenario of the transition to and self-sustenance of such turbulence. We also propose that the turbulent diffusion length scale scales as the local Rossby number of the mean flow. A new prescription for the turbulent viscosity is introduced. This viscosity reduces to the so-called β-prescription in the case of velocity profiles with a constant Rossby number, which includes Keplerian rotating flows.

A computational and experimental study of unsteady facilitated transport

Abstract Unsteady facilitated transport of nitric oxide across a thin liquid membrane of formamide containing ferrous chloride as a facilitator is investigated both experimentally and computationally. Predicted nitric oxide transport and flux are compared with experiments first reported by Ward. Unsteady transport is predicted qualitatively quite well, but precise quantitative agreement between the differential equation model and experiment depends on an accurate determination of the transport coefficients, especially the diffusion constants.

Lunar dust characterization by polarimetric signature I. Negative polarization branch of sphere aggregates of various porosities

Context. In support of NASAs exploration program and the return to the Moon, the polarimetric signature of dispersed individual Lunar regolith dust grains is studied to enable the characterization of the dust exopsheric environment by remote, in-situ, and standoff sensing. Aims. We explore the value of the negative polarization branch (NPB) as a signature for characterizing individual grains to determine if it can be used in the same way as for surfaces of planets and atmosphereless bodies. Methods. The linear polarization phase curve for single spheres of silicate and for aggregates of spherical silicate grains of different porosity are computed using the discrete dipole approximation (DDA) for a range of grain sizes. Features in these curves are identified and their evolution explored as a function of grain size and aggregate porosity. We focus particularly on the so-called negative polarization branch that has been historically used to characterize planetary surfaces. Results. Calculations show that polarization phase curves for spherical grains exhibit a sharp transition over a narrow range of size parameter between two distinct regimes, one typical of Rayleigh scattering and another dominated by a large NPB. The linear polarimetric signature observed for aggregates is a composite of a) the polarization induced by individual grains composing the aggregate and b) the polarization due to the aggregate as a whole dust grain. The weight of each component varies depending on the porosity of the aggregate. An NPB similar to the one observed for atmosphereless astronomical bodies is present for different ranges of the size parameter depending on the value of the porosity. It appears as a remnant of the negative branch exhibited by the single spherical grains. The sharper, narrow negative branch that is measured for some granular surfaces in the laboratory or seen in astronomical observations is not observed here. Conclusions. These results suggest that the wide negative branch is due to the scattering by individual grains and single aggregates, while the narrow negative branch is more likely due to coherent backscattering or shadowing effects in bulk material. The shape and evolution of the NPB could be used to characterize spherical grains and to differentiate between aggregates with the same porosity but different sizes, but does not appear to be a practical candidate for univocally differentiating between aggregates of different porosity.