The Spherically Symmetric Gravitational Collapse of a Clump of Solids in a Gas

Several mechanisms have been identified that create dense particle clumps in the solar nebula. The present work is concerned with the gravitational collapse of such clumps, idealized as being spherically symmetric. Calculations using the two-fluid model are performed (almost) up to the time when a central density singularity forms. The end result of the study is a parametrization for this time, in order that it may be compared with timescales for various disruptive effects to which clumps may be subject. An important effect is that as the clump compresses, it also compresses the gas due to drag. This increases gas pressure which retards particle collapse and leads to oscillation in the size and density of the clump. The ratio of gravitational force to gas pressure gives a two-phase Jeans parameter, $J_t$, which is the classical Jeans parameter with the sound speed replaced by an the wave speed in a coupled two-fluid medium. Its use makes the results insensitive to the initial density ratio of particles to gas as a separate parameter. An ordinary differential equation model is developed which takes the form of two coupled non-linear oscillators and reproduces key features of the simulations. Finally, a parametric study of the time to collapse is performed and a formula (fit to the simulations) is developed. In the incompressible limit $J_t \to 0$, collapse time equals sedimentation time. As $J_t$ increases, the collapse time decreases roughly linearly with $J_t$ until $J_t \gtrsim 0.4$ when it becomes approximately equal to the dynamical time

The Runaway Greenhouse: A History of Water on Venus

Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere. Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context

The Evolution of the Water Distribution in a Viscous Protoplanetary Disk

(Abridged) Astronomical observations have shown that protoplanetary disks are dynamic objects through which mass is transported and accreted by the central star. Age dating of meteorite constituents shows that their creation, evolution, and accumulation occupied several Myr, and over this time disk properties would evolve significantly. Moreover, on this timescale, solid particles decouple from the gas in the disk and their evolution follows a different path. Here we present a model which tracks how the distribution of water changes in an evolving disk as the water-bearing species experience condensation, accretion, transport, collisional destruction, and vaporization. Because solids are transported in a disk at different rates depending on their sizes, the motions will lead to water being concentrated in some regions of a disk and depleted in others. These enhancements and depletions are consistent with the conditions needed to explain some aspects of the chemistry of chondritic meteorites and formation of giant planets. The levels of concentration and depletion, as well as their locations, depend strongly on the combined effects of the gaseous disk evolution, the formation of rapidly migrating rubble, and the growth of immobile planetesimals. We present examples of evolution under a range of plausible assumptions and demonstrate how the chemical evolution of the inner region of a protoplanetary disk is intimately connected to the physical processes which occur in the outer regions.Comment: 45 pages, 7 figures, revised for publication in Icaru

Scale Dependence of Multiplier Distributions for Particle Concentration, Enstrophy and Dissipation in the Inertial Range of Homogeneous Turbulence

Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into sub-volumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, $Re$, finding good agreement with the asymptotic, infinite $Re$ inertial range theory of Zaichik and Alipchenkov [New Journal of Physics 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.Comment: 21 pages, 14 figures, accepted for publication in Physical Review

Towards Initial Mass Functions for Asteroids and Kuiper Belt Objects

Our goal is to understand primary accretion of the first planetesimals. The primitive meteorite record suggests that sizeable planetesimals formed in the asteroid belt over a period longer than a million years, each composed entirely of an unusual, but homogeneous, mixture of mm-size particles. We sketch a scenario in which primary accretion of 10-100km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted mm-size particles (generically "chondrules"). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100km diameter, which has been identified as a "fossil" property of the pre-erosion, pre-depletion population. We extend our primary accretion theory to make predictions for outer solar system planetesimals, which may also have a preferred size in the 100km diameter range. We estimate formation rates of planetesimals and assess the conditions needed to match estimates of both asteroid and Kuiper Belt Object (KBO) formation rates. For nebula parameters that satisfy observed mass accretion rates of Myr-old protoplanetary nebulae, the scenario is roughly consistent with not only the "fossil" sizes of the asteroids, and their estimated production rates, but also with the observed spread in formation ages of chondrules in a given chondrite, and with a tolerably small radial diffusive mixing during this time between formation and accretion (the model naturally helps explain the peculiar size distribution of chondrules within such objects). The scenario also produces 10-100km diameter primary KBOs. The optimum range of parameters, however, represents a higher gas density and fractional abundance of solids, and a smaller difference between keplerian and pressure-supported orbital velocities, than "canonical" models of the solar nebula. We discuss several potential explanations for these differences.Comment: Icarus, in pres

Cloud Base Signature in Transmission Spectra of Exoplanet Atmospheres

We present an analytical model for the transmission spectrum of a transiting exoplanet, showing that a cloud base can produce an observable inflection point in the spectrum. The wavelength and magnitude of the inflection can be used to break the degeneracy between the atmospheric pressure and the abundance of the main cloud material, however, the abundance still depends on cloud particle size. An observed inflection also provides a specific point on the atmospheric P-T profile, giving us a "thermometer" to directly validate or rule out postulated cloud species. We apply the model to the transit spectrum of HD 189733b

Planetary ring dynamics and morphology

Evidence for a moonlet belt in the region between Saturn's close-in moonrings Pandora and Prometheus is discussed. It is argued that little-known observations of magnetospheric electron density by Pioneer 11 imply substantial, ongoing injections of mass into the 2000 km region which surrounds the F ring. A hypothesis is presented that these events result naturally from interparticle collisions between the smaller members of an optically thin belt of moonlets. Also discussed is work on Uranus ring structure and photometry, image processing and analysis of the Jonian ring strucure, photometric and structural studies of the A ring of Saturn, and improvements to an image processing system for ring studies

Preferrential Concentration of Particles in Protoplanetary Nebula Turbulence

Preferential concentration in turbulence is a process that causes inertial particles to cluster in regions of high strain (in-between high vorticity regions), with specifics depending on their stopping time or Stokes number. This process is thought to be of importance in various problems including cloud droplet formation and aerosol transport in the atmosphere, sprays, and also in the formation of asteroids and comets in protoplanetary nebulae. In protoplanetary nebulae, the initial accretion of primitive bodies from freely-floating particles remains a problematic subject. Traditional growth-by-sticking models encounter a formidable "meter-size barrier" [1] in turbulent nebulae. One scenario that can lead directly from independent nebula particulates to large objects, avoiding the problematic m-km size range, involves formation of dense clumps of aerodynamically selected, typically mm-size particles in protoplanetary turbulence. There is evidence that at least the ordinary chondrite parent bodies were initially composed entirely of a homogeneous mix of such particles generally known as "chondrules" [2]. Thus, while it is arcane, turbulent preferential concentration acting directly on chondrule size particles are worthy of deeper study. Here, we present the statistical determination of particle multiplier distributions from numerical simulations of particle-laden isotopic turbulence, and a cascade model for modeling turbulent concentration at lengthscales and Reynolds numbers not accessible by numerical simulations. We find that the multiplier distributions are scale dependent at the very largest scales but have scale-invariant properties under a particular variable normalization at smaller scales