Direct observations show that the deep Earth contains rare gases of solar composition distinct from those in the atmosphere. We examine the implications of mantle rare gas characteristics on acquisition of rare gases from the solar nebula and subsequent losses due to a large impact. Deep mantle rare gas concentrations and isotopic compositions can be obtained from a model of transport and distribution of mantle rare gases. This model assumes the lower mantle closed early, while the upper mantle is open to subduction from the atmosphere and mass transfer from the lower mantle. Constraints are derived that can be incorporated into models for terrestrial volatile acquisition: (1) Calculated lower-mantle Xe-isotopic ratios indicate that the fraction of radiogenic Xe produced by I-129 and Pu-244 during the first about 10(exp 8) yr was lost, a conclusion also drawn for atmospheric Xe. Thus, either the Earth was made from materials that had lost >99% of rare gases about (0.7-2) x 10(exp 8) yr after the solar system formed, or gases were then lost from the fully formed Earth. (2) Concentrations of 3He and 20Ne in the lower mantle were established after these losses. (3) Neon-isotopic data indicates that mantle Ne has solar composition. The model allows for solar Ar/Ne and Xe/Ne in the lower mantle if a dominant fraction of upper mantle Ar and Xe are subduction-derived. If Earth formed in the presence of the solar nebula, it could have been melted by accretional energy and the blanketing effect of a massive, nebula-derived atmosphere. Gases from this atmosphere would have been sequestered within the molten Earth by dissolution at the surface and downward mixing. It was found that too much Ne would be dissolved in the Earth unless the atmosphere began to escape when the Earth was only partially assembled. Here we consider conditions required to initially dissolve sufficient rare gases to account for the present lower mantle concentrations after subsequent losses at 10(exp 8) yr. It is assumed that equilibration of the atmosphere with a thoroughly molten mantle was rapid, so that initial abundances of gases retained in any mantle layer reflected surface conditions when the layer solidified. For subsequent gas loss of 99.5% and typical solubility coefficients, a total pressure of 100 atm was required for an atmosphere of solar composition. Calculations of the pressure at the base of a primordial atmosphere indicate that this value might be exceeded by an order of magnitude or more for an atmosphere supported by accretional energy. Surface temperatures of about 4000 K would have been produced, probably high enough to melt the deep mantle. Initial distributions of retained rare gases would then be determined by the history of surface pressure and temperature during mantle cooling and solidification, i.e., the coupled cooling of Earth and atmosphere. The Earth's thermal state was determined by its surface temperature and the efficiency of convection in the molten mantle, estimated to be sufficient to maintain an adiabatic gradient. Because the melting curve is steeper than the adiabat, solidification of the mantle proceeded outward from the interior. Incorporation of atmospheric gases in the mantle therefore occurred over a range in surface temperature of a few thousand degrees Kelvin. The thermal state of the atmosphere was controlled by total luminosity of the Earth (energy) released by accreting planetesimals and the cooling Earth), nebular temperature and pressure, and atmospheric opacity. The energy released by accretion declined with time as did nebular pressure. Analytical solutions for an idealized (constant opacity radiative atmosphere show that declining energy sources under constant nebular conditions result in slowly diminishing surface temperature but dramatically increasing surface pressure. For such an atmosphere with declining nebular pressure but constant total luminosity, surface pressure decreases gradually with decreasing temperaure. A decline in accretion luminosity might be compensated by energy released as the mantle cools for about 10(exp 5) year, after which luminosity must decline. The total complement of dissolved rare gases will depend on the particular evolutionary path determined by the declining accretional luminosity, the Earth thermal history, removal of the nebula, and opacity variations of the atmosphere. Models for these coupled evolutionary histories for Earth's acquisition of nebular-derived noble gases are in progress. The later losses required at about 10(exp 8) yr (depleting the interior concentrations of the sequestered solar gases by a factor of > 100) were presumably related to the major impact in which the Moon formed.
Models of the structure and thermal evolution of the Galilean satellites based on the simplest assumptions are described, the most important complications that are likely to exist are identified, and their consequences are explored. Io's internal energy source is modeled based on dissipation of tidal heating due to gravitational interaction with Jupiter and Europa. A proposed contribution due to electrical heating is discussed. Three arguments bearing on Io's dissipation rate are addressed and models for the satellite's interior are discussed. Callisto and Ganymede are treated together in an attempt to model the reasons for their different appearance. It is concluded that the persistence of Ganymede's surface features is due to a prolonged thermal evolution relative to Callisto, probably caused by a higher radioactive content. Theoretical arguments concerning Europa's thermal evolution are more briefly presented.
view Abstract Citations (53) References (16) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Further Studies of Gravitationally Unstable Protostellar Disks Tomley, Leslie ; Steiman-Cameron, Thomas Y. ; Cassen, Patrick Abstract Models of the solar nebula reveal that it might have been gravitationally unstable, both early and later in its evolution. Such instabilities produce density waves and associated gravitational torques, which are potent agents of angular momentum transport. In previous work, we conducted a series of numerical simulations designed to quantify the effects of gravitational instabilities in a generalizable way (Tomley, Cassen, & Steiman-Cameron 1991). Here we present a second series of simulations in which we examine disks of greater size, increased star/disk mass ratio, and flatter surface density distribution than those in our initial study. The purpose is to represent disks at a later stage of evolution than those already studied, to test the quantitative relations derived in our earlier work and to explore the effects of mass ratio on the results. The new results indicate that the tendencies for unstable, uncooled disks to heat to stability and for dynamical evolution rates to be proportional to cooling rates are general characteristics of the behavior of gravitationally unstable disks. Nevertheless, there are quantitative, and (for strong cooling) even qualitative differences that are revealed in the new simulations, particularly with regard to the cooling rates at which clumping tends to occur. Publication: The Astrophysical Journal Pub Date: February 1994 DOI: 10.1086/173777 Bibcode: 1994ApJ...422..850T Keywords: Astronomical Models; Computerized Simulation; Gravitational Fields; Mathematical Models; Protostars; Solar Corona; Solar System Evolution; Stability; Star Formation; Stellar Envelopes; Clumps; Cooling; Density Distribution; Mass Ratios; Nonlinear Systems; Astrophysics; SOLAR SYSTEM: FORMATION; STARS: CIRCUMSTELLAR MATTER; STARS: FORMATION full text sources ADS |
The elements are those which condense (or evaporate) in the temperature range 650 - 1350 K, as a mix of material with solar abundances is cooled (or heated) tinder equilibrium conditions. Their relative abundances in chondritic meteorites are solar (or cosmic, as defined by the composition of Cl meteorites) to within a factor of several, but vary within that range in a way that correlates remarkably well with condensation temperature, independent of chemical affinity. It has been argued that this correlation reflects a systematically selective process which favored the accretion of refractory material over volatile material from a cooling nebula. Wasson and Chou (Meteoritics 9, 69-94, 1974, and Wasson and co-authors in subsequent papers) suggested that condensation and settling of solids contemporaneously with the cooling and removal of nebular gas could produce the observed abundance patterns, but a quantitative model has been lacking. We show that the abundance patterns of the moderately volatile elements in chondritic meteorites can be produced, in some degree of quantitative detail, by models of the solar nebula that are designed to conform to observations of T Tauri stars and the global conservation laws. For example, even if the local surface density of the nebula is not decreasing, condensation and accretion of solids from radially inflowing gas in a cooling nebula can result in depletions of volatiles, relative to refractories, like those observed, The details of the calculated abundance patterns depend on (but are not especially sensitive to) model parameters, and can exhibit the variations that distinguish the meteorite classes. Thus it appears that nebula characteristics such as cooling rates, radial flow velocities, and particle accumulation rates can be quantitatively constrained by demanding that they conform to meteoritic data; and the models, in turn, can produce testable hypotheses regarding the time and location of the formation of the chondrite parent bodies and the planets.
Solutions that describe the collapse of a molecular cloud core that is initially in unstable equilibrium, embedded within an envelope of uniform density, and rotating at the same rate as the envelope are given. Hydrodynamic equations, including self gravity, are deduced to a set of ordinary differential equations, which are solved by the method of matched asymptotic expansions. Results of these calculations are: (1) the range of stellar masses derived seems to correspond to realistic ranges of observed stellar masses and interstellar cloud parameters, (2) the proper measure of dissipation rate is the ratio of accretion time to viscous diffusion time, and (3) the pressure distribution on the surface of an accreting protostar is nonuniform in a way that favors the channeling of a stellar wind into a bipolar flow directed along the rotation axis.
