Turbulent convection may have played a major role in determining the structure and evolution of the primordial solar nebula, but current, incomplete models of convection and turbulence give very different results and remain largely untested in the absence of detailed astronomical observations. Numerical simulations provide an 'experimental' database for comparison with these models, and, to this end, direct numerical simulations of turbulent convection were performed with modifications intended to mimic some of the unique physical features of thin accretion disks, such as the primordial solar nebula: internal heating, a gravitational acceleration that is linearly proportional to the distance from midplane of the nebula, and rapid rotation. Peclet numbers in the simulations are comparable to those in solar nebula models; Rossby numbers in the simulations are an order of magnitude larger than those in solar nebula models because of the unrealistically high Prandtl and low, Reynolds numbers required to resolve all scales of the convective flow. We find that, despite the loss of buoyancy at midplane, turbulent motions easily penetrate the midplane region with little loss of intensity, providing efficient transport of heat and turbulent kinetic energy throughout the interior. A simple mixing length model modified to include rotation is found to give convective heat fluxes for the interior flow in rough agreement with the numerical simulations. We discuss these preliminary results with regard to assumptions about heating distributions and convective heat fluxes made in standard solar nebula models. More definitive comparisons with solar nebula modelling will become possible when more realistic effects of shear, density, stratification, and compression are included.

We describe results of 32 N-body planetary accretion simulations that investigate the dependence of terrestrial-planet formation on nebula surface density profile sigma and evolution of the eccentricities of Jupiter and Saturn e(J,S). Two surface density profiles are examined: a decaying profile with a proportional to 1/a, Where a is orbital semi-major axis, and a peaked profile in which a increases for a < 2 AU and decreases for a > 2 AU. The peaked profiles are generated by models of coagulation in an initially hot nebula. Models with initial e(J,S) = 0.05 (the current value) and 0.1 are considered. Simulations using the decaying profile with e(J,S) = 0.1 produce systems most like the observed planets in terms of mass-weighted mean a and the absence of a planet in the asteroid belt. Simulations with doubled a produce planets roughly twice as massive as the nominal case. Most initial embryos are removed in each simulation via ejection from the solar system or collision with the Sun. The asteroid belt is almost entirely cleared on a timescale of 10-100 Ma that depends sensitively on e(J,S). Most initial mass with a < 2 AU survives, with the degree of mass loss increasing with a. Mass loss from the terrestrial region occurs on a timescale that is long compared to the mass loss time for the asteroid belt. Substantial radial mixing of material occurs in all simulations, but is greater in simulations with initital e(J,S) = 0.05. The degree of mixing is equivalent to a feeding zone of half width 1.5 and 0.9 AU for an Earth mass planet at 1 AU for the cases e(J,S) = 0.05 and 0.1, respectively. In simulations with e(J,S) = 0.05, roughly one-third and 5-10% of the mass contained in final terrestrial planets originated in the region a > 2.5 AU for the decaying and peaked profiles, respectively. In the case e(J,S) = 0.1, the median mass accreted from a > 2.5 AU is zero for both profiles.

The implications of mantle rare gas characteristics for both the acquisition of rare gases from the solar nebula and subsequent losses to space are examined. There is at least one deep mantle reservoir rich in 3He and Ne that was trapped early in Earth history, with minimum concentrations obtained by closed system calculations. Ne isotopes indicate the presence of a component that has a solar composition. Xe isotopes indicate that extensive late losses occurred from the mantle as well as from the atmosphere. Calculations based on a simple two-stage evolution provide times of losses of up to ∼100 Ma after the formation of the solar system from both the mantle and the atmosphere. These losses appear to have depleted the rare gases by ≥97%; therefore, there originally was at least two orders of magnitude more rare gases than now present. Mechanisms for the capture of rare gases soon after the start of the solar system into the deep Earth (or Earth-forming materials) must provide these high initial concentrations, presumably in the high-energy environment of planetary accretion where strong degassing of solids might be expected to have occurred. A mechanism that satisfies these requirements is the dissolution in a magma ocean of rare gases from a dense primary atmosphere. A massive atmosphere of solar composition would have been captured if the Earth had formed prior to dispersal of the solar nebula. The underlying mantle would have melted due to the energy of accretion and the blanketing effect of this atmosphere. Rare gases would then have entered the molten Earth by dissolution at the surface and downward advection. For typical solubility coefficients, a total pressure of ∼100 atm and surface temperatures of >∼2500°C are required to dissolve sufficient rare gases to account for the initial lower mantle concentrations. While Xe in the mantle is isotopically exchanging with the primary atmosphere, it will be buffered to a solar composition; therefore, somewhat less Xe must be trapped prior to the late loss event for longer periods of exchange. As solidification of the mantle proceeded outward during cooling, the distributions of retained rare gases would have been determined by the history of surface pressure and temperature during the coupled cooling of the Earth and atmosphere. The giant impact proposed for Moon formation may have been responsible for the inferred substantial and late gas losses from the deep mantle as well as from the atmosphere. Constraints on the timing of Moon formation derived from Hf–W systematics and simulations of the giant impact are consistent with the Xe isotope constraints for gas loss.

It is remarkable that we possess samples of Solar System solids which have retained a record of galactic and stellar events that occurred well before the birth of the Sun, as well as samples which contain evidence of Solar System processes that occurred during the earliest stages of planet building. The signatures of such processes are most commonly recognized in isotopic anomalies, identifiable against a pervasive background of isotopic homogeneity, and systematic trends in the elemental abundance patterns of primitive meteoritic materials. Although the significance of these anomalies and patterns is unmistakable, their interpretation in terms of specific processes is problematic. Central to such interpretations are questions of spatial scale: do cosmogonically significant isotopic and elemental compositions reflect processes that occurred on the grand scale of the proto–solar cloud, or do they result from many localized events within a nebular or planetary environment? The question is fundamental to our understanding of the formation of solid objects in the Solar System. This question will be examined here, with specific reference to theoretical models of nebular evolution and planet building, and evidence regarding the survival of presolar signatures, the origin of short–lived radionuclides and oxygen isotopic systematics.

This paper reviews the evidence for short-lived radionuclides in the early Solar System and critically evaluates models for their origin. Radionuclides with half-lives of less than 50 Myr for which firm and consistent evidence has been found are Be-10, Al-26, Ca-41, Mn-53, Fe-60, Pd-107, I-129 and Hf-182. The oldest Solar System objects, calcium-aluminium-rich inclusions (CAIs), contained Be-10, Al-26, Ca-41 and Mn-53 on formation. We discuss whether a spallation. or stellar origin for the radionuclides is more likely, and conclude that the initial presence of short-lived radionuclides in CAIs can be most easily explained if these formed by spallation reactions close to the protosun.

The presence of solar noble gases in the deep interior of the Earth is inferred from the Ne isotopic compositions of MORB (Mid-ocean Ridge Basalts) and OIB (Oceanic Island Basalt); Ar data may also consistent with a solar component in the deep mantle. Models of the transport and distribution of noble gases in the earth's mantle allow for the presence of solar Ar/Ne and Xe/Ne ratios and permit the calculation of lower mantle noble gas concentrations. These mantle data and models also indicate that the Earth suffered early (0.7 to 2 x 10(exp 8) yr) and large (greater than 99 percent) losses of noble gases from the interior, a result previously concluded for atmospheric Xe. We have pursued the suggestion that solar noble gases were incorporated in the forming Earth from a massive, nebula-derived atmosphere which promoted large-scale melting, so that gases from this atmosphere dissolved in the magma ocean and were mixed downward. Models of a primitive atmosphere captured from the solar nebula and supported by accretion luminosity indicate that pressures at the Earth's surface were adequate (and largely more than the required 100 Atm) to dissolve sufficient gases. We have calculated the coupled evolution of the magma ocean and the overlying atmosphere under conditions corresponding to the cessation (or severe attenuation) of the sustaining accretion luminosity, prior to the complete removal of the solar nebula. Such a condition was likely to obtain, for instance, when most of the unaccumulated mass resided in large bodies which were only sporadically accreted. The luminosity supporting the atmosphere is then that provided by the cooling Earth, consideration of which sets a lower limit to the time required to solidify the mantle and terminate the incorporation of atmospheric gases within it. In our initial calculations, we have fixed the nebula temperature at To = 300K, a value likely to be appropriate for nebular temperatures at lAU in the early planet-building epoch. We treated the background (nebula) pressure as an adjustable, time-dependent parameter. Additional information is contained within the original extended abstract.

The presolar grains found in meteorites survived potentially destructive processes in the protosolar environment: the radiation field of the collapsing protosolar envelope; the protoplanetary disk formed by the collapse, known as the solar nebula; and the accretion shock through which material passed from the envelope to the disk. Theoretical models of these regimes, combined with experimentally determined destruction criteria, can be used, in principle, to put constraints on the physical conditions that prevailed prior to and during the formation of meteorite parent bodies. Preliminary studies, in which interstellar species are assumed to be destroyed at well-defined, critical temperatures, indicate that refractory species (e.g., silicates) survived envelope and shock to enter the nebula at or within about 1 AU of the Sun; volatile species such as water ice and simple organics retained interstellar characteristics only beyond several AU, the destruction distances being dependent on the protosolar accretion luminosity and, to a lesser extent, the precise density configuration of the protosolar envelope. Upon entering the nebula it is likely that even refractory grains were destroyed out to some distance in the terrestrial planet region, but subsequent nebular cooling and radial advection resulted in the survivors' incorporation into the meteorite parent bodies. Presolar volatiles would have been incorporated in comets formed at distances at and beyond the orbits of Uranus and Neptune. These preliminary conclusions should be tested by better theoretical models of the protosolar environment, a search for survival patterns among meteorite classes, and the application of rigorously defined destruction criteria which take into account the nonequilibrium character of surviving species.

The heating and vaporization of dust grains in the protosolar environment is modeled in order to assess the survivability of interstellar solids during the formation of the solar system. A multidimensional, discrete ordinate radiative transfer code is used to compute thermal transport in the collapsing protosolar cloud. The results are combined with estimates of heating at the shock where infalling material arrives at the surface of the solar nebula/accretion disk, and in the interior of the disk, to determine the distances at which various solid phases are vaporized. The thermal coupling between the envelope and the accretion disk (backheating) is treated self-consistently, so its effect on the disk's radial temperature profile is included. This treatment also permits evaluation of the effect of backheating on the observational inference of disk properties.Calculations are performed for various values of cloud collapse rate, rotation rate, and disk accretion rate. The latter factor is the main determinant of the total luminosity, and we consider both ''low-luminosity'' cases, in which disk accretion is inefficient, and high-luminosity'' cases, in which disk accretion keeps pace with cloud collapse. We also examine situations in which a polar, optically thin cavity is swept clear by a protosolar wind.We conclude that refractory grains, such as silicates, can generally survive the envelope and accretion shock, and enter the nebula at or within 1 AU. Inside the nebula, their vaporization distances are controlled by the disk accretion rate and optical depth. In contrast, the vaporization distances of volatiles such as water ice are sensitive to envelope conditions, which control the thermal state of the outer, optically thin regions of the disk. The ice vaporization distance lies between about 2 and 30 AU, depending on the total source luminosity and characteristics of the collapsing cloud. Moderately volatile organics (methanol, formaldehyde, and polymerized formaldehyde) may survive as solids in the terrestrial planet region; they generally are not vaporized outside of several AU, which supports the idea that comets inherit this material from the parent molecular cloud.

We present a simplified analysis of some effects of disk accretion on the early evolution of fully convective, low-mass pre-main-sequence stars. Our analysis builds on the previous seminal work of Stahler, but it differs in that the accretion of material occurs over a small area of the stellar surface, such as through a disk or magnetospheric accretion column, so that most of the stellar photosphere is free to radiate to space. This boundary condition is similar to the limiting case considered by Palla & Stahler for intermediate-mass stars. We argue that for a wide variety of disk mass accretion rates, material will be added to the star with relatively small amounts of thermal energy. Protostellar evolution calculated assuming this ''low-temperature'' limit of accretion generally follows the results of Stahler because of the thermostatic nature of deuterium fusion, which prevents protostars from contracting below a ''birthline'' in the H-R diagram. Our calculated protostellar radii tend to fall below Stahler's at higher masses; the additional energy loss from the stellar photosphere in the case of disk accretion tends to make the protostar contract. The low-temperature disk accretion evolutionary tracks never fall below the deuterium-fusion birthline until the internal deuterium is depleted, but protostellar tracks can lie above the birthline in the H-R diagram if the initial radius of the protostellar core is large enough or if rapid disk accretion (such as might occur during FU Ori outbursts) adds significant amounts of thermal energy to the star. These possibilities cannot be ruled out by either theoretical arguments or observational constraints at present, so that individual protostars might evolve along a multiplicity of birthlines with a modest range of luminosity at a given mass. Our results indicate that there are large uncertainties in assigning ages for the youngest stars from H-R diagram positions, given the uncertainty in birthline positions. Our calculations also suggest that the relatively low disk accretion rates characteristic of T Tauri stars below the birthline cause low-mass stars to contract only slightly faster than normal Hayashi track evolution, so that ages for older pre-main-sequence stars estimated from H-R diagram positions are relatively secure.

Major fractions of the primitive meteorites experienced temperatures high enough to melt or evaporate them. Ubiquitous chemical fractionations are plausibly the result of an early, hot epoch of solar nebular evolution [1,2,3], and chondrules are apparently the products of localized heating in the proto-solar environment. Yet such processed components coexist with interstellar grains, some of which are essentially unscathed by cosmogonic events [4]. Such grains must have avoided or survived at least three potentially destructive environments through which most solar system material passed: the collapsing protosolar cloud, the accretion shock, and the nebula itself. We are examining theoretical models of these environments with the aim of determining what factors affect interstellar grain survival; what patterns one might expect to find in the abundances, type and composition of interstellar material in primitive meteorites; and what can be deduced about the formation of the solar system if such patterns exist. Rigorous calculations of radiative heat transfer in model protosolar envelopes are used to determine the pre-shock survival distances of interstellar components. Shock destruction is evaluated from the detailed shock models of Neufeld and Hollenbach [5]. Nebula midplane temperatures are calculated from simple radiative models [6,7], extended to include the backheating effects of the envelope. The primary environmental determinant of survivability is the accretion rate through the nebula, which affects the thermal state of both the nebula and the collapsing cloud. During periods of rapid accretion, silicate grains might survive collapse and the accretion shock to within 2 AU, but would be destroyed in the nebula to distances beyond the terrestrial planet region. During periods of very slow accretion (mass buildup in the disk), those grains could remain intact to well within 1 AU.

The redistribution of angular momentum and mass in circumstellar disks by spiral density waves is governed by processes that dissipate the waves. Dissipation is usually attributed to unspecified nonlinear processes or an ad hoc viscosity. In this paper, we examine dissipation by radiative losses associated with the cyclic compression and expansion of disk material by the density waves. We consider linear, discrete modes in optically thick disks and use a simplified treatment of the radiative losses in order to assess the parameter dependences and importance of radiative damping. Wave action conservation principles are generalized to describe the effect of dissipation (by any means) and the consequent coupling of wave and disk energy and momenta. A relation is derived (in the WKBJ limit) between radial mass transport of disk: material and the azimuthally averaged dissipation rate. A wave amplitude equation is similarly derived, which describes the radial evolution of wave angular momentum, and therefore the radial deposition of angular momentum in the disk. Associated with the equation is a characteristic damping length, proportional to the cooling time from the base state temperature times the radial wave speed, and a factor that depends weakly on optical depth. The damping length is used to define, in terms of the disk base state temperature and surface density, regimes of strong and weak radiative damping. Waves in warm disks may be damped close to the resonances at which they are excited, while waves in cold disks can propagate to distances at which other dissipative mechanisms may dominate. It is found that the boundary between these regimes cuts across values that are thought to have characterized the primitive solar nebula. Thus both strong and weak radiative damping may be encountered in circumstellar disks in general.

We present a discrete ordinate solution for gray radiation transport in axisymmetric protostellar envelopes, for the purpose of defining the patterns of interstellar-grain survival during the formation of the solar system. The gray transfer problem is nonlinear because the opacity depends on temperature, with discontinuities at temperatures where various species of dust vaporize. The standard lambda iteration techniques that are required for accurate solutions to the transfer equation tend to be nonconvergent under these conditions. We show that accuracy can be achieved through a relaxation method.We first compare the thermal profiles in spherically symmetric envelopes computed by the discrete ordinate solution with those predicted by the diffusion approximation. The more accurate discrete ordinate solutions tend to yield steeper temperature gradients, and the central vaporized cavity around the protostar is larger than that given by the diffusion approximation. The transport solution is then applied to an axisymmetric model envelope in which the cloud is flattened due to rotation, and in which a wind evacuates the polar regions of the cloud. The resulting cavity beams the emergent intensity in the polar direction. When the cloud is uniformly opaque, the polar cavity enhances the diffusive escape of radiation and globally reduces temperatures in the cloud. Modeled temperature profiles are used to predict the radial distances at which various dust, species survive infall in the cloud. The results indicate that survival boundaries range from within 1 AU for the most refractory solids, to several AU for volatile organics, and that water ice is excluded from within 20-30 AU of the protostar during the collapse phase. We compare dust vaporization due to heating in the cloud with destruction in the accretion shock; based on the test case, heating in the cloud during collapse is potentially more destructive.

A theoretical model of aerodynamic heating of a meteoric particle upon entry into a parent body atmosphere is presented. The model includes the effects of melting, vaporization, and heat conduction into the particle interior. Properties of chondrule rims are interpreted in the context of the model. We conclude that the formation of true melt rims by atmospheric entry requires that a low-melting-temperature component be fractionated in the outer part of the chondrule prior to rim formation, and that the range of thermal alteration effects observed in UOC chondrites reflects the variety of encounter conditions and chondrite types. Further tests of the model are suggested.