Formation of solar nebula and mass distribution in the planetary system

The formation of the solar nebula and the distribution of mass in its planetary system is studied. The underlying idea is that the protosun, fragmented out from an interstellar cloud as a result of cluster formation, gathered the planetary material and, hence, spin angular momentum by gravitational accretion during its orbital motion around the centre of the Galaxy. The study gives the initial angular momentum of the solar nebula nearly equal to the present value of the solar system.     

Hydrodynamic instability of the solar nebula in the presence of a planetary core

When a planetary core composed of condensed matter is accumulated in the primitive solar nebula, the gas of the nebula becomes gravitationally concentrated as an envelope surrounding the planetary core. Models of such gaseous envelopes have been constructed subject to the assumption that the gas everywhere is on the same adiabat as that in the surrounding nebula. The gaseous envelope extends from the surface of the core to the distance at which the gravitational attraction of core plus envelope becomes equal to the gradient of the gravitational potential in the solar nebula; at this point the pressure and temperature of the gas in the envelope are required to attain the background values characteristics of the solar nebula. In general, as the mass of the condensed core increases, increasing amounts of gas became concentrated in the envelope, and these envelopes are stable against hydrodynamic instabilities. However, the core mass then goes through a maximum and starts to decrease. In most of the models tested, the envelopes were hydrodynamically unstable beyond the peak in the core mass. An unstable situation was always created if it was insisted that the core mass contain a larger amount of matter than given by these solutions. For an initial adiabat characterized by a temperature of 450°K and a pressure of 5 × 10^?6 atm, the maximum core mass at which instability occurs is approximately 115 earth masses; this value is rather insensitive to the position in the solar nebula or to the background pressure of the solar nebula. However, if the adiabat is lowered, then the core mass corresponding to instability is decreased. Since the core masses found by Podolak and Cameron for the giant planets are significantly less than the critical core mass corresponding to the initial solar nebula adiabat, we conclude that the giant planets obtained their large amounts of hydrogen and helium by a hydrodynamic collapse process in the solar nebula only after the nebula had been subjected to a considerable period of cooling.     

Gas capture and rare gas retention by accreting planets in the solar nebula

In this paper, the physico-chemical effects of the nebula gas on the planets are reviewed from a standpoint of planetary formation in the solar nebula.The proto-Earth growing in the nebula was surrounded by a primordial atmosphere with a solar chemical composition and solar isotopic composition. When the mass of the proto-Earth was greater than 0.3 times the present Earth mass, the surface was molten because of the blanketing effect of the atmosphere. Therefore, the primordial rare gasses contained in the primordial atmosphere dissolved into the molten Earth material without fractionation and in particular the dissolved neon is expected to be conserved in the present Earth material. Hence, if dissolved neon with a solar isotopic ratio is discovered in the Earth material, it will indicate that the Earth was formed in the nebula and that the dissolved rare gases were one of the sources which degassed to form the present atmosphere.     

The first ten million years in the solar nebula

Abstract— The ²⁶Al/²⁷Al ratio in a large number of calcium-aluminum inclusions (CAIs) is a rather uniform 5 × 10^?5, whereas in chondrules the ratio is either undetectable or has a much lower value; the simplest interpretation of this is that there was an interval of a few million years between the times that these two meteoritic constituents formed stable solids. The present investigation was undertaken as an exploration of the physics of the processes in the solar nebula during and after the accumulation of the Sun. Understanding the time scales of events in this nebular model, to see if this would cast light on this apparent CAI to chondrule time interval, was the major motivation for the exploration. There were four stages in the history of the solar nebula; in stage 1, a fragment of an interstellar molecular cloud collapsed to form the Sun and solar nebula; in stage 2, the nebula was in approximate steady state balance between infall from the cloud and accretion onto the Sun and was in its FU Orionis accumulation stage; in stage 3, the Sun had been mainly accumulated and there was a slow residual mass flow into the Sun while it was in its classical T Tauri stage; and in stage 4, the nebula had finished accreting material onto the Sun (now a weak-lined T Tauri star) and was in a static condition with no significant dissipation or motions, other than removal at the inner edge due to the T Tauri solar wind and photoevaporation beyond 9 astronomical units (AU). It is found that the energy source keeping the nebula warm during stages 3 and 4 is recombination of ionized H in the ionized bipolar jets and the T Tauri coronal expansion solar wind. The parameters of the heating model were adjusted to locate the ice sublimation line at 5.2 AU. In this work, a nebular model is used with a surface density of 4.25 × 10³ gm/cm² at 1 AU and a variation with radial distance as the inverse first power. Under normal conditions in the nebula, there is a negative pressure gradient that provides partial radial support for the gas, which thus circles the Sun more slowly than large solid objects do. Large objects undergo a slow inward spiral due to the gas drag; very small objects move essentially with the gas but have a slow inward drift; and intermediate objects (e.g., 1 m) have a fairly large inward drift velocity that traverses the full radial extent of the nebula in considerably less than the CAI to chondrule time interval. Such objects are thus lost unless they can grow rapidly to larger sizes. Near the inner edge (bow) of the nebula during stage 4, the pressure gradient becomes positive, creating a narrow zone of zero gas drag toward which solids drift from both directions, facilitating planetesimal formation in the inner solar nebula. Recent theoretical and experimental results on sticking probabilities of solids show that icy surfaces have the best sticking properties, but icy interstellar grains can only stick together when subjected to impact velocities of less than 2000 cm/sec. However, if the solid objects are very underdense, then a collision leads to interpenetration and many points at which the small constituent grains can adhere to one another, and thus coagulation becomes possible for such underdense objects. Simulations were made of such coagulation in the outer solar nebula, and it was found that the central plane of the nebula quickly becomes filled with meter-sized and larger bodies that rapidly accumulated near the top of the nebula and rapidly descended; in a few thousand years this quickly leads to gravitational instabilities that can form planetesimals. These processes led to the rapid formation of Jupiter in the nebula (and the slightly less rapid formation of the other giant planets). The early formation of Jupiter opens an annular gap in the nebula, and thus a second region is created in the nebula with zero gas drag. It is concluded that CAIs were formed at the end of stage 2 of the nebula history and moved out into the nebula for long-term storage, and that most chondrules were formed by magnetic reconnection flares in the bow region of the nebula during stage 4, several million years later. Carbonaceous meteorites should be formed on the far side of the Jovian gap, with the chondrules being heated by flares on the early Jupiter irradiating materials in the nearby zone of zero gas drag, and they should have essentially the same ²⁶Al ages as the CAIs (this will be very hard to confirm owing to scarcity of Al mineral phases in these chondrules).     

The distributions and ages of refractory objects in the solar nebula

Refractory objects such as Calcium, Aluminum-rich Inclusions, Amoeboid Olivine Aggregates, and crystalline silicates, are found in primitive bodies throughout our Solar System. It is believed that these objects formed in the hot, inner solar nebula and were redistributed during the mass and angular momentum transport that took place during its early evolution. The ages of these objects thus offer possible clues about the timing and duration of this transport. Here we study how the dynamics of these refractory objects in the evolving solar nebula affected the age distribution of the grains that were available to be incorporated into planetesimals throughout the Solar System. It is found that while the high temperatures and conditions needed to form these refractory objects may have persisted for millions of years, it is those objects that formed in the first 10⁵ years that dominate (make up over 90%) those that survive throughout most of the nebula. This is due to two effects: (1) the largest numbers of refractory grains are formed at this time period, as the disk is rapidly drained of mass during subsequent evolution and (2) the initially rapid spreading of the disk due to angular momentum transport helps preserve this early generation of grains as opposed to later generations. This implies that most refractory objects found in meteorites and comets formed in the first 10⁵ years after the nebula formed. As these objects contained live ²⁶Al, this constrains the time when short-lived radionuclides were introduced to the Solar System to no later than 10⁵ years after the nebula formed. Further, this implies that the t=0 as defined by meteoritic materials represents at most, the instant when the solar nebula finished accreting significant amounts of materials from its parent molecular cloud.     

eta Carinae: Binarity Confirmed

Gas giant planets have been detected in orbit around an increasing number of nearby stars. Two theories have been advanced for the formation of such planets: core accretion and disk instability. Core accretion, the generally accepted mechanism, requires several million years or more to form a gas giant planet in a protoplanetary disk like the solar nebula. Disk instability, on the other hand, can form a gas giant protoplanet in a few hundred years. However, disk instability has previously been thought to be important only in relatively massive disks. New three-dimensional, "locally isothermal," hydrodynamical models without velocity damping show that a disk instability can form Jupiter-mass clumps, even in a disk with a mass (0.091 M middle dot in circle within 20 AU) low enough to be in the range inferred for the solar nebula. The clumps form with initially eccentric orbits, and their survival will depend on their ability to contract to higher densities before they can be tidally disrupted at successive periastrons. Because the disk mass in these models is comparable to that apparently required for the core accretion mechanism to operate, the models imply that disk instability could obviate the core accretion mechanism in the solar nebula and elsewhere.     

The interaction between giant gaseous protoplanets and the primitive solar nebula

The manner in which a giant gaseous protoplanet becomes embedded in the primitive solar nebula determines surface boundary conditions which must be used in studying the evolution of such objects. On the one hand, if the system resembles a contact binary system, then the envelope of the protoplanet should approach the entropy of the surrounding nebula. On the other hand angular. momentum transfer by resonance and tidal effects between the nebula and the protoplanet may cause the nebula to exhibit a zone of avoidance near the protoplanet, thus inhibiting exchange of material. This problem has been studied with a computer program developed by D. N. C. Lin which simulates disk hydrodynamics by particle motions with dissipation. These studies suggest that for expected values of the protoplanet/protosun mass ratios, significant inhibition of mass exchange is likely, so that it is a reasonable next step to undertake protoplanet evolution studies with the imposition of minimum protoplanet surface temperatures.     

On the composition of ices incorporated in Ceres

We use the clathrate hydrate trapping theory and gas drag formalism to calculate the composition of ices incorporated in the interior of Ceres. Utilizing a time-dependent solar nebula model, we show that icy solids can drift from beyond 5 au to the present location of the asteroid and be preserved from vaporization. We argue that volatiles were trapped in the outer solar nebula in the form of clathrate hydrates, hydrates and pure condensates prior to having been incorporated in icy solids and subsequently in Ceres. Under the assumption that most of volatiles were not vaporized during the accretion phase and the thermal evolution of Ceres, we determine the per mass abundances with respect to H₂O of CO₂, CO, CH₄, N₂, NH₃, Ar, Xe and Kr in the interior of the asteroid. The Dawn space mission, scheduled to explore Ceres in August 2014, may have the capacity to test some predictions. We also show that an in situ measurement of the D/H ratio in H₂O in Ceres could constrain the distance range in the solar nebula where its icy planetesimals were produced.     

3. Solar System Formation and Early Evolution: the First 100 Million Years

The solar system, as we know it today, is about 4.5 billion years old. It is widely believed that it was essentially completed 100 million years after the formation of the Sun, which itself took less than 1 million years, although the exact chronology remains highly uncertain. For instance: which, of the giant planets or the terrestrial planets, formed first, and how? How did they acquire their mass? What was the early evolution of the “primitive solar nebula” (solar nebula for short)? What is its relation with the circumstellar disks that are ubiquitous around young low-mass stars today? Is it possible to define a “time zero” (t ₀), the epoch of the formation of the solar system? Is the solar system exceptional or common? This astronomical chapter focuses on the early stages, which determine in large part the subsequent evolution of the proto-solar system. This evolution is logarithmic, being very fast initially, then gradually slowing down. The chapter is thus divided in three parts: (1) The first million years: the stellar era. The dominant phase is the formation of the Sun in a stellar cluster, via accretion of material from a circumstellar disk, itself fed by a progressively vanishing circumstellar envelope. (2) The first 10 million years: the disk era. The dominant phase is the evolution and progressive disappearance of circumstellar disks around evolved young stars; planets will start to form at this stage. Important constraints on the solar nebula and on planet formation are drawn from the most primitive objects in the solar system, i.e., meteorites. (3) The first 100 million years: the “telluric” era. This phase is dominated by terrestrial (rocky) planet formation and differentiation, and the appearance of oceans and atmospheres.     

Evolution of giant gaseous protoplanets embedded in the primitive solar nebula

Evolutionary calculations are presented, in a spherically symmetric approximation, for a protoplanet of 1 Jovian mass with homogeneous solar composition during the early phase of quasi-static contraction prior to the dissociation of molecular hydrogen. In contrast to earlier calculations which assume that protoplanets are isolated, this study invokes a time-dependent surface boundary condition that simulates physical conditions in an evolving primitive solar nebula. In a first set of calculations the protoplanet is surrounded by a “thermal bath” whose temperature varies with time and whose pressure is small and constant in time. Under a wide range of parameters the result is evaporation and complete dispersal of the object. Conditions required for the protoplanet to survive are discussed. In a second set of calculations both the temperature and pressure at the surface vary with time according to models of the solar nebula. In this case the protoplanet is not dispersed, but the evolution is accelerated or retarded relative to that of an isolated protoplanet, depending upon whether the entropy in the nebula is lower than or higher than, respectively, the entropy in the outer layers of the protoplanet. Processes by which terrestrial planets can form in the cores of giant gaseous protoplanets are discussed.     

The supernova fragmentation model of solar system formation

We have further developed Brown's model of solar system formation. In this model, each fragment of an ejected supernova shell evolves into a separate solar system. Specifically, we have formulated the reverse-flow hypothesis that may be responsible for the inner, earthlike planets. We have written a computer program with which it is possible to calculate mass distributions within a solar nebula. We have found mass distributions similar to our solar system over a wide range of the model parameters.Los Alamos National Laboratory is operated by the University of California for the U.S. Dept. of Energy under contract W-7405-ENG-36.     

Accumulation processes in the primitive solar nebula

Particle accumulation processes are discussed for a variety of physical environments, ranging from the collapse phase of an interstellar cloud to the different parts of the models of the primitive solar nebula constructed by Cameron and Pine. Because of turbulence in the collapsing interstellar gas, it is concluded that interstellar grains accumulate into bodies with radii of a few tens of centimeters before the outer parts of the solar nebula are formed. These bodies can descend quite rapidly through the gas toward midplane of the nebula, and accumulation to planetary size can occur in a few thousand years. Substantial modifications of these processes take place in the outer convection zone of the solar nebula, but again it is concluded that bodies in that zone can grow to planetary size in a few thousand years.From the discussion of the interstellar collapse phase it is concluded that the angular momentum of the primitive solar nebula was predominantly of random turbulent origin, and that it is plausible that the primitive solar nebula should have possessed satellite nebulae in highly elliptical orbits. It is proposed that the comets were formed in these satellite nebulae.A number of other detailed conclusions are drawn from the analysis. It is shown to be plausible that an iron-rich planet should be formed in the inner part of the outer nebular convection zone. Discussions are given of the processes of planetary gas accretion, the formation of satellites, the T Tauri solar wind, and the dissipation of excess condensed material after the nebular gases have been removed by the T Tauri solar wind. It is shown that the present radial distances of the planets (but not Bode's Law) should be predicted reasonably well by a solar nebula model intermediate between the uniform and linear cases of Cameron and Pine.     

Dust concentration and chondrule formation

Meteoritical and astrophysical models of planet formation make contradictory predictions for dust concentration factors in chondrule-forming regions of the solar nebula. Meteoritical and cosmochemical models strongly suggest that chondrules, a key component of the meteoritical record, formed in regions with solids-to-gas mass ratios orders above the solar nebula average. However, models of dust grain dynamics in protoplanetary disks struggle to surpass concentration factors of a few except during very short-lived stages in a dust grain's life. Worse, those models do not predict significant concentration factors for dust grains the size of chondrule precursors. We briefly develop the difficulty in concentrating dust particles in the context of nebular chondrule formation and show that the disagreement is sufficiently stark that cosmochemists should explore ideas that might revise the concentration factor requirements downward.     

Growth and sedimentation of dust grains in the primordial solar nebula

Of the formation processes in the solar system, the process of growth and sedimentation of dust grains in the primordial solar nebula is investigated for a region near the Earth's orbit. The growth equation for dust grains, which are sinking as well as being in thermal motion, is solved numerically in the wide mass range between 10^?12 and 10⁶ g. Any turbulent motions in the nebula are assumed to have already decayed when the sedimentation begins. The numerical simulation shows that the growth and sedimentation proceed faster than was found by Kusaka et al. (1970) but in accordance with the estimate of Safronov (1969) owing to a cooperative interaction of the growth and the sedimentation; that is, at about 3 × 10³ years after the beginning of the growth and sedimentation a dust layer, composed of centimeter-sized grains, is formed at the equator of the solar nebula. Furthermore, the mass density of dust grains floating in the outer layers of the nebula is found to be of the order of 10^?5 after 10⁵ years compared with that before the sedimentation. From these results, it can be estimated that at about 5 × 10³ years after the beginning of sedimentation the dust layer breaks up owing to the onset of gravitational instability.     

The partial volatilization of Mercury

During recent years my research on the primitive solar nebular has followed two main themes: (1) Very early in the development of the nebula conditions probably favored the occurence of major gaseous instabilities leading to the formation of giant gaseous protoplanets, but the rapid rise of the external temperature soon evaporated the envelopes of these protoplanets, possibly leaving behind precipitated solids which formed the cores and mantles of the terrestrial planets. (2) Models of the nebula indicate a later stage when conditions in the inner Solar System became very hot; at the position of Mercury the temperature was probably in the range 2500–3500°K. This leads to the hypothesis that the original protomercury was a body substantially more massive than the present planet and of normal composition, but that when it was immersed in the high-temperature field of the dissipating solar nebula, most of the rocky mantle was vaporized and mixed into the solar nebula gases and carried away by them. This hypothesis is investigated in the present paper. For simplicity the vaporization of a mantle composed of enstatite, MgSiO₃, was computed for a planet with 2.25 the mass of Mercury at a temperature of 3000°K. It is argued that the mantle could probably be largely removed in the available time of 3 × 10⁴ years. Subsequent accretion would restore some magnesium silicates to the mantle of the planet.     

Sweeping of the Jovian resonances and the evolution of the asteroids

During the formation of the solar system the variation of the gravitational field produced by removal of a nebula with its moderately massive accretion disk led to sweeping of the Jovian commensurability resonances through the asteroid zone. This process produced increased eccentricities and random velocities of the early planetesimals which resulted in collisional comminution rather than accretion. The existence of the asteroids, their low mass density, and their high relative velocities are interpreted as due to disruption of the accretion processes of the terrestrial planets by the influence of Jupiter.     

Iron/silicate fractionation and the origin of Mercury

Compared with the other terrestrial planets, Mercury has anomalously low mass and high iron content. Equilibrium condensation and inhomogeneous accretional models are not compatible with these properties, unless the solar nebula's thermal structure and history meet stringent conditions. Also, such models predict a composition which does not allow a presently molten core. It appears that most of the solid matter which originally condensed in Mercury's zone has been removed. The planet's composition may be explained if the removal process was only slightly more effective for silicates than for iron. It is proposed that planetesimal orbits in the inner solar nebula decayed because of gas drag. This process is a natural consequence of the non-Keplerian rotation of a centrally condensed nebula. A simple quantitative model shows good agreement with the observed mass distribution of the terrestrial planets. The rate of orbital decay is slower for larger and/or denser bodies, because of their smaller area-to-mass ratios. With plausible assumptions as to planetesimal sizes and compositions, this process can produce fractionation of the sense required to produce an iron-rich planet. Cosmogonical implications are discussed.     

Ice lines, planetesimal composition and solid surface density in the solar nebula

To date, there is no core accretion simulation that can successfully account for the formation of Uranus or Neptune within the observed 2–3 Myr lifetimes of protoplanetary disks. Since solid accretion rate is directly proportional to the available planetesimal surface density, one way to speed up planet formation is to take a full accounting of all the planetesimal-forming solids present in the solar nebula. By combining a viscously evolving protostellar disk with a kinetic model of ice formation, which includes not just water but methane, ammonia, CO and 54 minor ices, we calculate the solid surface density of a possible giant planet-forming solar nebula as a function of heliocentric distance and time. Our results can be used to provide the starting planetesimal surface density and evolving solar nebula conditions for core accretion simulations, or to predict the composition of planetesimals as a function of radius. We find three effects that favor giant planet formation by the core accretion mechanism: (1) a decretion flow that brings mass from the inner solar nebula to the giant planet-forming region, (2) the fact that the ammonia and water ice lines should coincide, according to recent lab results from Collings et al. [Collings, M.P., Anderson, M.A., Chen, R., Dever, J.W., Viti, S., Williams, D.A., McCoustra, M.R.S., 2004. Mon. Not. R. Astron. Soc. 354, 1133–1140], and (3) the presence of a substantial amount of methane ice in the trans-saturnian region. Our results show higher solid surface densities than assumed in the core accretion models of Pollack et al. [Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y., 1996. Icarus 124, 62–85] by a factor of 3–4 throughout the trans-saturnian region. We also discuss the location of ice lines and their movement through the solar nebula, and provide new constraints on the possible initial disk configurations from gravitational stability arguments.     

On the Origin of Binary Transneptunian Objects

The observed transneptunian binaries, with components of comparable mass and large separations, cannot be the result of collisions in the present dynamical environment of the Kuiper belt. They could be produced by collision of two planetesimals within the sphere of influence of a third body during low-velocity accretion in the solar nebula. Thus, they are primordial.     

Numerical models of the primitive solar nebula

Numerical models have been constructed to represent probable conditions in the primitive solar nebula. A two solar mass fragment of a collapsing interstellar gas cloud has been represented by a uniformly rotating sphere. Two cases have been considered: one in which the internal density of the sphere is uniform and the other in which the density falls linearly from a central value to zero at the surface (the uniform and linear models). These assumptions served to define the distribution of angular momentum per unit mass with mass fraction. The spheres were flattened into disks, and models of the disks were found in which there was a force balance in the radial and vertical directions, subject to certain approximations, and with everywhere the assigned values of angular momentum per unit mass. The radial pressure gradient of the gas was included in the force balance. The energy transport in the vertical direction involved convection and radiative equilibrium; the principal contributors to opacity at lower temperatures were metallic iron grains and ice. The models contained two convection zones, an inner one due to the dissociation of hydrogen molecules, and an outer one in which there was a high opacity due to metallic iron grains. The characteristic semithickness of the disks ranged from about 0.1 astronomical units near the center to about one astronomical unit near the exterior. Characteristic angular momentum transport times and radiation lifetimes for these models of the initial solar nebula were estimated. Both types of characteristic lifetime were as short as a few years near the inner part of the models, and became about 10⁴ years or longer at distances greater than ten astronomical units.