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1.
As planetary embryos grow, gravitational stirring of planetesimals by embryos strongly enhances random velocities of planetesimals and makes collisions between planetesimals destructive. The resulting fragments are ground down by successive collisions. Eventually the smallest fragments are removed by the inward drift due to gas drag. Therefore, the collisional disruption depletes the planetesimal disk and inhibits embryo growth. We provide analytical formulae for the final masses of planetary embryos, taking into account planetesimal depletion due to collisional disruption. Furthermore, we perform the statistical simulations for embryo growth (which excellently reproduce results of direct N-body simulations if disruption is neglected). These analytical formulae are consistent with the outcome of our statistical simulations. Our results indicate that the final embryo mass at several AU in the minimum-mass solar nebula can reach about ∼0.1 Earth mass within 107 years. This brings another difficulty in formation of gas giant planets, which requires cores with ∼10 Earth masses for gas accretion. However, if the nebular disk is 10 times more massive than the minimum-mass solar nebula and the initial planetesimal size is larger than 100 km, as suggested by some models of planetesimal formation, the final embryo mass reaches about 10 Earth masses at 3-4 AU. The enhancement of embryos’ collisional cross sections by their atmosphere could further increase their final mass to form gas giant planets at 5-10 AU in the Solar System. 相似文献
2.
S.J. Weidenschilling 《Icarus》2011,214(2):671-684
The present size frequency distribution (SFD) of bodies in the asteroid belt appears to have preserved some record of the primordial population, with an excess of bodies of diameter D ∼ 100 km relative to a simple power law. The survival of Vesta’s basaltic crust also implies that the early SFD had a shallow slope in the range ∼10-100 km. (Morbidelli, A., Bottke, W.F., Nesvorny, D., Levison, H.F. [2009]. Icarus 204, 558-573) were unable to produce these features by accretion from an initial population of km-sized planetesimals. They concluded that bodies with sizes in the range ∼100-1000 km and a SFD similar to the current population were produced directly from solid particles of sub-meter scale, without experiencing accretion through intermediate sizes. We present results of new accretion simulations in the primordial asteroid region. The requisite SFD can be produced from an initial population of planetesimals of sizes ?0.1 km, smaller than the usual assumption of km-sized bodies. The bump at D ∼ 100 km is produced by a transition from dispersion-dominated runaway growth to a regime dominated by Keplerian shear, before the formation of large protoplanetary embryos. Thus, accretion of the asteroids from an initial population of small (sub-km) planetesimals cannot be ruled out. 相似文献
3.
How big were the first planetesimals? We attempt to answer this question by conducting coagulation simulations in which the planetesimals grow by mutual collisions and form larger bodies and planetary embryos. The size frequency distribution (SFD) of the initial planetesimals is considered a free parameter in these simulations, and we search for the one that produces at the end objects with a SFD that is consistent with Asteroid belt constraints. We find that, if the initial planetesimals were small (e.g. km-sized), the final SFD fails to fulfill these constraints. In particular, reproducing the bump observed at diameter in the current SFD of the asteroids requires that the minimal size of the initial planetesimals was also ∼100 km. This supports the idea that planetesimals formed big, namely that the size of solids in the proto-planetary disk “jumped” from sub-meter scale to multi-kilometer scale, without passing through intermediate values. Moreover, we find evidence that the initial planetesimals had to have sizes ranging from 100 to several 100 km, probably even 1000 km, and that their SFD had to have a slope over this interval that was similar to the one characterizing the current asteroids in the same size range. This result sets a new constraint on planetesimal formation models and opens new perspectives for the investigation of the collisional evolution in the Asteroid and Kuiper belts as well as of the accretion of the cores of the giant planets. 相似文献
4.
We present results from a suite of N-body simulations that follow the formation and accretion history of the terrestrial planets using a new parallel treecode that we have developed. We initially place 2000 equal size planetesimals between 0.5 and 4.0 AU and the collisional growth is followed until the completion of planetary accretion (>100 Myr). A total of 64 simulations were carried out to explore sensitivity to the key parameters and initial conditions. All the important effect of gas in laminar disks are taken into account: the aerodynamic gas drag, the disk-planet interaction including Type I migration, and the global disk potential which causes inward migration of secular resonances as the gas dissipates. We vary the initial total mass and spatial distribution of the planetesimals, the time scale of dissipation of nebular gas (which dissipates uniformly in space and exponentially in time), and orbits of Jupiter and Saturn. We end up with 1-5 planets in the terrestrial region. In order to maintain sufficient mass in this region in the presence of Type I migration, the time scale of gas dissipation needs to be 1-2 Myr. The final configurations and collisional histories strongly depend on the orbital eccentricity of Jupiter. If today’s eccentricity of Jupiter is used, then most of bodies in the asteroidal region are swept up within the terrestrial region owing to the inward migration of the secular resonance, and giant impacts between protoplanets occur most commonly around 10 Myr. If the orbital eccentricity of Jupiter is close to zero, as suggested in the Nice model, the effect of the secular resonance is negligible and a large amount of mass stays for a long period of time in the asteroidal region. With a circular orbit for Jupiter, giant impacts usually occur around 100 Myr, consistent with the accretion time scale indicated from isotope records. However, we inevitably have an Earth size planet at around 2 AU in this case. It is very difficult to obtain spatially concentrated terrestrial planets together with very late giant impacts, as long as we include all the above effects of gas and assume initial disks similar to the minimum mass solar nebular. 相似文献
5.
When preplanetary bodies reach proportions of ∼1 km or larger in size, their accretion rate is enhanced due to gravitational focusing (GF). We have developed a new numerical model to calculate the collisional evolution of the gravitationally-enhanced growth stage. The numerical model is novel as it attempts to preserve the individual particle nature of the bodies (like N-body codes); yet it is statistical in nature since it must incorporate the very large number of planetesimals. We validate our approach against existing N-body and statistical codes. Using the numerical model, we explore the characteristics of the runaway growth and the oligarchic growth accretion phases starting from an initial population of single planetesimal radius R0. In models where the initial random velocity dispersion (as derived from their eccentricity) starts out below the escape speed of the planetesimal bodies, the system experiences runaway growth. We associate the initial runaway growth phase with increasing GF-factors for the largest body. We find that during the runaway growth phase the size distribution remains continuous but evolves into a power-law at the high-mass end, consistent with previous studies. Furthermore, we find that the largest body accretes from all mass bins; a simple two-component approximation is inapplicable during this stage. However, with growth the runaway body stirs up the random motions of the planetesimal population from which it is accreting. Ultimately, this feedback stops the fast growth and the system passes into oligarchy, where competitor bodies from neighboring zones catch up in terms of mass. We identify the peak of GF with the transition between the runaway growth and oligarchy accretion stages. Compared to previous estimates, we find that the system leaves the runaway growth phase at a somewhat larger radius, especially at the outer disk. Furthermore, we assess the relevance of small, single-size fragments on the growth process. In classical models, where the initial velocity dispersion of bodies is small, these do not play a critical role during the runaway growth; however, in models that are characterized by large initial relative velocities due to external stirring of their random motions, a situation can emerge where fragments dominate the accretion, which could lead to a very fast growth. 相似文献
6.
We have calculated formation of gas giant planets based on the standard core accretion model including effects of fragmentation and planetary envelope. The accretion process is found to proceed as follows. As a result of runaway growth of planetesimals with initial radii of ∼10 km, planetary embryos with a mass of ∼1027 g (∼ Mars mass) are found to form in ∼105 years at Jupiter's position (5.2 AU), assuming a large enough value of the surface density of solid material (25 g/cm2) in the accretion disk at that distance. Strong gravitational perturbations between the runaway planetary embryos and the remaining planetesimals cause the random velocities of the planetesimals to become large enough for collisions between small planetesimals to lead to their catastrophic disruption. This produces a large number of fragments. At the same time, the planetary embryos have envelopes, that reduce energies of fragments by gas drag and capture them. The large radius of the envelope increases the collision rate between them, resulting in rapid growth of the planetary embryos. By the combined effects of fragmentation and planetary envelope, the largest planetary embryo with 21M⊕ forms at 5.2 AU in 3.8×106 years. The planetary embryo is massive enough to start a rapid gas accretion and forms a gas giant planet. 相似文献
7.
《Icarus》1998,132(1):113-124
We present results of two-dimensional gravitationalN-body simulations of the late stage of planetary formation. This stage is characterized by the direct accretion of hundreds of lunar-sized planetesimals into planetary bodies. Our simulation code is based on the Hermite Individual Timestep integration algorithm, and gravitational interactions among all bodies are included throughout the simulations. We compare our simulation with earlier works that do not include all interactions, and we find very good agreement. A previously published collisional fragmentation model is included in our simulation to study the effects of the production of fragments on the subsequent evolution of the larger planetary bodies. It is found that for realistic two-body collisions that, according to this model, both bodies will suffer fragmentation, and that the outcome of the collision will be a relatively large core containing most of the mass and a few small fragments. We present the results of simulations that include this simple fragmentation model. They indicate that the presence of small fragments have only a small effect on the growth or orbital evolution of the large planet-sized bodies. 相似文献
8.
Our goal is to understand primary accretion of the first planetesimals. Some examples are seen today in the asteroid belt, providing the parent bodies for the primitive meteorites. The primitive meteorite record suggests that sizeable planetesimals formed over a period longer than a million years, each of which being composed entirely of an unusual, but homogeneous, mixture of millimeter-size particles. We sketch a scenario that might help explain how this occurred, in which primary accretion of 10-100 km size planetesimals proceeds directly, if sporadically, from aerodynamically-sorted millimeter-size particles (generically “chondrules”). These planetesimal sizes are in general agreement with the currently observed asteroid mass peak near 100 km 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 100 km diameter range. We estimate formation rates of planetesimals and explore parameter space to assess the conditions needed to match estimates of both asteroid and Kuiper Belt Object (KBO) formation rates. For 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. As previously noted, the model naturally helps explain the peculiar size distribution of chondrules within such objects. 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. The scenario also produces 10-100 km diameter primary KBOs, and also requires an enhanced abundance of solids to match the mass production rate estimates for KBOs (and presumably the planetesimal precursors of the ice giants themselves). We discuss the advantages and plausibility of the scenario, outstanding issues, and future directions of research. 相似文献
9.
S. J. Weidenschilling 《Meteoritics & planetary science》2019,54(5):1115-1132
Thermal models of asteroids generally assume that they accreted either instantaneously or over an extended interval with a prescribed growth rate. It is conventionally assumed that the onset of accretion of chondrite parent bodies was delayed until a substantial fraction of the initial 26Al had decayed. However, this interval is not consistent with the early melting, and differentiation of parent bodies of iron meteorites. Formation time scales are tested by dynamical simulations of accretion from small primary planetesimals. Gravitational accretion yields rapid runaway growth of large planetary embryos until most smaller bodies are depleted. In a given simulation, all asteroid‐sized bodies have comparable growth times, regardless of size. For plausible parameters, growth times are shorter than the lifetime of 26Al, consistent with thermal models that assume instantaneous accretion. Rapid growth after planetesimal formation is consistent with differentiation of parent bodies of iron meteorites, but not with the assumed delay in formation of chondritic bodies. After the initial growth stage, there is an interval of slower evolution until the belt is stirred and the embryos are dynamically removed. During this interval, a fraction of asteroid‐sized bodies experience large accretional impacts, allowing bodies of the same final size to have very different histories of radius versus time. Accretion from small primary planetesimals leaves some fraction of material in bodies small enough to preserve CAIs while avoiding heating by 26Al. Unheated material can be a significant fraction of the mass that remains after large embryos are removed from the Main Belt. 相似文献
10.
Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m−3, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating. 相似文献
11.
The final stage in the formation of terrestrial planets consists of the accumulation of ∼1000-km “planetary embryos” and a swarm of billions of 1-10 km “planetesimals.” During this process, water-rich material is accreted by the terrestrial planets via impacts of water-rich bodies from beyond roughly 2.5 AU. We present results from five high-resolution dynamical simulations. These start from 1000-2000 embryos and planetesimals, roughly 5-10 times more particles than in previous simulations. Each simulation formed 2-4 terrestrial planets with masses between 0.4 and 2.6 Earth masses. The eccentricities of most planets were ∼0.05, lower than in previous simulations, but still higher than for Venus, Earth and Mars. Each planet accreted at least the Earth's current water budget. We demonstrate several new aspects of the accretion process: (1) The feeding zones of terrestrial planets change in time, widening and moving outward. Even in the presence of Jupiter, water-rich material from beyond 2.5 AU is not accreted for several millions of years. (2) Even in the absence of secular resonances, the asteroid belt is cleared of >99% of its original mass by self-scattering of bodies into resonances with Jupiter. (3) If planetary embryos form relatively slowly, then the formation of embryos in the asteroid belt may have been stunted by the presence of Jupiter. (4) Self-interacting planetesimals feel dynamical friction from other small bodies, which has important effects on the eccentricity evolution and outcome of a simulation. 相似文献
12.
Richard Greenberg Stuart J. Weidenschilling Clark R. Chapman Donald R. Davis 《Icarus》1984,59(1):87-113
Numerical simulations of planet growth in the outer solar system shows thatgrwoth of Uranus and Neptune occurs in reasonably short time, well below the actual age of the system, without the need for ad hoc assumptions about excess mass or artificially low relative velocities among the icy planetesimals. Low velocities, which speed accretion, are a natural consequence of the non-power-law size distribution of planetesimals, just as in our earlier simulations of terrestial planet growth. Initial planetesimals of size ～ 100 km, predicted by formal expressions for gravitational instability in a thin disk of solid material, failed to produce sufficient debris in the size range 1 to 10 km to account for population of the Oort cloud with comet-sized bodies. However, our model of nonhomologous settling of grains to the midplane of the solar system shows that gravitational clumping did not wait until all solid material had settled to the midplane, as had been assumed in earlier models. Rather, the clumping occurred in successive portions of the material that reached the midplane, producing “initial” planetesimals probably of comet-like sizes. Models of subsequent collisional evolution show that such an initial size distribution, similar to known comets, would have been required in order to have an adequate comet-like size distribution available to feed the Oort cloud as the other planets reach full size. Comets are probably unaltered remnants of the initial population of planetesimals in the outer solar system, not fragments of larger bodies. 相似文献
13.
14.
Thermal evolution of trans‐Neptunian objects,icy satellites,and minor icy planets in the early solar system 
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下载免费PDF全文 Numerical simulations are performed to understand the early thermal evolution and planetary scale differentiation of icy bodies with the radii in the range of 100–2500 km. These icy bodies include trans‐Neptunian objects, minor icy planets (e.g., Ceres, Pluto); the icy satellites of Jupiter, Saturn, Uranus, and Neptune; and probably the icy‐rocky cores of these planets. The decay energy of the radionuclides, 26Al, 60Fe, 40K, 235U, 238U, and 232Th, along with the impact‐induced heating during the accretion of icy bodies were taken into account to thermally evolve these planetary bodies. The simulations were performed for a wide range of initial ice and rock (dust) mass fractions of the icy bodies. Three distinct accretion scenarios were used. The sinking of the rock mass fraction in primitive water oceans produced by the substantial melting of ice could lead to planetary scale differentiation with the formation of a rocky core that is surrounded by a water ocean and an icy crust within the initial tens of millions of years of the solar system in case the planetary bodies accreted prior to the substantial decay of 26Al. However, over the course of billions of years, the heat produced due to 40K, 235U, 238U, and 232Th could have raised the temperature of the interiors of the icy bodies to the melting point of iron and silicates, thereby leading to the formation of an iron core. Our simulations indicate the presence of an iron core even at the center of icy bodies with radii ≥500 km for different ice mass fractions. 相似文献
15.
Most stars reside in binary/multiple star systems; however, previous models of planet formation have studied growth of bodies orbiting an isolated single star. Disk material has been observed around both components of some young close binary star systems. Additionally, it has been shown that if planets form at the right places within such disks, they can remain dynamically stable for very long times. Herein, we numerically simulate the late stages of terrestrial planet growth in circumbinary disks around ‘close’ binary star systems with stellar separations 0.05 AU?aB?0.4 AU and binary eccentricities 0?eB?0.8. In each simulation, the sum of the masses of the two stars is 1 M⊙, and giant planets are included. The initial disk of planetary embryos is the same as that used for simulating the late stages of terrestrial planet formation within our Solar System by Chambers [Chambers, J.E., 2001. Icarus 152, 205-224], and around each individual component of the α Centauri AB binary star system by Quintana et al. [Quintana, E.V., Lissauer, J.J., Chambers, J.E., Duncan, M.J., 2002. Astrophys. J. 576, 982-996]. Multiple simulations are performed for each binary star system under study, and our results are statistically compared to a set of planet formation simulations in the Sun-Jupiter-Saturn system that begin with essentially the same initial disk of protoplanets. The planetary systems formed around binaries with apastron distances QB≡aB(1+eB)?0.2 AU are very similar to those around single stars, whereas those with larger maximum separations tend to be sparcer, with fewer planets, especially interior to 1 AU. We also provide formulae that can be used to scale results of planetary accretion simulations to various systems with different total stellar mass, disk sizes, and planetesimal masses and densities. 相似文献
16.
The fossilized size distribution of the main asteroid belt 总被引：1，自引：0，他引：1
Planet formation models suggest the primordial main belt experienced a short but intense period of collisional evolution shortly after the formation of planetary embryos. This period is believed to have lasted until Jupiter reached its full size, when dynamical processes (e.g., sweeping resonances, excitation via planetary embryos) ejected most planetesimals from the main belt zone. The few planetesimals left behind continued to undergo comminution at a reduced rate until the present day. We investigated how this scenario affects the main belt size distribution over Solar System history using a collisional evolution model (CoEM) that accounts for these events. CoEM does not explicitly include results from dynamical models, but instead treats the unknown size of the primordial main belt and the nature/timing of its dynamical depletion using innovative but approximate methods. Model constraints were provided by the observed size frequency distribution of the asteroid belt, the observed population of asteroid families, the cratered surface of differentiated Asteroid (4) Vesta, and the relatively constant crater production rate of the Earth and Moon over the last 3 Gyr. Using CoEM, we solved for both the shape of the initial main belt size distribution after accretion and the asteroid disruption scaling law . In contrast to previous efforts, we find our derived function is very similar to results produced by numerical hydrocode simulations of asteroid impacts. Our best fit results suggest the asteroid belt experienced as much comminution over its early history as it has since it reached its low-mass state approximately 3.9-4.5 Ga. These results suggest the main belt's wavy-shaped size-frequency distribution is a “fossil” from this violent early epoch. We find that most diameter D?120 km asteroids are primordial, with their physical properties likely determined during the accretion epoch. Conversely, most smaller asteroids are byproducts of fragmentation events. The observed changes in the asteroid spin rate and lightcurve distributions near D∼100-120 km are likely to be a byproduct of this difference. Estimates based on our results imply the primordial main belt population (in the form of D<1000 km bodies) was 150-250 times larger than it is today, in agreement with recent dynamical simulations. 相似文献
17.
Collisions between planetesimals at speeds of several kilometres per second were common during the early evolution of our Solar System. However, the collateral effects of these collisions are not well understood. In this paper, we quantify the efficiency of heating during high-velocity collisions between planetesimals using hydrocode modelling. We conducted a series of simulations to test the effect on shock heating of the initial porosity and temperature of the planetesimals, the relative velocity of the collision and the relative size of the two colliding bodies. Our results show that while heating is minor in collisions between non-porous planetesimals at impact velocities below 10 km s−1, in agreement with previous work, much higher temperatures are reached in collisions between porous planetesimals. For example, collisions between nearly equal-sized, porous planetesimals can melt all, or nearly all, of the mass of the bodies at collision velocities below 7 km s−1. For collisions of small bodies into larger ones, such as those with an impactor-to-target mass ratio below 0.1, significant localised heating occurs in the target body. At impact velocities as low as 5 km s−1, the mass of melt will be nearly double the mass of the impactor, and the mass of material shock heated by 100 K will be nearly 10 times the mass of the impactor. We present a first-order estimate of the cumulative effects of impact heating on a porous planetesimal parent body by simulating the impact of a population of small bodies until a disruptive event occurs. Before disruption, impact heating is volumetrically minor and highly localised; in no case was more than about 3% of the parent body heated by more than 100 K. However, heating during the final disruptive collision can be significant; in about 10% of cases, almost all of the parent body is heated to 700 K (from an initial temperature of ∼300 K) and more than a tenth of the parent body mass is melted. Hence, energetic collisions between planetesimals could have had important effects on the thermal evolution of primitive materials in the early Solar System. 相似文献
18.
We investigate classical planetesimal accretion in a binary star system of separation ab?50 AU by numerical simulations, with particular focus on the region at a distance of 1 AU from the primary. The planetesimals orbit the primary, are perturbed by the companion and are in addition subjected to a gas drag force. We concentrate on the problem of relative velocities Δv among planetesimals of different sizes. For various stellar mass ratios and binary orbital parameters we determine regions where Δv exceed planetesimal escape velocities vesc (thus preventing runaway accretion) or even the threshold velocity vero for which erosion dominates accretion. Gaseous friction has two crucial effects on the velocity distribution: it damps secular perturbations by forcing periastron alignment of orbits, but at the same time the size-dependence of this orbital alignment induces a significant Δv increase between bodies of different sizes. This differential phasing effect proves very efficient and almost always increases Δv to values preventing runaway accretion, except in a narrow eb?0 domain. The erosion threshold Δv>vero is reached in a wide (ab,eb) space for small <10-km planetesimals, but in a much more limited region for bigger ?50-km objects. In the intermediate vesc<Δv<vero domain, a possible growth mode would be the type II runaway growth identified by Kortenkamp et al. [Kortenkamp, S., Wetherill, G., Inaba, S., 2001. Science 293, 1127-1129]. 相似文献
19.
Abstract— Numerical simulations have been performed for the differentiation of planetesimals undergoing linear accretion growth with 26Al and 60Fe as the heat sources. Planetesimal accretion was started at chosen times up to 3 Ma after Ca‐Al‐rich inclusions (CAIs) were formed, and was continued for periods of 0.001–1 Ma. The planetesimals were initially porous, unconsolidated bodies at 250 K, but became sintered at around 700 K, ending up as compact bodies whose final radii were 20, 50, 100, or 270 km. With further heating, the planetesimals underwent melting and igneous differentiation. Two approaches to core segregation were tried. In the first, labelled A, the core grew gradually before silicate began to melt, and in the second, labelled B, the core segregated once the silicate had become 40% molten. In A, when the silicate had become 20% molten, the basaltic melt fraction began migrating upward to the surface, carrying 26Al with it. The 60Fe partitioned between core and mantle. The results show that the rate and timing of core and crust formation depend mainly on the time after CAIs when planetesimal accretion started. They imply significant melting where accretion was complete before 2 Ma, and a little melting in the deep interiors of planetesimals that accreted as late as 3 Ma. The latest melting would have occurred at <10 Ma. The effect on core and crust formation of the planetesimal's final size, the duration of accretion, and the choice of (60Fe/56Fe)initial were also found to be important, particularly where accretion was late. The results are consistent with the isotopic ages of differentiated meteorites, and they suggest that the accretion of chondritic parent bodies began more than 2 or 3 Ma after CAIs. 相似文献
20.
We model the growth of Jupiter via core nucleated accretion, applying constraints from hydrodynamical processes that result from the disk-planet interaction. We compute the planet's internal structure using a well tested planetary formation code that is based upon a Henyey-type stellar evolution code. The planet's interactions with the protoplanetary disk are calculated using 3-D hydrodynamic simulations. Previous models of Jupiter's growth have taken the radius of the planet to be approximately one Hill sphere radius, RH. However, 3-D hydrodynamic simulations show that only gas within ∼0.25RH remains bound to the planet, with the more distant gas eventually participating in the shear flow of the protoplanetary disk. Therefore in our new simulations, the planet's outer boundary is placed at the location where gas has the thermal energy to reach the portion of the flow not bound to the planet. We find that the smaller radius increases the time required for planetary growth by ∼5%. Thermal pressure limits the rate at which a planet less than a few dozen times as massive as Earth can accumulate gas from the protoplanetary disk, whereas hydrodynamics regulates the growth rate for more massive planets. Within a moderately viscous disk, the accretion rate peaks when the planet's mass is about equal to the mass of Saturn. In a less viscous disk hydrodynamical limits to accretion are smaller, and the accretion rate peaks at lower mass. Observations suggest that the typical lifetime of massive disks around young stellar objects is ∼3 Myr. To account for the dissipation of such disks, we perform some of our simulations of Jupiter's growth within a disk whose surface gas density decreases on this timescale. In all of the cases that we simulate, the planet's effective radiating temperature rises to well above 1000 K soon after hydrodynamic limits begin to control the rate of gas accretion and the planet's distended envelope begins to contract. According to our simulations, proto-Jupiter's distended and thermally-supported envelope was too small to capture the planet's current retinue of irregular satellites as advocated by Pollack et al. [Pollack, J.B., Burns, J.A., Tauber, M.E., 1979. Icarus 37, 587-611]. 相似文献