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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.
John Chambers 《Icarus》2006,180(2):496-513
A new semi-analytic model for the oligarchic growth phase of planetary accretion is developed. The model explicitly calculates damping and excitation of planetesimal eccentricities e and inclinations i due to gas drag and perturbations from embryos. The effects of planetesimal fragmentation, enhanced embryo capture cross sections due to atmospheres, inward planetesimal drift, and embryo-embryo collisions are also incorporated. In the early stages of oligarchic growth, embryos grow rapidly as e and i fall below their equilibrium values. The formation of planetesimal collision fragments also speeds up embryo growth as fragments have low-e, low-i orbits, thereby optimizing gravitational focussing. At later times, the presence of thick atmospheres captured from the nebula aids embryo growth by increasing their capture cross sections. Planetesimal drift due to gas drag can lead to substantial inward transport of solid material. However, inward drift is greatly reduced when embryo atmospheres are present, as the drift timescale is no longer short compared to the accretion timescale. Embryo-embryo collisions increase embryo growth rates by 50% compared to the case where growth is solely due to accretion of planetesimals. Formation of 0.1-Earth-mass protoplanets at 1 AU and 10-Earth-mass cores at 5 AU requires roughly 0.1 and 1 million years respectively, in a nebula where the local solid surface density is 7 g cm−2 at each of these locations. 相似文献
3.
We present N-body simulations of planetary accretion beginning with 1 km radius planetesimals in orbit about a 1 M⊙ star at 0.4 AU. The initial disk of planetesimals contains too many bodies for any current N-body code to integrate; therefore, we model a sample patch of the disk. Although this greatly reduces the number of bodies, we still track in excess of 105 particles. We consider three initial velocity distributions and monitor the growth of the planetesimals. The masses of some particles increase by more than a factor of 100. Additionally, the escape speed of the largest particle grows considerably faster than the velocity dispersion of the particles, suggesting impending runaway growth, although no particle grows large enough to detach itself from the power law size-frequency distribution. These results are in general agreement with previous statistical and analytical results. We compute rotation rates by assuming conservation of angular momentum around the center of mass at impact and that merged planetesimals relax to spherical shapes. At the end of our simulations, the majority of bodies that have undergone at least one merger are rotating faster than the breakup frequency. This implies that the assumption of completely inelastic collisions (perfect accretion), which is made in most simulations of planetary growth at sizes 1 km and above, is inappropriate. Our simulations reveal that, subsequent to the number of particles in the patch having been decreased by mergers to half its initial value, the presence of larger bodies in neighboring regions of the disk may limit the validity of simulations employing the patch approximation. 相似文献
4.
We present results from 44 simulations of late stage planetary accretion, focusing on the delivery of volatiles (primarily water) to the terrestrial planets. Our simulations include both planetary “embryos” (defined as Moon to Mars sized protoplanets) and planetesimals, assuming that the embryos formed via oligarchic growth. We investigate volatile delivery as a function of Jupiter's mass, position and eccentricity, the position of the snow line, and the density (in solids) of the solar nebula. In all simulations, we form 1-4 terrestrial planets inside 2 AU, which vary in mass and volatile content. In 44 simulations we have formed 43 planets between 0.8 and 1.5 AU, including 11 “habitable” planets between 0.9 and 1.1 AU. These planets range from dry worlds to “water worlds” with 100+oceans of water (1 ocean=1.5×1024 g), and vary in mass between 0.23M⊕ and 3.85M⊕. There is a good deal of stochastic noise in these simulations, but the most important parameter is the planetesimal mass we choose, which reflects the surface density in solids past the snow line. A high density in this region results in the formation of a smaller number of terrestrial planets with larger masses and higher water content, as compared with planets which form in systems with lower densities. We find that an eccentric Jupiter produces drier terrestrial planets with higher eccentricities than a circular one. In cases with Jupiter at 7 AU, we form what we call “super embryos,” 1-2M⊕ protoplanets which can serve as the accretion seeds for 2+M⊕ planets with large water contents. 相似文献
5.
Edward R.D. Scott 《Icarus》2006,185(1):72-82
Thermal models and radiometric ages for meteorites show that the peak temperatures inside their parent bodies were closely linked to their accretion times. Most iron meteorites come from bodies that accreted <0.5 Myr after CAIs formed and were melted by 26Al and 60Fe, probably inside 2 AU. Rare carbon-rich differentiated meteorites like ureilites probably also come from bodies that formed <1 Myr after CAIs, but in the outer part of the asteroid belt. Chondrite groups accreted intermittently from diverse batches of chondrules and other materials over a 4 Myr period starting 1 Myr after CAI formation when planetary embryos may already have formed at ∼1 AU. Meteorite evidence precludes accretion of late-forming chondrites on the surface of early-formed bodies; instead chondritic and non-chondritic meteorites probably formed in separate planetesimals. Maximum metamorphic temperatures in chondrite groups are correlated with mean chondrule age, as expected if 26Al and 60Fe were the predominant heat sources. Because late-forming bodies could not accrete close to large, early-formed bodies, planetesimal formation may have spread across the nebula from regions where the differentiated bodies formed. Dynamical models suggest that the asteroids could not have accreted in the main belt if Jupiter formed before the asteroids. Therefore Jupiter probably reached its current mass >3-5 Myr after CAIs formed. This precludes formation of Jupiter via a gravitational instability <1 Myr after the solar nebula formed, and strongly favors core accretion. Jupiter probably formed too late to make chondrules by generating shocks directly, or indirectly by scattering Ceres-sized bodies across the belt. Nevertheless, shocks formed by gravitational instabilities or Ceres-sized bodies scattered by planetary embryos may have produced some chondrules. The minimum lifetime for the solar nebula of 3-5 Myr inferred from the total spread of CAI and chondrule ages may exceed the median lifetime of 3 Myr for protoplanetary disks, but is well within the 1-10 Myr observed range. Shorter formation times for extrasolar planets may help to explain their unusual orbits compared to those of solar giant planets. 相似文献
6.
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
7.
An earlier investigation of the formation of approximately 10(26) g planetary embryos from much smaller planetesimals (G.W. Wetherill and G.R. Stewart 1989, Icarus 77, 350-357) has been extended to include the effects of collisional fragmentation, the low relative velocity regime in which the effects due to solar gravity are important, and independent perturbations of eccentricity and inclination. In agreement with this earlier work, it if found that at 1 AU runaway growth occurs on a approximately 10(-5)-year time scale as a consequence of equipartition of energy between large and small planetesimals. It is now seen that the runaway is initiated after approximately 10(4) years, when the relative velocities of the larger bodies temporarily fall into the low-velocity regime, lowering their inclinations and increasing their gravitational capture rates. After approximately 2 X 10(4) years, relative velocities between most bodies emerge from the low-velocity regime, and these higher velocities tend to inhibit further runaway growth. This rapid runaway growth is self-regulated, however, by these same higher velocities, causing fragmentation of the smaller bodies. The velocities of the collision fragments are reduced by gas drag, facilitating their capture by the growing runaway embryos. Variations in which different fragmentation models are used, or long-range forces between nonrunaway bodies are absent, give similar results. When fragmentation is not included, the time scale for growth increases to approximately 3 X 10(5) years as a result of loss of the self-regulating process described above. 相似文献
8.
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
9.
We model the subnebulae of Jupiter and Saturn wherein satellite accretion took place. We expect each giant planet subnebula to be composed of an optically thick (given gaseous opacity) inner region inside of the planet’s centrifugal radius (where the specific angular momentum of the collapsing giant planet gaseous envelope achieves centrifugal balance, located at rCJ ∼ 15RJ for Jupiter and rCS ∼ 22RS for Saturn) and an optically thin, extended outer disk out to a fraction of the planet’s Roche-lobe (RH), which we choose to be ∼RH/5 (located at ∼150 RJ near the inner irregular satellites for Jupiter, and ∼200RS near Phoebe for Saturn). This places Titan and Ganymede in the inner disk, Callisto and Iapetus in the outer disk, and Hyperion in the transition region. The inner disk is the leftover of the gas accreted by the protoplanet. The outer disk may result from the nebula gas flowing into the protoplanet during the time of giant planet gap-opening (or cessation of gas accretion). For the sake of specificity, we use a solar composition “minimum mass” model to constrain the gas densities of the inner and outer disks of Jupiter and Saturn (and also Uranus). Our model has Ganymede at a subnebula temperature of ∼250 K and Titan at ∼100 K. The outer disks of Jupiter and Saturn have constant temperatures of 130 and 90 K, respectively.Our model has Callisto forming in a time scale ∼106 years, Iapetus in 106-107 years, Ganymede in 103-104 years, and Titan in 104-105 years. Callisto takes much longer to form than Ganymede because it draws materials from the extended, low density portion of the disk; its accretion time scale is set by the inward drift times of satellitesimals with sizes 300-500 km from distances ∼100RJ. This accretion history may be consistent with a partially differentiated Callisto with a ∼300-km clean ice outer shell overlying a mixed ice and rock-metal interior as suggested by Anderson et al. (2001), which may explain the Ganymede-Callisto dichotomy without resorting to fine-tuning poorly known model parameters. It is also possible that particulate matter coupled to the high specific angular momentum gas flowing through the gap after giant planet gap-opening, capture of heliocentric planetesimals by the extended gas disk, or ablation of planetesimals passing through the disk contributes to the solid content of the disk and lengthens the time scale for Callisto’s formation. Furthermore, this model has Hyperion forming just outside Saturn’s centrifugal radius, captured into resonance by proto-Titan in the presence of a strong gas density gradient as proposed by Lee and Peale (2000). While Titan may have taken significantly longer to form than Ganymede, it still formed fast enough that we would expect it to be fully differentiated. In this sense, it is more like Ganymede than like Callisto (Saturn’s analog of Callisto, we expect, is Iapetus). An alternative starved disk model whose satellite accretion time scale for all the regular satellites is set by the feeding of planetesimals or gas from the planet’s Roche-lobe after gap-opening is likely to imply a long accretion time scale for Titan with small quantities of NH3 present, leading to a partially differentiated (Callisto-like) Titan. The Cassini mission may resolve this issue conclusively. We briefly discuss the retention of elements more volatile than H2O as well as other issues that may help to test our model. 相似文献
10.
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
11.
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
12.
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
13.
G.P. Horedt 《Icarus》1985,64(3):448-470
We derive first-order differential equations for the late stages of planetary accretion (planetesimal mass >1013 g). The effect of gravitational encounters, energy exchange, collisions, and gas drag has been included. Two simple models are discussed, namely, (i) when all planetesimals have the same mass and (ii) when there is one large planetesimal and numerous small planetesmals. Gravitational two-body encounters are modeled according to Chandrasekhar's classical theory from stellar dynamics. It is shown that the velocity increase due to mutual encounters can be modeled according to the simple theory of random flights. We find analytical equations for the average velocity decrease due to collisions. Gas drag, if present, is modeled in averaged form up to the first order in the eccentricities and inclinations of the planetesimals. Characteristic time scales for the formation of the terrestrial planets are found for the most favorable models to be of order 108 year. The calculated mass of rock and ice of the giant planets is too low as compared to the observed one. This difficulty of our model could be overcome by assuming a several times larger surface density, an enlarged accretion cross section, and gas accretion during the final stages of accretion of the solid cores of the giant planets. Analytical and numerical results are presebted, the evolutionary tracks showing satisfactory agreement with observations for some models. 相似文献
14.
Assuming that an unknown mechanism (e.g., gas turbulence) removes most of the subnebula gas disk in a timescale shorter than that for satellite formation, we develop a model for the formation of regular (and possibly at least some of the irregular) satellites around giant planets in a gas-poor environment. In this model, which follows along the lines of the work of Safronov et al. [1986. Satellites. Univ. of Arizona Press, Tucson, pp. 89-116], heliocentric planetesimals collide within the planet's Hill sphere and generate a circumplanetary disk of prograde and retrograde satellitesimals extending as far out as ∼RH/2. At first, the net angular momentum of this proto-satellite swarm is small, and collisions among satellitesimals leads to loss of mass from the outer disk, and delivers mass to the inner disk (where regular satellites form) in a timescale ?105 years. This mass loss may be offset by continued collisional capture of sufficiently small <1 km interlopers resulting from the disruption of planetesimals in the feeding zone of the giant planet. As the planet's feeding zone is cleared in a timescale ?105 years, enough angular momentum may be delivered to the proto-satellite swarm to account for the angular momentum of the regular satellites of Jupiter and Saturn. This feeding timescale is also roughly consistent with the independent constraint that the Galilean satellites formed in a timescale of 105-106 years, which may be long enough to accommodate Callisto's partially differentiated state [Anderson et al., 1998. Science 280, 1573; Anderson et al., 2001. Icarus 153, 157-161]. In turn, this formation timescale can be used to provide plausible constraints on the surface density of solids in the satellitesimal disk (excluding satellite embryos for satellitesimals of size ∼1 km), which yields a total disk mass smaller than the mass of the regular satellites, and means that the satellites must form in several ∼10 collisional cycles. However, much more work will need to be conducted concerning the collisional evolution both of the circumplanetary satellitesimals and of the heliocentric planetesimals following giant planet formation before one can assess the significance of this agreement. Furthermore, for enough mass to be delivered to form the regular satellites in the required timescale one may need to rely on (unproven) mechanisms to replenish the feeding zone of the giant planet. We compare this model to the solids-enhanced minimum mass (SEMM) model of Mosqueira and Estrada [2003a. Icarus 163, 198-231; 2003b. Icarus 163, 232-255], and discuss its main consequences for Cassini observations of the saturnian satellite system. 相似文献
15.
The core accretion theory of planet formation has at least two fundamental problems explaining the origins of Uranus and Neptune: (1) dynamical times in the trans-saturnian solar nebula are so long that core growth can take >15 Myr and (2) the onset of runaway gas accretion that begins when cores reach ∼10M⊕ necessitates a sudden gas accretion cutoff just as Uranus and Neptune’s cores reach critical mass. Both problems may be resolved by allowing the ice giants to migrate outward after their formation in solid-rich feeding zones with planetesimal surface densities well above the minimum-mass solar nebula. We present new simulations of the formation of Uranus and Neptune in the solid-rich disk of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672-693) using the initial semimajor axis distribution of the Nice model (Gomes, R., Levison, H.F., Tsiganis, K., Morbidelli, A. [2005]. Nature 435, 466-469; Morbidelli, A., Levison, H.F., Tsiganis, K., Gomes, R. [2005]. Nature 435, 462-465; Tsiganis, K., Gomes, R., Morbidelli, A., Levison, H.F. [2005]. Nature 435, 459-461), with one ice giant forming at 12 AU and the other at 15 AU. The innermost ice giant reaches its present mass after 3.8-4.0 Myr and the outermost after 5.3-6 Myr, a considerable time decrease from previous one-dimensional simulations (e.g. Pollack, J.B., Hubickyj, O., Bodenheimer, P., Lissauer, J.J., Podolak, M., Greenzweig, Y. [1996]. Icarus 124, 62-85). The core masses stay subcritical, eliminating the need for a sudden gas accretion cutoff.Our calculated carbon mass fractions of 22% are in excellent agreement with the ice giant interior models of Podolak et al. (Podolak, M., Weizman, A., Marley, M. [1995]. Planet. Space Sci. 43, 1517-1522) and Marley et al. (Marley, M.S., Gómez, P., Podolak, M. [1995]. J. Geophys. Res. 100, 23349-23354). Based on the requirement that the ice giant-forming planetesimals contain >10% mass fractions of methane ice, we can reject any Solar System formation model that initially places Uranus and Neptune inside of Saturn’s orbit. We also demonstrate that a large population of planetesimals must be present in both ice giant feeding zones throughout the lifetime of the gaseous nebula. This research marks a substantial step forward in connecting both the dynamical and chemical aspects of planet formation. Although we cannot say that the solid-rich solar nebula model of Dodson-Robinson et al. (Dodson-Robinson, S.E., Willacy, K., Bodenheimer, P., Turner, N.J., Beichman, C.A. [2009]. Icarus 200, 672-693) gives exactly the appropriate initial conditions for planet formation, rigorous chemical and dynamical tests have at least revealed it to be a viable model of the early Solar System. 相似文献
16.
Sedimentation rates of silicate grains in gas giant protoplanets formed by disk instability are calculated for protoplanetary masses between 1 MSaturn to 10 MJupiter. Giant protoplanets with masses of 5 MJupiter or larger are found to be too hot for grain sedimentation to form a silicate core. Smaller protoplanets are cold enough to allow grain settling and core formation. Grain sedimentation and core formation occur in the low mass protoplanets because of their slow contraction rate and low internal temperature. It is predicted that massive giant planets will not have cores, while smaller planets will have small rocky cores whose masses depend on the planetary mass, the amount of solids within the body, and the disk environment. The protoplanets are found to be too hot to allow the existence of icy grains, and therefore the cores are predicted not to contain any ices. It is suggested that the atmospheres of low mass giant planets are depleted in refractory elements compared with the atmospheres of more massive planets. These predictions provide a test of the disk instability model of gas giant planet formation. The core masses of Jupiter and Saturn were found to be ∼0.25 M⊕ and ∼0.5 M⊕, respectively. The core masses of Jupiter and Saturn can be substantially larger if planetesimal accretion is included. The final core mass will depend on planetesimal size, the time at which planetesimals are formed, and the size distribution of the material added to the protoplanet. Jupiter's core mass can vary from 2 to 12 M⊕. Saturn's core mass is found to be ∼8 M⊕. 相似文献
17.
The final composition of giant planets formed as a result of gravitational instability in the disk gas depends on their ability to capture solid material (planetesimals) during their ‘pre-collapse’ stage, when they are extended and cold, and contracting quasi-statically. The duration of the pre-collapse stage is inversely proportional roughly to the square of the planetary mass, so massive protoplanets have shorter pre-collapse timescales and therefore limited opportunity for planetesimal capture. The available accretion time for protoplanets with masses of 3, 5, 7, and 10 Jupiter masses is found to be and 5.67×103 years, respectively. The total mass that can be captured by the protoplanets depends on the planetary mass, planetesimal size, the radial distance of the protoplanet from the parent star, and the local solid surface density. We consider three radial distances, 24, 38, and 68 AU, similar to the radial distances of the planets in the system HR 8799, and estimate the mass of heavy elements that can be accreted. We find that for the planetary masses usually adopted for the HR 8799 system, the amount of heavy elements accreted by the planets is small, leaving them with nearly stellar compositions. 相似文献
18.
We compute the growth of isolated gaseous giant planets for several values of the density of the protoplanetary disk, several distances from the central star and two values for the (fixed) radii of accreted planetesimals. Calculations were performed in the frame of the core instability mechanism and the solids accretion rate adopted is that corresponding to the oligarchic growth regime. We find that for massive disks and/or for protoplanets far from the star and/or for large planetesimals, the planetary growth occurs smoothly. However, notably, there are some cases for which we find an envelope instability in which the planet exchanges gas with the surrounding protoplanetary nebula. The timescale of this instability shows that it is associated with the process of planetesimals accretion. The presence of this instability makes it more difficult the formation of gaseous giant planets. 相似文献
19.
The influence of gas drag and gravitational perturbations by a planetary embryo on the orbit of a planetesimal in the solar nebula was examined. Non-Keplerian rotation of the gas causes secular decay of the orbit. If the planetesimal's orbit is exterior to the perturber's, resonant perturbations oppose this drag and can cause it to be trapped in a stable orbit at a commensurability of order j/(j + 1), where j is an integer. Numerical and analytical demonstrations show that resonant trapping occurs for wide ranges of perturbing mass, planetesimal size, and j. Induced eccentricities are large, causing overlap of orbits for bodies in different resonances with j > 2. Collisions between planetesimals in different resonances, or between resonant and nonresonant bodies, result in their disruption. Fragments smaller than a critical size can pass through resonances under the influence of drag and be accreted by the embryo. This effect speeds accretion and tends to prevent dynamical isolation of planetary embryos, making gas-rich scenarios for planetary formation more plausible. 相似文献
20.
We have performed N-body simulations on the stage of protoplanet formation from planetesimals, taking into account so-called “type-I migration,” and damping of orbital eccentricities and inclinations, as a result of tidal interaction with a gas disk without gap formation. One of the most serious problems in formation of terrestrial planets and jovian planet cores is that the migration time scale predicted by the linear theory is shorter than the disk lifetime (106-107 years). In this paper, we investigate retardation of type-I migration of a protoplanet due to a torque from a planetesimal disk in which a gap is opened up by the protoplanet, and torques from other protoplanets which are formed in inner and outer regions. In the first series of runs, we carried out N-body simulations of the planetesimal disk, which ranges from 0.9 to 1.1 AU, with a protoplanet seed in order to clarify how much retardation can be induced by the planetesimal disk and how long such retardation can last. We simulated six cases with different migration speeds. We found that in all of our simulations, a clear gap is not maintained for more than 105 years in the planetesimal disk. For very fast migration, a gap cannot be created in the planetesimal disk. For migration slower than some critical speed, a gap does form. However, because of the growth of the surrounding planetesimals, gravitational perturbation of the planetesimals eventually becomes so strong that the planetesimals diffuse into the vicinity of the protoplanets, resulting in destruction of the gap. After the gap is destroyed, close encounters with the planetesimals rather accelerate the protoplanet migration. In this way, the migration cannot be retarded by the torque from the planetesimal disk, regardless of the migration speed. In the second series of runs, we simulated accretion of planetesimals in wide range of semimajor axis, 0.5 to 2-5 AU, starting with equal mass planetesimals without a protoplanet seed. Since formation of comparable-mass multiple protoplanets (“oligarchic growth”) is expected, the interactions with other protoplanets have a potential to alter the migration speed. However, inner protoplanets migrate before outer ones are formed, so that the migration and the accretion process of a runaway protoplanet are not affected by the other protoplanets placed inner and outer regions of its orbit. From the results of these two series of simulations, we conclude that the existence of planetesimals and multiple protoplanets do not affect type-I migration and therefore the migration shall proceed as the linear theory has suggested. 相似文献