Dynamical behaviour of planetesimals temporarily captured by a planet from heliocentric orbits: basic formulation and the case of low random velocity

Planetesimals encountering with a planet cannot be captured permanently unless energy dissipation is taken into account, but some of them can be temporarily captured in the vicinity of the planet for an extended period of time. Such a process would be important for the origin and dynamical evolution of irregular satellites, short-period comets, and Kuiper-belt binaries. In this paper, we describe the basic formulation for the study of temporary capture of planetesimals from heliocentric orbits using three-body orbital integration, such as the definition of the duration and rate of temporary capture, and present results in the case of low random velocity of planetesimals. In the case of planetesimals initially on circular orbits, we find that planetesimals undergo a close encounter with the planet before they become temporarily captured. When planetesimals are scattered by the planet into the vicinity of one of periodic orbits around the planet, the duration of temporary capture tends to be extended. Typically, these capture orbits are in the retrograde direction around the planet. We evaluate the rate of temporary capture of planetesimals, and find that the ratio of this rate to their collision rate on to the planet increases with increasing semimajor axis of the planet. Similar results are obtained for planetesimals with non-zero but small random velocities, as long as Kepler shear dominates the relative velocity between the planet and planetesimals. For larger initial random velocities of planetesimals, temporary capture in both prograde and retrograde directions with much longer duration becomes possible.     

Simulations of planet migration driven by planetesimal scattering

Evidence has mounted for some time that planet migration is an important part of the formation of planetary systems, both in the Solar System [Malhotra, R., 1993. Nature 365, 819-821] and in extrasolar systems [Mayor, M., Queloz, D., 1995. Nature 378, 355-359; Lin, D.N.C., Bodenheimer, P., Richardson, D.C., 1996. Nature 380, 606-607]. One mechanism that produces migration (the change in a planet's semi-major axis a over time) is the scattering of comet- and asteroid-size bodies called planetesimals [Fernandez, J.A., Ip, W.-H., 1984. Icarus 58, 109-120]. Significant angular momentum exchange can occur between the planets and the planetesimals during local scattering, enough to cause a rapid, self-sustained migration of the planet [Ida, S., Bryden, G., Lin, D.N.C., Tanaka, H., 2000. Astrophys. J. 534, 428-445]. This migration has been studied for the particular case of the four outer planets of the Solar System (as in Gomes et al. [Gomes, R.S., Morbidelli, A., Levison, H.F., 2004. Icarus 170, 492-507]), but is not well understood in general. We have used the Miranda [McNeil, D., Duncan, M., Levison, H.F., 2005. Astron. J. 130, 2884-2899] computer simulation code to perform a broad parameter-space survey of the physical variables that determine the migration of a single planet in a planetesimal disk. Migration is found to be predominantly inwards, and the migration rate is found to be independent of planet mass for low-mass planets in relatively high-mass disks. Indeed, a simple scaling relation from Ida et al. [Ida, S., Bryden, G., Lin, D.N.C., Tanaka, H., 2000. Astrophys. J. 534, 428-445] matches well with the dependencies of the migration rate:

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High‐resolution simulations and visualization of protoplanetary disks: structure of the flow in the vicinity of a massive planet

A problem of mass flow in the immediate vicinity of a planet embedded in a protoplanetary disk is studied numerically in two dimensions. Large differences in temporal and spatial scales involved suggest that a specialized discretization method for solution of hydrodynamical equations may offer great savings in computational resources, and can make extensive parameter studies feasible. Preliminary results obtained with help of Adaptive Mesh Refinement technique and high‐order explicit Eulerian solver are presented. This combination of numerical techniques appears to be an excellent tool which allows for direct simulations of mass flow in vicinity of the accretor at moderate computational cost. The present communication is focused on the structure of the outer part of the circumplanetary disk. We employ the multifluid option to the hydrodynamical solver to prove that the circumplanetary disk is composed of the gas transfered into it from the edges of the gap.     

Dynamical evolution of galactic disks driven by interaction with a satellite

Dynamical evolution of galactic disks driven by interaction with satellite galaxies, particularly the problem of the disk warping and thickening is studied numerically. One of the main purpose of the study is to resolve the long standing problem of the origin of the disk warping. A possible cause of the warp is interaction with a satellite galaxy. In the case of the Milky Way, the LMC has been considered as the candidate. Some linear analysis have already given a positive result, but one had to wait for a fully self-consistent simulation as a proof. I have accomplished the numerical simulations with a million particles, by introducing a hybrid algorithm, SCF-TREE. Those simulations give us quantitative estimates for the Milky Way system. We have found an example in which large warp amplitudes are developed. We also found that the warp amplitudes depend on the halo distribution. Among our three models, the most massive and spherical halo is preferable for the observable warp excitation. This revised version was published online in August 2006 with corrections to the Cover Date.     

Galactic chaos driven by an oscillating massive particle

The effect of an oscillating massive particle on the motion of stars in a spherical Plummer gravitational system is examined for chaotic behaviour for ratios of satellite to parent galaxy masses ranging from .001 to .15. Thee-folding times for chaos are calculated for non-zero angular momentum orbits and discussed in relation to the time-scales for dynamical friction.     

Hydrodynamic simulations of molecular outflows driven by slow-precessing protostellar jets

We present hydrodynamic simulations of molecular outflows driven by jets with a long period of precession, motivated by observations of arc-like features and S-symmetry in outflows associated with young stars. We simulate images of not only H₂ vibrational and CO rotational emission lines, but also of atomic emission. The density cross-section displays a jaw-like cavity, independent of precession rate. In molecular hydrogen, however, we find ordered chains of bow shocks and meandering streamers which contrast with the chaotic structure produced by jets in rapid precession. A feature particularly dominant in atomic emission is a stagnant point in the flow that remains near the inlet and alters shape and brightness as the jet skims by. Under the present conditions, slow jet precession yields a relatively high fraction of mass accelerated to high speeds, as also attested to in simulated CO line profiles. Many outflow structures, characterized by HH 222 (continuous ribbon), HH 240 (asymmetric chains of bow shocks) and RNO 43N (protruding cavities), are probably related to the slow-precession model.     

Making other earths: dynamical simulations of terrestrial planet formation and water delivery

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.     

Dynamical properties of a centrifugally driven outflow from a disc near a black hole

The inclination of the field lines at the surface of the disc plays a crucial role on the nature of the magnetically driven flows. For the non-relativistic case, a centrifugally driven outflow of matter from the disc is possible, if the poloidal component of the magnetic field makes an angle of less than a critical 60° with the disc surface (Blandford and Payne 1982). We investigate the dynamical properties of the magnetically driven flows from the disc near a non-rotating black hole and find that the critical angle becomes larger than 60° when the flows start from the region near the black hole.     

Capture of planetesimals by the giant planets

We investigate the possibility of gravitational capture of planetesimals as temporary or permanent satellites of Uranus and Neptune during the process of planetary growth. The capture mechanism is based in the enhancement of the Hill's sphere of action not only due to the mass acquired by the planet, but also by the variation of the planet-Sun distance as a consequence of the scattering of planetesimals by the planets of the outer solar system. Our calculations indicate that satellite capture was very important, specially during the first stages of the accretion process, contributing in a significant way to the planetary growth.     

First lightcurve observations and rotation of minor planet 127 Johanna

Photoelectric observations of the minor planet 127 Johanna were made in the UBV (RI)_c photometric system during its apparition in 1991 at the Piszkéstetõ mountain-station of Konkoly Observatory from August to December, when it showed a brightness variation with an amplitude of about 0.2 magnitude. The derived H, G values in the two-parameter magnitude system in V are 8.459 ± 0.013 and 0.114 ± 0.020, respectively. The determined V linear phase coefficient is of 0.036 ± 0.001 (mag/deg). The value of G and the observed values of color indices (U-B), (B-V) confirm that this asteroid belongs to the C taxonomic class as it was previously classified. The estimated effective diameter is between 96 and 118 km if the assumed V geometric albedo is of 0.06 and 0.04, respectively. The available data suggest a pure principal axis rotation mode. The mean synodic rotational period of the asteroid 127 Johanna is 6.94 ± 0.29 h. The uncertainty is due to the changing of aspect geometry. This value of the synodic rotation period means that this asteroid has an intermediate rotation period. The sense of rotation is prograde as indicated by the temporal evolution of the time derivative of the ecliptic longitude of the phase angle bisector as well as with the increasing synodic period of rotation during the same interval (October/November and December in 1991). The composite lightcurves created for short arc time data reveal structures with breakings and linear portions in V; this fact and the Fourier coefficients indicate a probably irregularly shaped body. There are slight indications that the B-V is redder close to the brightness minimum and the V-R_c is redder at the brightness maximum, and the periodic behavior cannot be proved in V-I_c. The less full rotational phase coverage of the observational data is insufficient to construct a shape model. The accurate pole orientation obviously cannot be determined using one opposition lightcurve data only. Further observations are required to get a more accurate knowledge of the physical parameters of this asteroid. For this purpose, a good opportunity to perform observations arose in December 1996, when this asteroid was in opposition at the northernmost declination.     

Mars: a small terrestrial planet

Mars is characterized by geological landforms familiar to terrestrial geologists. It has a tenuous atmosphere that evolved differently from that of Earth and Venus and a differentiated inner structure. Our knowledge of the structure and evolution of Mars has strongly improved thanks to a huge amount of data of various types (visible and infrared imagery, altimetry, radar, chemistry, etc) acquired by a dozen of missions over the last two decades. In situ data have provided ground truth for remote-sensing data and have opened a new era in the study of Mars geology. While large sections of Mars science have made progress and new topics have emerged, a major question in Mars exploration—the possibility of past or present life—is still unsolved. Without entering into the debate around the presence of life traces, our review develops various topics of Mars science to help the search of life on Mars, building on the most recent discoveries, going from the exosphere to the interior structure, from the magmatic evolution to the currently active processes, including the fate of volatiles and especially liquid water.     

From planetesimals to terrestrial planets: N-body simulations including the effects of nebular gas and giant planets

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.     

Chondrule formation by the ablation of small planetesimals

Abstract— Numerous models have been proposed to explain the formation of chondrules, but none can be reconciled with the highly diverse properties of these objects. Here the formation of chondrules by the surface melting and ablation of small planetesimals in nebula shock waves is investigated using a numerical model. It is shown that bodies between ～1 mm and 500 m in diameter would have produced molten droplets by ablation during gas drag in nebula shocks stronger than ～2.0 Mach. The properties of chondrules produced by ablation are estimated by comparison with meteorite fusion crusts and through consideration of the environment within the bow shock envelope of ablating planetesimals. It is suggested that most ablation chondrules will have broadly chondritic compositions with depletions in siderophile and chalcophile elements and relatively high volatile contents and textures that are mainly porphyritic. The formation of chondrules by ablation of planetesimals in shock waves was probably most important at a late stage in nebula history and occurred at the same time as chondrules formed by the melting of dust particles. The high abundance of dust particles relative to larger bodies at all stages of accretion implies that only a proportion of chondrules may have been formed by ablation and that genetic groups of chondrules with very different origins may coexist in meteorites.     

Numerical simulations of the differentiation of accreting planetesimals with 26Al and 60Fe as the heat sources

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.     

Orbital stability of massive protoplanets in the terrestrial planet region of the solar system

A number of theories of the formation of the planets advocate that the terrestrial planets were originally of cosmic composition and that it is only subsequent evolution that has removed their volatile components. This paper shows that such protoplanets could have remained in the terrestrial planet region without significant changes occurring in their orbits for an acceptable time interval.     

Numerical simulations of driven MHD waves in coronal loops

The solar corona, modeled by a low-, resistive plasma slab, sustains MHD wave propagations due to footpoint motions in the photosphere. Simple test cases are undertaken to verify the code. Uniform, smooth and steep density, magnetic profile and driver are considered. The numerical simulations presented here focus on the evolution and properties of the Alfvén, fast and slow waves in coronal loops. The plasma responds to the footpoint motion by kink or sausage waves depending on the amount of shear in the magnetic field. The larger twist in the magnetic field of the loop introduces more fast-wave trapping and destroys initially developed sausage-like wave modes. The transition from sausage to kink waves does not depend much on the steep or smooth profile. The slow waves develop more complex fine structures, thus accounting for several local extrema in the perturbed velocity profiles in the loop. Appearance of the remnants of the ideal singularities characteristic of ideal plasma is the prominent feature of this study. The Alfvén wave which produces remnants of the ideal x ^–1 singularity, reminiscent of Alfvén resonance at the loop edges, becomes less pronounced for larger twist. Larger shear in the magnetic field makes the development of pseudo-singularity less prominent in case of a steep profile than that in case of a smooth profile. The twist also causes heating at the edges, associated with the resonance and the phase mixing of the Alfvén and slow waves, to slowly shift to layers inside the slab corresponding to peaks in the magnetic field strength. In addition, increasing the twist leads to a higher heating rate of the loop. Remnants of the ideal log ¦x¦ singularity are observed for fast waves for larger twist. For slow waves they are absent when the plasma experiences large twist in a short time. The steep profiles do not favour the creation of pseudo-singularities as easily as in the smooth case.