Impact angle influence in high velocity dust collisions during planetesimal formation

We have examined the influence of impact angle in collisions between small dust aggregates and larger dust targets through laboratory experiments. Targets consisted of μm-sized quartz dust and had a porosity of about 67%; the projectiles, between 1 and 5 mm in diameter, were slightly more compact (64% porosity). The collision velocity was centered at 20 m/s and impact angles range from 0° to 45°. At a given impact angle, the target gained mass for projectiles smaller than a threshold size, which decreases with increasing angle from about 3 mm to 1 mm. The fact that growth is possible up to the largest angles studied supports the idea of planetesimal formation by sweep-up of small dust aggregates.     

Does the gas flow through a porous dust aggregate help its growth in a protoplanetary disk?

Sekiya and Takeda [2003, Earth Planets Space 55, 263-269] showed that the hydrodynamic gas flow around a dust aggregate larger than the mean free path of gas molecules prevents the growth of the body. In contrast to Wurm et al. [2004, Astrophys. J. 606, 983-987], we argue that this conclusion is not altered even if we take account of the effect of the flow through a porous dust aggregate.     

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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Compaction and fragmentation of porous gypsum targets from low-velocity impacts

We performed low-velocity impact experiments of gypsum spheres with porosity ranging from 0 to 61% and diameter ranging from 25 to 83 mm. The impact velocity was from 0.2 to 22 m/s. The target was an iron plate. The outcome of gypsum spheres with porosity 31-61% was different from those of non-porous ice [Higa M., Arakawa, M., Maeno, N., 1996. Planet. Space Sci. 44, 917-925; Higa M., Arakawa, M., Maeno, N., 1998. Icarus 133, 310-320] and non-porous gypsum. In between the intact and fragmentation modes, the outcome of the non-porous ice and gypsum was crack growth at the impact point. However, the outcome of the porous gypsum was compaction. We found that the restitution coefficients of the porous gypsum spheres were all in a similar range, in spite of the difference of the porosity and size at impact velocities up to about 10 m/s where they begin to be fragmented in pieces. Moreover, there is not a large difference between the restitution coefficient of porous and non-porous gypsum. These results collectively indicate that restitution coefficient of gypsum spheres of cm-size is not strongly dependent upon the porosity and compaction process.     

Clumps in the outer disk by disk instability: Why they are initially gas giants and the legacy of disruption

We explore the initial conditions for fragments in the extended regions of gravitationally unstable disks. We combine analytic estimates for the fragmentation of spiral arms with 3D SPH simulations to show that initial fragment masses are in the gas giant regime. These initial fragments will have substantial angular momentum, and should form disks with radii of a few AU. We show that clumps will survive for multiple orbits before they undergo a second, rapid collapse due to H₂ dissociation and that it is possible to destroy bound clumps by transporting them into the inner disk. The consequences of disrupted clumps for planet formation, dust processing, and disk evolution are discussed. We argue that it is possible to produce Earth-mass cores in the outer disk during the earliest phases of disk evolution.     

The distributions and ages of refractory objects in the solar nebula

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

An efficient, low-velocity, resonant mechanism for capture of satellites by a protoplanet

Numerical simulations of the gravitational scattering of planetesimals by a protoplanet reveal that a significant fraction of scattered planetesimals can become trapped as so-called quasi-satellites in heliocentric 1:1 co-orbital resonance with the protoplanet. While trapped, these resonant planetesimals can have deep low-velocity encounters with the protoplanet that result in temporary or permanent capture onto highly eccentric prograde or retrograde circumplanetary orbits. The simulations include solar nebula gas drag and use planetesimals with diameters ranging from ∼1 to ∼1000 km. Initial protoplanet eccentricities range from ep=0 to 0.15 and protoplanet masses range from 300 Earth-masses (M_⊕) down to 0.1M_⊕. This mass range effectively covers the final masses of all planets currently thought to be in possession of captured satellites—Jupiter, Saturn, Neptune, Uranus, and Mars. For protoplanets on moderately eccentric orbits (ep?0.1) most simulations show from 5-20% of all scattered planetesimals becoming temporarily trapped in the quasi-satellite co-orbital resonance. Typically, 20-30% of the temporarily trapped quasi-satellites of all sizes came within half the Hill radius of the protoplanet while trapped in the resonance. The efficiency of the resonance trapping combined with the subsequent low-velocity circumplanetary capture suggests that this trapped-to-captured transition may be important not only for the origin of captured satellites but also for continued growth of protoplanets.     

Impacts into weak dust targets under microgravity and the formation of planetesimals

We carried out 16 collision experiments in the drop tower in Bremen, Germany. Dust projectiles and solid projectiles of several mm in size impacted a dust target 5 cm in depth and width at velocities between 3.5 and 21.5 m/s. For solid impactors we found significant mass loss on the front (impact) side of the target. Mass loss depended on the impact velocity and projectile type (solid sphere or dust) and was up to 35 times the projectile mass for targets of the lowest tensile strength. Typical fragment velocities on the front side of the target ranged from 3 to 12 cm/s. The ejecta velocity was independent of the impact velocity but it increased with projectile mass. On the back side of the target (opposite to the impact side) mass was ejected from the target above a certain threshold impact velocity. Ejection velocity on the back side increased with impact velocity and is larger for solid projectiles than for dust projectiles. In one case a slightly stronger target gained mass in a slow dust-dust collision. We verified that collisions of dust projectiles with compact, very strong dust targets lead to a more massive target accreting part of the projectile. Applied to planetesimal formation, the experiments suggest that the maximum possible ejecta velocity from a body of several cm in size after a collision is small. Ejecta were slow enough that they were reaccreted by means of gas flow if large pores were part of the body's morphology. While very weak bodies cannot grow in the primary collision at the given velocities, this can lead to growth by secondary collisions. Slight compression, which could result from preceding collisions, might lead to immediate growth of a body in slow collisions by adding projectile mass.     

Low velocity impacts into dust: results from the COLLIDE-2 microgravity experiment

We present the results of the second flight of the Collisions Into Dust Experiment (COLLIDE-2), a space shuttle payload that performs six impact experiments into simulated planetary regolith at speeds between 1 and 100 cm/s. COLLIDE-2 flew on the STS-108 mission in December 2001 following an initial flight in April 1998. The experiment was modified since the first flight to provide higher quality data, and the impact parameters were varied. Spherical quartz projectiles of 1-cm radius were launched into quartz sand and JSC-1 lunar regolith simulant targets 2-cm deep. At impact speeds below ∼20 cm/s the projectile embedded itself in the target material and did not rebound. Some ejecta were produced at ∼10 cm/s. At speeds >25 cm/s the projectile rebounded and significant ejecta was produced. We present coefficients of restitution, ejecta velocities, and limits on ejecta masses. Ejecta velocities are typically less than 10% of the impact velocity, and the fraction of impact kinetic energy partitioned into ejecta kinetic energy is also less than 10%. Taken together with a proposed aerodynamic planetesimal growth mechanism, these results support planetesimal growth at impact speeds above the nominal observed threshold of about 20 cm/s.     

A semi-analytic model for oligarchic growth

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.