Direct N-body Simulations of Rubble Pile Collisions

There is increasing evidence that many km-sized bodies in the Solar System are piles of rubble bound together by gravity. We present results from a project to map the parameter space of collisions between km-sized spherical rubble piles. The results will assist in parameterization of collision outcomes for Solar System formation models and give insight into fragmentation scaling laws. We use a direct numerical method to evolve the positions and velocities of the rubble pile particles under the constraints of gravity and physical collisions. We test the dependence of the collision outcomes on impact parameter and speed, impactor spin, mass ratio, and coefficient of restitution. Speeds are kept low (< 10 m/s, appropriate for dynamically cool systems such as the primordial disk during early planet formation) so that the maximum strain on the component material does not exceed the crushing strength. We compare our results with analytic estimates and hydrocode simulations. Off-axis collisions can result in fast-spinning elongated remnants or contact binaries while fast collisions result in smaller fragments overall. Clumping of debris escaping from the remnant can occur, leading to the formation of smaller rubble piles. In the cases we tested, less than 2% of the system mass ends up orbiting the remnant. Initial spin can reduce or enhance collision outcomes, depending on the relative orientation of the spin and orbital angular momenta. We derive a relationship between impact speed and angle for critical dispersal of mass in the system. We find that our rubble piles are relatively easy to disperse, even at low impact speed, suggesting that greater dissipation is required if rubble piles are the true progenitors of protoplanets.Comment: 30 pages including 4 tables, 8 figures. Revised version to be published in Icarus

The Collisional Divot in the Kuiper belt Size Distribution

This paper presents the results of collisional evolution calculations for the Kuiper belt starting from an initial size distribution similar to that produced by accretion simulations of that region - a steep power-law large object size distribution that breaks to a shallower slope at r ~1-2 km, with collisional equilibrium achieved for objects r ~0.5 km. We find that the break from the steep large object power-law causes a divot, or depletion of objects at r ~10-20 km, which in-turn greatly reduces the disruption rate of objects with r> 25-50 km, preserving the steep power-law behavior for objects at this size. Our calculations demonstrate that the roll-over observed in the Kuiper belt size distribution is naturally explained as an edge of a divot in the size distribution; the radius at which the size distribution transitions away from the power-law, and the shape of the divot from our simulations are consistent with the size of the observed roll-over, and size distribution for smaller bodies. Both the kink radius and the radius of the divot center depend on the strength scaling law in the gravity regime for Kuiper belt objects. These simulations suggest that the sky density of r ~1 km objects is ~10^6-10^7 objects per square degree. A detection of the divot in the size distribution would provide a measure of the strength of large Kuiper belt objects, and constrain the shape of the size distribution at the end of accretion in the Kuiper belt.Comment: 32 pages, 10 figures, accepted to the Astrophysical Journa

Modelling circumbinary protoplanetary disks II. Gas disk feedback on planetesimal dynamical and collisional evolution in the circumbinary systems Kepler-16 and 34

Aims. We investigate the feasibility of planetesimal growth in circumbinary protoplanetary disks around the observed systems Kepler- 16 and Kepler-34 under the gravitational influence of a precessing eccentric gas disk. Methods. We embed the results of our previous hydrodynamical simulations of protoplanetary disks around binaries into an N-body code to perform 3D, high-resolution, inter-particle gravity-enabled simulations of planetesimal growth and dynamics that include the gravitational force imparted by the gas. Results. Including the full, precessing asymmetric gas disk generates high eccentricity orbits for planetesimals orbiting at the edge of the circumbinary cavity, where the gas surface density and eccentricity have their largest values. The gas disk is able to efficiently align planetesimal pericenters in some regions leading to phased, non-interacting orbits. Outside of these areas eccentric planetesimal orbits become misaligned and overlap leading to crossing orbits and high relative velocities during planetesimal collisions. This can lead to an increase in the number of erosive collisions that far outweighs the number of collisions that result in growth. Gravitational focusing from the static axisymmetric gas disk is weak and does not significantly alter collision outcomes from the gas free case. Conclusions. Due to asymmetries in the gas disk, planetesimals are strongly perturbed onto highly eccentric orbits. Where planetesimals orbits are not well aligned, orbit crossings lead to an increase in the number of erosive collisions. This makes it difficult for sustained planetesimal accretion to occur at the location of Kepler-16b and Kepler-34b and we therefore rule out in-situ growth. This adds further support to our initial suggestions that most circumbinary planets should form further out in the disk and migrate inwards.Comment: 12 pages and 12 figure

Fragment properties at the catastrophic disruption threshold: The effect of the parent body's internal structure

Numerical simulations of asteroid break-ups, including both the fragmentation of the parent body and the gravitational interactions between the fragments, have allowed us to reproduce successfully the main properties of asteroid families formed in different regimes of impact energy, starting from a non-porous parent body. In this paper, using the same approach, we concentrate on a single regime of impact energy, the so-called catastrophic threshold usually designated by Q*D, which results in the escape of half of the target's mass. Thanks to our recent implementation of a model of fragmentation of porous materials, we can characterize Q*D for both porous and non-porous targets with a wide range of diameters. We can then analyze the potential influence of porosity on the value of Q*D, and by computing the gravitational phase of the collision in the gravity regime, we can characterize the collisional outcome in terms of the fragment size and ejection speed distributions, which are the main outcome properties used by collisional models to study the evolutions of the different populations of small bodies. We also check the dependency of Q*D on the impact speed of the projectile. In the strength regime, which corresponds to target sizes below a few hundreds of meters, we find that porous targets are more difficult to disrupt than non-porous ones. In the gravity regime, the outcome is controlled purely by gravity and porosity in the case of porous targets. In the case of non-porous targets, the outcome also depends on strength. We then propose some power-law relationships between Q*D and both target's size and impact speed that can be used in collisional evolution models.Comment: 18 pages, 19 Figures. Accepted for publication in Icaru

Mycobacterial species causing pulmonary tuberculosis At the korle bu teaching hospital, Accra,

Objective: Characterize mycobacterial species causing pulmonary tuberculosis (PTB) at the Korle-Bu Teaching Hospital in Ghana.Design: Sputum smear positive samples, two (2) from 70 patients diagnosed as having tuberculosis, after they had consented, were collected from the Korle-Bu Teaching Hospital Chest Clinic betweenJanuary and July 2003. Setting: Korle-Bu Teaching Hospital Chest Clinic, Accra. Results: Sixty-four mycobacterial isolates wereobtained and confirmed as members of Mycobacterium tuberculosis complex by colonial morphology and conventional biochemical assays. Fortyseven (73%) were M. tuberculosis, the human strain, 2 (3%) M. bovis, the bovine strain, 13 (20%) M. africanum I (West Africa type), and 2 (3%) M. africanum II (East Africa type). Conclusion: The results indicate that, there are various strains causing PTB at the Korle-BuTeaching Hospital and of great concern is M. bovis, which mostly causes extra-PTB in humans but found to cause PTB in this study. This calls for the need to conduct a nationwide survey using bothconventional and molecular techniques to characterize various mycobacterial species causing TB in Ghana. This will result in better understanding of the various strains circulating in the country andinform individual TB treatment regimen especially the inclusion or exclusion of pyrazinamide

Characterisation of candidate members of (136108) Haumea's family: II. Follow-up observations

From a dynamical analysis of the orbital elements of transneptunian objects (TNOs), Ragozzine & Brown reported a list of candidate members of the first collisional family found among this population, associated with (136108) Haumea (a.k.a. 2003 EL61). We aim to distinguish the true members of the Haumea collisional family from interlopers. We search for water ice on their surfaces, which is a common characteristic of the known family members. The properties of the confirmed family are used to constrain the formation mechanism of Haumea, its satellites, and its family. Optical and near-infrared photometry is used to identify water ice. We use in particular the CH4 filter of the Hawk-I instrument at the European Southern Observatory Very Large Telescope as a short H-band (Hs), the (J-Hs) colour being a sensitive measure of the water ice absorption band at 1.6 {\mu}m. Continuing our previous study headed by Snodgrass, we report colours for 8 candidate family members, including near-infrared colours for 5. We confirm one object as a genuine member of the collisional family (2003 UZ117), and reject 5 others. The lack of infrared data for the two remaining objects prevent any conclusion from being drawn. The total number of rejected members is therefore 17. The 11 confirmed members represent only a third of the 36 candidates. The origin of Haumea's family is likely to be related to an impact event. However, a scenario explaining all the peculiarities of Haumea itself and its family remains elusive.Comment: 8 pages, 4 figures, accepted for publication in A&

The effect of gas drag on the growth of protoplanets -- Analytical expressions for the accretion of small bodies in laminar disks

Planetary bodies form by accretion of smaller bodies. It has been suggested that a very efficient way to grow protoplanets is by accreting particles of size <<km (e.g., chondrules, boulders, or fragments of larger bodies) as they can be kept dynamically cold. We investigate the effects of gas drag on the impact radii and the accretion rates of these particles. As simplifying assumptions we restrict our analysis to 2D settings, a gas drag law linear in velocity, and a laminar disk characterized by a smooth (global) pressure gradient that causes particles to drift in radially. These approximations, however, enable us to cover an arbitrary large parameter space. The framework of the circularly restricted three body problem is used to numerically integrate particle trajectories and to derive their impact parameters. Three accretion modes can be distinguished: hyperbolic encounters, where the 2-body gravitational focusing enhances the impact parameter; three-body encounters, where gas drag enhances the capture probability; and settling encounters, where particles settle towards the protoplanet. An analysis of the observed behavior is presented; and we provide a recipe to analytically calculate the impact radius, which confirms the numerical findings. We apply our results to the sweepup of fragments by a protoplanet at a distance of 5 AU. Accretion of debris on small protoplanets (<50 km) is found to be slow, because the fragments are distributed over a rather thick layer. However, the newly found settling mechanism, which is characterized by much larger impact radii, becomes relevant for protoplanets of ~10^3 km in size and provides a much faster channel for growth.Comment: accepted for publication in Astronomy & Astrophysic

The TAOS Project: Upper Bounds on the Population of Small KBOs and Tests of Models of Formation and Evolution of the Outer Solar System

We have analyzed the first 3.75 years of data from TAOS, the Taiwanese American Occultation Survey. TAOS monitors bright stars to search for occultations by Kuiper Belt Objects (KBOs). This dataset comprises 5e5 star-hours of multi-telescope photometric data taken at 4 or 5 Hz. No events consistent with KBO occultations were found in this dataset. We compute the number of events expected for the Kuiper Belt formation and evolution models of Pan & Sari (2005), Kenyon & Bromley (2004), Benavidez & Campo Bagatin (2009), and Fraser (2009). A comparison with the upper limits we derive from our data constrains the parameter space of these models. This is the first detailed comparison of models of the KBO size distribution with data from an occultation survey. Our results suggest that the KBO population is comprised of objects with low internal strength and that planetary migration played a role in the shaping of the size distribution.Comment: 18 pages, 16 figures, Aj submitte