Growth of Dust as the Initial Step Toward Planet Formation

We discuss the results of laboratory measurements and theoretical models concerning the aggregation of dust in protoplanetary disks, as the initial step toward planet formation. Small particles easily stick when they collide and form aggregates with an open, often fractal structure, depending on the growth process. Larger particles are still expected to grow at collision velocities of about 1m/s. Experiments also show that, after an intermezzo of destructive velocities, high collision velocities above 10m/s on porous materials again lead to net growth of the target. Considerations of dust-gas interactions show that collision velocities for particles not too different in surface-to-mass ratio remain limited up to sizes about 1m, and growth seems to be guaranteed to reach these sizes quickly and easily. For meter sizes, coupling to nebula turbulence makes destructive processes more likely. Global aggregation models show that in a turbulent nebula, small particles are swept up too fast to be consistent with observations of disks. An extended phase may therefore exist in the nebula during which the small particle component is kept alive through collisions driven by turbulence which frustrates growth to planetesimals until conditions are more favorable for one or more reasons.Comment: Protostars and Planets V (PPV) review. 18 pages, 5 figure

The outcome of protoplanetary dust growth: pebbles, boulders, or planetesimals? I. Mapping the zoo of laboratory collision experiments

The growth processes from protoplanetary dust to planetesimals are not fully understood. Laboratory experiments and theoretical models have shown that collisions among the dust aggregates can lead to sticking, bouncing, and fragmentation. However, no systematic study on the collisional outcome of protoplanetary dust has been performed so far so that a physical model of the dust evolution in protoplanetary disks is still missing. We intend to map the parameter space for the collisional interaction of arbitrarily porous dust aggregates. This parameter space encompasses the dust-aggregate masses, their porosities and the collision velocity. With such a complete mapping of the collisional outcomes of protoplanetary dust aggregates, it will be possible to follow the collisional evolution of dust in a protoplanetary disk environment. We use literature data, perform own laboratory experiments, and apply simple physical models to get a complete picture of the collisional interaction of protoplanetary dust aggregates. In our study, we found four different types of sticking, two types of bouncing, and three types of fragmentation as possible outcomes in collisions among protoplanetary dust aggregates. We distinguish between eight combinations of porosity and mass ratio. For each of these cases, we present a complete collision model for dust-aggregate masses between 10^-12 and 10^2 g and collision velocities in the range 10^-4 to 10^4 cm/s for arbitrary porosities. This model comprises the collisional outcome, the mass(es) of the resulting aggregate(s) and their porosities. We present the first complete collision model for protoplanetary dust. This collision model can be used for the determination of the dust-growth rate in protoplanetary disks.Comment: accepted by Astronomy and Astrophysic

Collisions between equal sized ice grain agglomerates

Following the recent insight in the material structure of comets, protoplanetesimals are assumed to have low densities and to be highly porous agglomerates. It is still unclear if planetesimals can be formed from these objects by collisional growth. Therefore, it is important to study numerically the collisional outcome from low velocity impacts of equal sized porous agglomerates which are too large to be examined in a laboratory experiment. We use the Lagrangian particle method Smooth Particle Hydrodynamics to solve the equations that describe the dynamics of elastic and plastic bodies. Additionally, to account for the influence of porosity, we follow a previous developed equation of state and certain relations between the material strength and the relative density. Collisional growth seems possible for rather low collision velocities and particular material strengths. The remnants of collisions with impact parameters that are larger than 50% of the radius of the colliding objects tend to rotate. For small impact parameters, the colliding objects are effectively slowed down without a prominent compaction of the porous structure, which probably increases the possibility for growth. The protoplanetesimals, however, do not stick together for the most part of the employed material strengths. An important issue in subsequent studies has to be the influence of rotation to collisional growth. Moreover, for realistic simulations of protoplanetesimals it is crucial to know the correct material parameters in more detail.Comment: 7 pages, 11 figures, accepted by A&

Numerical determination of the material properties of porous dust cakes

The formation of planetesimals requires the growth of dust particles through collisions. Micron-sized particles must grow by many orders of magnitude in mass. In order to understand and model the processes during this growth, the mechanical properties, and the interaction cross sections of aggregates with surrounding gas must be well understood. Recent advances in experimental (laboratory) studies now provide the background for pushing numerical aggregate models onto a new level. We present the calibration of a previously tested model of aggregate dynamics. We use plastic deformation of surface asperities as the physical model to bring critical velocities for sticking into accordance with experimental results. The modified code is then used to compute compression strength and the velocity of sound in the aggregate at different densities. We compare these predictions with experimental results and conclude that the new code is capable of studying the properties of small aggregates.Comment: Accepted for publication in A&

Aharonov-Bohm-Coulomb Problem in Graphene Ring

We study the Aharonov-Bohm-Coulomb problem in a graphene ring. We investigate, in particular, the effects of a Coulomb type potential of the form $\xi/r$ on the energy spectrum of Dirac electrons in the graphene ring in two different ways: one for the scalar coupling and the other for the vector coupling. It is found that, since the potential in the scalar coupling breaks the time-reversal symmetry between the two valleys as well as the effective time-reversal symmetry in a single valley, the energy spectrum of one valley is separated from that of the other valley, demonstrating a valley polarization. In the vector coupling, however, the potential does not break either of the two symmetries and its effect appears only as an additive constant to the spectrum of Aharonov-Bohm potential. The corresponding persistent currents, the observable quantities of the symmetry-breaking energy spectra, are shown to be asymmetric about zero magnetic flux in the scalar coupling, while symmetric in the vector coupling.Comment: 20 pages, 12 figures (V2) 18 pages, accepted in JPHYS

Low-velocity collisions of centimeter-sized dust aggregates

Collisions between centimeter- to decimeter-sized dusty bodies are important to understand the mechanisms leading to the formation of planetesimals. We thus performed laboratory experiments to study the collisional behavior of dust aggregates in this size range at velocities below and around the fragmentation threshold. We developed two independent experimental setups with the same goal to study the effects of bouncing, fragmentation, and mass transfer in free particle-particle collisions. The first setup is an evacuated drop tower with a free-fall height of 1.5 m, providing us with 0.56 s of microgravity time so that we observed collisions with velocities between 8 mm/s and 2 m/s. The second setup is designed to study the effect of partial fragmentation (when only one of the two aggregates is destroyed) and mass transfer in more detail. It allows for the measurement of the accretion efficiency as the samples are safely recovered after the encounter. Our results are that for very low velocities we found bouncing as could be expected while the fragmentation velocity of 20 cm/s was significantly lower than expected. We present the critical energy for disruptive collisions Q*, which showed up to be at least two orders of magnitude lower than previous experiments in the literature. In the wide range between bouncing and disruptive collisions, only one of the samples fragmented in the encounter while the other gained mass. The accretion efficiency in the order of a few percent of the particle's mass is depending on the impact velocity and the sample porosity. Our results will have consequences for dust evolution models in protoplanetary disks as well as for the strength of large, porous planetesimal bodies

Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states

We study the influence of different edge types on the electronic density of states of graphene nanostructures. To this end we develop an exact expansion for the single particle Green's function of ballistic graphene structures in terms of multiple reflections from the system boundary, that allows for a natural treatment of edge effects. We first apply this formalism to calculate the average density of states of graphene billiards. While the leading term in the corresponding Weyl expansion is proportional to the billiard area, we find that the contribution that usually scales with the total length of the system boundary differs significantly from what one finds in semiconductor-based, Schr\"odinger type billiards: The latter term vanishes for armchair and infinite mass edges and is proportional to the zigzag edge length, highlighting the prominent role of zigzag edges in graphene. We then compute analytical expressions for the density of states oscillations and energy levels within a trajectory based semiclassical approach. We derive a Dirac version of Gutzwiller's trace formula for classically chaotic graphene billiards and further obtain semiclassical trace formulae for the density of states oscillations in regular graphene cavities. We find that edge dependent interference of pseudospins in graphene crucially affects the quantum spectrum.Comment: to be published in Phys. Rev.