Roland Speith

A comparative study of disc–planet interaction

We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analysed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5 per cent for the Eulerian simulations. The SPH results predict the correct shape of the gap although have less resolution in the low-density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10 per cent. The spread is larger in the tidal torques acting on the planet which agree within a factor of 2 at the end of the simulation. In the Neptune case, the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.

THE PHYSICS OF PROTOPLANETESIMAL DUST AGGLOMERATES. IV. TOWARD A DYNAMICAL COLLISION MODEL

Recent years have shown many advances in our knowledge of the collisional evolution of protoplanetary dust. Based on a variety of dust-collision experiments in the laboratory, our view of the growth of dust aggregates in protoplanetary disks is now supported by a deeper understanding of the physics involved in the interaction between dust agglomerates. However, the parameter space, which determines the collisional outcome, is huge and sometimes inaccessible to laboratory experiments. Very large or fluffy dust aggregates and extremely low collision velocities are beyond the boundary of todays laboratories. It is therefore desirable to augment our empirical knowledge of dust-collision physics with a numerical method to treat arbitrary aggregate sizes, porosities, and collision velocities. In this paper, we implement experimentally determined material parameters of highly porous dust aggregates into a smooth particle hydrodynamics (SPH) code, in particular an omnidirectional compressive-strength and a tensile-strength relation. We also give a prescription of calibrating the SPH code with compression and low-velocity impact experiments. In the process of calibration, we developed a dynamic compressive-strength relation and estimated a relation for the shear strength. Finally, we defined and performed a series of benchmark tests and found the agreement between experimental results and numerical simulations to be very satisfactory. SPH codes have been used in the past to study collisions at rather high velocities. At the end of this work, we show examples of future applications in the low-velocity regime of collisional evolution.

Accretion dynamics in neutron star-black hole binaries

We perform three-dimensional, Newtonian hydrodynamic simulations with a nuclear equation of state to investigate the accretion dynamics in neutron star black hole systems. We find as a general result that non-spinning donor stars yield larger circularization radii than corotating donors. Therefore, the matter from a neutron star without spin will more likely settle into an accretion disk outside the Schwarzschild radius. With the used stiff equation of state we find it hard to form an accretion disk that is promising to launch a gamma-ray burst. In all relevant cases the core of the neutron star survives and keeps orbiting the black hole as a mini neutron star for the rest of the simulation time (up to several hundred dynamical neutron star times scales). The existence of this mini neutron star leaves a clear imprint on the gravitational wave signal which thus can be used to probe the physics at supra-nuclear densities.

Collisions between equal-sized ice grain agglomerates

Context. 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. Aims. 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. Methods. 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. Results. 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. Conclusions. 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.

The four-population model: a new classification scheme for pre-planetesimal collisions

Context. Within the collision growth scenario for planetesimal formation, the growth step from centimetre-sized pre-planetesimals to kilometre-sized planetesimals remains unclear. The formation of larger objects from the highly porous pre-planetesimals may be halted by a combination of fragmentation in disruptive collisions and mutual rebound with compaction. However, the right amount of fragmentation is necessary to explain the observed dust features in late T Tauri discs. Therefore, detailed data on the outcome of pre-planetesimal collisions is required and has to be presented in a suitable and precise format. Aims. We wish to develop a new classification scheme broad enough to encompass all events with sticking, bouncing, and fragmentation contributions, accurate enough to capture the important collision outcome nuances, and at the same time simple enough to be implementable in global dust coagulation simulations. We furthermore wish to demonstrate the reliability of our numerical smoothed particle hydrodynamics (SPH) model and the applicability of our new collision outcome classification to previous results as well as our simulation results. Methods. We propose and apply a scheme based on the quantitative aspects of four fragment populations: the largest and second largest fragment, a power-law population, and a sub-resolution population. For the simulations of pre-planetesimal collisions, we adopt the SPH numerical scheme with extensions for the simulation of porous solid bodies. On the basis of laboratory benchmark experiments, this model was previously calibrated and tested for the correct simulation of the compaction, bouncing, and fragmentation behaviour of macroscopic highly porous SiO2 dust aggregates. Results. We demonstrate that previous attempts to map collision data were much too oriented on qualitatively categorising into sticking, bouncing, and fragmentation events. Intermediate categories are found in our simulations that are difficult to map to existing qualitative categorisations. We show that the four-population model encompasses all previous categorisations and in addition allows for transitions. This is because it is based on quantitative characteristic attributes of each population such as the mass, kinetic energy, and filling factor. In addition, the numerical porosity model successfully passes another benchmark test: the correct simulation of the entire list of collision outcome types yielded by laboratory experiments. As a demonstration of the applicability and the power of the four-population model, we utilise it to present the results of a study on the influence of collision velocity in head-on collisions of intermediate porosity aggregates.

Numerical simulations of highly porous dust aggregates in the low-velocity collision regime - Implementation and calibration of a smooth particle hydrodynamics code

Context. A highly favoured mechanism of planetesimal formation is collisional growth. Single dust grains hit each other with relative velocities produced by gas flows in the protoplanetary disc. They stick together with van der Waals forces and form fluffy aggregates up to a centimetre size. The mechanism responsible for any additional growth is unclear since the outcome of aggregate collisions in the relevant velocity and size regime cannot be investigated in the laboratory under protoplanetary disc conditions. Realistic statistics for dust aggregate collisions beyond decimetre size are required to obtain a deeper understanding of planetary growth. Aims. By combining experimental and numerical efforts, we wish to calibrate and validate a computer program capable of accurately simulating the macroscopic behaviour of highly porous dust aggregates. After testing its numerical limitations thoroughly, we check the program especially for a realistic reproduction of the compaction, bouncing, and fragmentation behaviour. This demonstrates the validity of our code, which will be utilised to simulate dust aggregate collisions and accurately determine the fragmentation statistics in future work. Methods. We adopt the smooth particle hydrodynamics (SPH) numerical scheme with extensions to the simulation of solid bodies and a modified version of the Sirono porosity model. Experimentally measured macroscopic material properties of SiO2 dust are implemented. By simulating three different setups, we calibrate and test for the compressive strength relation (compaction experiment) and the bulk modulus (bouncing and fragmentation experiments). Data from experiments and simulations will be compared directly. Results. SPH has already proven to be a suitable tool for simulating collisions at rather high velocities. In this work, we demonstrate that its area of application may be beyond low-velocity experiments and collisions. It can also be used to simulate the behaviour of highly porous objects in this velocity regime to very high accuracy. A correct reproduction of density structures in the compaction experiment, of the coefficient of restitution in the bouncing experiment, and of the fragment mass distribution in the fragmentation experiment illustrate the validity and consistency of our code for the simulation of the elastic and plastic properties of the simulated dust aggregates. The result of this calibration process is an SPH code that can be utilised to investigate the collisional outcome of porous dust in the low-velocity regime.

Compression Behaviour of Porous Dust Agglomerates

Context. The early planetesimal growth proceeds through a sequence of sticking collisions of dust agglomerates. Very uncertain is still the relative velocity regime in which growth rather than destruction can take place. The outcome of a collision depends on the bulk properties of the porous dust agglomerates. Aims. Continuum models of dust agglomerates require a set of material parameters that are often difficult to obtain from laboratory experiments. Here, we aim at determining those parameters from ab initio molecular dynamics simulations. Our goal is to improve on the existing model that describe the interaction of individual monomers. Methods. We use a molecular dynamics approach featuring a detailed micro-physical model of the interaction of spherical grains. The model includes normal forces, rolling, twisting and sliding between the dust grains. We present a new treatment of wall-particle interaction that allows us to perform customized simulations that directly correspond to laboratory experiments. Results. We find that the existing interaction model by Dominik & Tielens leads to a too soft compressive strength behavior for uniand omni-directional compression. Upon making the rolling and sliding coefficients stiffer we find excellent agreement in both cases. Additionally, we find that the compressive strength curve depends on the velocity with which the sample is compressed. Conclusions. The modified interaction strengths between two individual dust grains will lead to a different behavior of the whole dust agglomerate. This will influences the sticking probabilities and hence the growth of planetesimals. The new parameter set might possibly lead to an enhanced sticking as more energy can be stored in the system before breakup.

Collisions of inhomogeneous pre-planetesimals

In the framework of the coagulation scenario, kilometre-sized planetesimals form by subsequent collisions of pre-planetesimals of sizes from centimetre to hundreds of metres. Pre-planetesimals are fluffy, porous dust aggregates, which are inhomogeneous owing to their collisional history. Planetesimal growth can be prevented by catastrophic disruption in pre-planetesimal collisions above the destruction velocity threshold. We develop an inhomogeneity model based on the density distribution of dust aggregates, which is assumed to be a Gaussian distribution with a well-defined standard deviation. As a second input parameter, we consider the typical size of an inhomogeneous clump. These input parameters are easily accessible by laboratory experiments. For the simulation of the dust aggregates, we utilise a smoothed particle hydrodynamics (SPH) code with extensions for modelling porous solid bodies. The porosity model was previously calibrated for the simulation of silica dust, which commonly serves as an analogue for pre-planetesimal material. The inhomogeneity is imposed as an initial condition on the SPH particle distribution. We carry out collisions of centimetre-sized dust aggregates of intermediate porosity. We vary the standard deviation of the inhomogeneous distribution at fixed typical clump size. The collision outcome is categorised according to the four-population model. We show that inhomogeneous pre-planetesimals are more prone to destruction than homogeneous aggregates. Even slight inhomogeneities can lower the threshold for catastrophic disruption. For a fixed collision velocity, the sizes of the fragments decrease with increasing inhomogeneity. Pre-planetesimals with an active collisional history tend to be weaker. This is a possible obstacle to collisional growth and needs to be taken into account in future studies of the coagulation scenario.

The steady-state structure of accretion discs in central magnetic fields

We develop a new analytic solution for the steady-state structure of a thin accretion disc under the influence of a magnetic field that is anchored to the central star. The solution takes a form similar to that of Shakura and Sunyaev and tends to their solution as the magnetic moment of the star tends to zero. As well as the Kramers law case, we obtain a solution for a general opacity. The effects of varying the mass transfer rate, spin period and magnetic field of the star and the opacity model applied to the disc are explored for a range of objects. The solution depends on the position of the magnetic truncation radius. We propose a new approach for the identification of the truncation radius and present an analytic expression for its position.

Growth and fragmentation of centimetre-sized dust aggregates: the dependence on aggregate size and porosity

We carry out three-dimensional smoothed particle hydrodynamics simulations of spherical homogeneous SiO 2 dust aggregates to investigate how the mass and the porosity of the aggregates affect their ability to survive an impact at various different collision velocities (between 1 and 27.5 m s −1 ). We explore how the threshold velocities for fragmentation vary with these parameters. Crucially, we find that the porosity plays a part of utmost importance in determining the outcome of collisions. In particular, we find that aggregates with filling factors ≳37 per cent are significantly weakened and that the velocity regime in which the aggregates grow is reduced or even non-existent (instead, the aggregates either rebound off each other or break apart). At filling factors less than ≈37 per cent we find that more porous objects are weaker but not as weak as highly compact objects with filling factors ≳37 per cent. In addition, we find that (for a given aggregate density) collisions between very different mass objects have higher threshold velocities than those between very similar mass objects. We find that fragmentation velocities are higher than the typical values of 1 m s −1 and that growth can even occur for velocities as high as 27.5 m s −1 . Therefore, while the growth of aggregates is more likely if collisions between different sized objects occurs or if the aggregates are porous with filling factor <37 per cent, it may also be hindered if the aggregates become too compact.