We describe the implementation and performance of the ${rm P^3T}$ (Particle-Particle Particle-Tree) scheme for simulating dense stellar systems. In ${rm P^3T}$, the force experienced by a particle is split into short-range and long-range contribution
s. Short-range forces are evaluated by direct summation and integrated with the fourth order Hermite predictor-corrector method with the block timesteps. For long-range forces, we use a combination of the Barnes-Hut tree code and the leapfrog integrator. The tree part of our simulation environment is accelerated using graphical processing units (GPU), whereas the direct summation is carried out on the host CPU. Our code gives excellent performance and accuracy for star cluster simulations with a large number of particles even when the core size of the star cluster is small.
The discovery of 2012VP113 initiated the debate on the origin of the Sedna family of planetesimals in orbit around the Sun. Sednitos roam the outer regions of the Solar System between the Egeworth--Kuiper belt and the Oort cloud, in extraordinary wid
e (a>150au) orbits with a large perihelion distance of q>30au compared to the Earths (a=1au and eccentricity e=(1-q/a) ~ 0.0167 or q=1au). This population is composed of a dozen objects, which we consider a family because they have similar perihelion distance and inclination with respect to the ecliptic i=10--30deg. They also have similar argument of perihelion omega=340+/-55deg. There is no ready explanation for their origin. Here we show that these orbital parameters are typical for a captured population from the planetesimal disk of another star.Assuming the orbital elements of Sednitos have not changed since they acquired their orbits, we reconstruct the encounter that led to their capture. We conclude that they might have been captured in a near miss with a 1.8MSun star that impacted the Sun at ~340au at an inclination with respect to the ecliptic of 17--34deg with a relative velocity at infinity of ~4.3km/s. We predict that the Sednitos-region is populated by 930 planetesimals and the inner Oort cloud acquired ~440 planetesimals through the same encounter.
We specify the range to which perturbations penetrate a planetesimal system. Such perturbations can originate from massive planets or from encounters with other stars. The latter can have an origin in the star cluster in which the planetary system wa
s born, or from random encounters once the planetary system has escaped its parental cluster. The probability of a random encounter, either in a star cluster or in the Galactic field depends on the local stellar density, the velocity dispersion and the time spend in that environment. By adopting order of magnitude estimates we argue that the majority of planetary systems born in open clusters will have a {em Parking zone}, in which planetesimals are affected by encounters in their parental star cluster but remain unperturbed after the star has left the cluster. Objects found in this range of semi-major axis and eccentricity preserve the memory of the encounter that last affected their orbits, and they can therefore be used to reconstruct this encounter. Planetary systems born in a denser environment, such as in a globular cluster are unlikely to have a Parking zone. We further argue that some planetary systems may have a {em Frozen zone}, in which orbits are not affected either by the more inner massive planets or by external influences. Objects discovered in this zone will have preserved information about their formation in their orbital parameters.
The 13 Myr old star HD106906 is orbited by a debris disk of at least 0.067 M_Moon with an inner and outer radius of 20 AU and 120 AU, respectively, and by a planet at a distance of 650 AU. We use this curious combination of a close low-mass disk and
a wide planet to motivate our simulations of this system. We study the parameter space of the initial conditions to quantify the mass loss from the debris disk and its lifetime under the influence of the planet. We find that when the planet orbits closer to the star than about 50 AU and with low inclination relative to the disk (less than about 10 degrees), more disk material is perturbed outside than inside the region constrained by observations on timescales shorter than 1 Myr. Considering the age of the system, such a short lifetime of the disk is incompatible with the timescale for planet--planet scattering which is one of the scenarios suggested to explain the wide separation of the planet. For some configurations when the planets orbit is inclined with respect to the disk, the latter will start to wobble. We argue that this wobbling is caused by a mechanism similar to the Kozai--Lidov oscillations. We also observe various resonant structures (such as rings and spiral arms) induced in the disk by the planet.
The general consensus in the N-body community is that statistical results of an ensemble of collisional N-body simulations are accurate, even though individual simulations are not. A way to test this hypothesis is to make a direct comparison of an en
semble of solutions obtained by conventional methods with an ensemble of true solutions. In order to make this possible, we wrote an N-body code called Brutus, that uses arbitrary-precision arithmetic. In combination with the Bulirsch--Stoer method, Brutus is able to obtain converged solutions, which are true up to a specified number of digits. We perform simulations of democratic 3-body systems, where after a sequence of resonances and ejections, a final configuration is reached consisting of a permanent binary and an escaping star. We do this with conventional double-precision methods, and with Brutus; both have the same set of initial conditions and initial realisations. The ensemble of solutions from the conventional simulations is compared directly to that of the converged simulations, both as an ensemble and on an individual basis to determine the distribution of the errors. We find that on average at least half of the conventional simulations diverge from the converged solution, such that the two solutions are microscopically incomparable. For the solutions which have not diverged significantly, we observe that if the integrator has a bias in energy and angular momentum, this propagates to a bias in the statistical properties of the binaries. In the case when the conventional solution has diverged onto an entirely different trajectory in phase-space, we find that the errors are centred around zero and symmetric; the error due to divergence is unbiased, as long as the time-step parameter, eta <= 2^(-5) and when simulations which violate energy conservation by more than 10% are excluded.
The evolution of triples has not attracted much attention in the literature, although their evolution can be dramatically different from binaries and single stars. Triples are quite common, and we find that for about 1% of the triples in the Tokovini
n catalogue of multiple stellar systems in the solar neighbourhood, the tertiary star will overflow its Roche lobe at some time in its evolution, before any of the inner stars leave the main sequence. For two of these systems, Xi Tauri and HD97131 we simulate in detail this phase of mass transfer, during which stellar evolution, gravitational dynamics and hydrodynamics all play an important role. We have used the Astrophysical Multi-purpose Software Environment (AMUSE) to solve these physical processes in a self-consistent way. The resulting evolution, mass transfer and the effects on the inner as well as on the outer orbit are profound, although it is not trivial to predict the eventual consequence of the phase of mass transfer and the appearance of the resulting system.
In young dense clusters repeated collisions between massive stars may lead to the formation of a very massive star (above 100 Msun). In the past the study of the long-term evolution of merger remnants has mostly focussed on collisions between low-mas
s stars (up to about 2 Msun) in the context of blue-straggler formation. The evolution of collision products of more massive stars has not been as thoroughly investigated. In this paper we study the long-term evolution of a number of stellar mergers formed by the head-on collision of a primary star with a mass of 5-40 Msun with a lower mass star at three points in its evolution in order to better understand their evolution. We use smooth particle hydrodynamics (SPH) calculations to model the collision between the stars. The outcome of this calculation is reduced to one dimension and imported into a stellar evolution code. We follow the subsequent evolution of the collision product through the main sequence at least until the onset of helium burning. We find that little hydrogen is mixed into the core of the collision products, in agreement with previous studies of collisions between low-mass stars. For collisions involving evolved stars we find that during the merger the surface nitrogen abundance can be strongly enhanced. The evolution of most of the collision products proceeds analogously to that of normal stars with the same mass, but with a larger radius and luminosity. However, the evolution of collision products that form with a hydrogen depleted core is markedly different from that of normal stars with the same mass. They undergo a long-lived period of hydrogen shell burning close to the main-sequence band in the Hertzsprung-Russell diagram and spend the initial part of core helium burning as compact blue supergiants.
We describe AMUSE, the Astrophysical Multipurpose Software Environment, a programming framework designed to manage multi-scale, multi-physics simulations in a hierarchical, extensible, and internally consistent way. Constructed as a collection of ind
ividual modules, AMUSE allows computational tools for different physical domains to be easily combined into a single task. It facilitates the coupling of modules written in different languages by providing inter-language tools and a standard programming interface that represents a balance between generality and computational efficiency. The framework currently incorporates the domains of stellar dynamics, stellar evolution, gas dynamics, and radiative transfer. We present some applications of the framework and outline plans for future development of the package.
We introduce a general-purpose framework for interconnecting scientific simulation programs using a homogeneous, unified software interface. Our framework is intrinsically parallel, and conveniently separates all components in memory. It performs uni
t conversion between different modules automatically and defines common data structures to communicate across different codes. We use the framework to simulate embedded star clusters. For this purpose we couple solvers for gravitational dynamics, stellar evolution and hydrodynamics to self consistently resolve the dynamical evolution simultaneousy with the internal nuclear evolution of the stars and the hydrodynamic response of the gas. We find, in contrast to earlier studies, that the survival of a young star cluster depends only weakly on the efficiency of star formation. The main reason for this weak dependency is the asymmetric expulsion of the embedding gas from the cluster.
Understanding the universe is hampered by the elusiveness of its most common constituent, cold dark matter. Almost impossible to observe, dark matter can be studied effectively by means of simulation and there is probably no other research field wher
e simulation has led to so much progress in the last decade. Cosmological N-body simulations are an essential tool for evolving density perturbations in the nonlinear regime. Simulating the formation of large-scale structures in the universe, however, is still a challenge due to the enormous dynamic range in spatial and temporal coordinates, and due to the enormous computer resources required. The dynamic range is generally dealt with by the hybridization of numerical techniques. We deal with the computational requirements by connecting two supercomputers via an optical network and make them operate as a single machine. This is challenging, if only for the fact that the supercomputers of our choice are separated by half the planet, as one is located in Amsterdam and the other is in Tokyo. The co-scheduling of the two computers and the gridification of the code enables us to achieve a 90% efficiency for this distributed intercontinental supercomputer.
