arXiv subjects

Sverre J. Aarseth

Publications and source records attributed to Sverre J. Aarseth.

16 recordsLinked to original sources

arXiv2022

Asymmetrical tidal tails of open star clusters: stars crossing their cluster's prah challenge Newtonian gravitation

After their birth a significant fraction of all stars pass through the tidal threshold (prah) of their cluster of origin into the classical tidal tails. The asymmetry between the number of stars in the leading and trailing tails tests gravitational theory. All five open clusters with tail data (Hyades, Praesepe, Coma Berenices, COIN-Gaia 13, NGC 752) have visibly more stars within dcl = 50 pc of their centre in their leading than their trailing tail. Using the Jerabkova-compact-convergent-point (CCP) method, the extended tails have been mapped out for four nearby 600-2000 Myr old open clusters to dcl>50 pc. These are on near-circular Galactocentric orbits, a formula for estimating the orbital eccentricity of an open cluster being derived. Applying the Phantom of Ramses code to this problem, in Newtonian gravitation the tails are near-symmetrical. In Milgromian dynamics (MOND) the asymmetry reaches the observed values for 50 < dcl/pc < 200, being maximal near peri-galacticon, and can slightly invert near apo-galacticon, and the Küpper epicyclic overdensities are asymmetrically spaced. Clusters on circular orbits develop orbital eccentricity due to the asymmetrical spill-out, therewith spinning up opposite to their orbital angular momentum. This positive dynamical feedback suggests Milgromian open clusters to demise rapidly as their orbital eccentricity keeps increasing. Future work is necessary to better delineate the tidal tails around open clusters of different ages and to develop a Milgromian direct n-body code.

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arXiv2016

A dynamical gravitational wave source in a dense cluster

Making use of a new N-body model to describe the evolution of a moderate-size globular cluster we investigate the characteristics of the population of black holes within such a cluster. This model reaches core-collapse and achieves a peak central density typical of the dense globular clusters of the Milky Way. Within this high-density environment we see direct confirmation of the merging of two stellar remnant black-holes in a dynamically-formed binary, a gravitational wave source. We describe how the formation, evolution and ultimate ejection/destruction of binary systems containing black holes impacts the evolution of the cluster core. Also, through comparison with previous models of lower density, we show that the period distribution of black hole binaries formed through dynamical interactions in this high-density model favours the production of gravitational wave sources. We confirm that the number of black holes remaining in a star cluster at late times and the characteristics of the binary black hole population depend on the nature of the star cluster, critically on the number density of stars and by extension the relaxation timescale.

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arXiv2014

Migration and Growth of Protoplanetary Embryos II: Emergence of Proto-Gas-Giants Cores versus Super Earths' Progenitor

Nearly $15-20%$ of solar type stars contain one or more gas giant planet. According to the core-accretion scenario, the acquisition of their gaseous envelope must be preceded by the formation of super-critical cores with masses ten times or larger than that of the Earth. It is natural to link the formation probability of gas giant planets with the supply of gas and solid in their natal disks. However, a much richer population of super Earths suggests that 1) there is no shortage of planetary building-block material, 2) gas giants' growth barrier is probably associated with whether they can merge into super-critical cores, and 3) super Earths are probably failed cores which did not attain sufficient mass to initiate efficient accretion of gas before it is severely depleted. Here we construct a model based on the hypothesis that protoplanetary embryos migrated extensively before they were assembled into bona fide planets. We construct a Hermite-Embryo code based on a unified viscous-irradiation disk model and a prescription for the embryo-disk tidal interaction. This code is used to simulate 1) the convergent migration of embryos, and 2) their close encounters and coagulation. Around the progenitors of solar-type stars, the progenitor super-critical-mass cores of gas giant planets primarily form in protostellar disks with relatively high ($\gtrsim 10^{-7} M_\odot$ yr$^{-1}$) mass accretion rates whereas systems of super Earths (failed cores) are more likely to emerge out of natal disks with modest mass accretion rates, due to the mean motion resonance barrier and retention efficiency.

astro-ph.EP↗

arXiv2014

Pre-mainsequence stellar evolution in N-body models

We provide a set of analytic fits to the radii of pre-mainsequence stars in the mass range 0.1 < M/Msun < 8.0. We incorporate the formulae in N-body cluster models for evolution from the beginning of pre-main sequence. In models with 1,000 stars and high initial cluster densities, pre-mainsequence evolution causes roughly twice the number of collisions between stars than in similar models with evolution begun only from the zero-age main sequence. The collisions are often all part of a runaway sequence that creates one relatively massive star.

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arXiv2012

Accelerating NBODY6 with Graphics Processing Units

We describe the use of Graphics Processing Units (GPUs) for speeding up the code NBODY6 which is widely used for direct $N$-body simulations. Over the years, the $N^2$ nature of the direct force calculation has proved a barrier for extending the particle number. Following an early introduction of force polynomials and individual time-steps, the calculation cost was first reduced by the introduction of a neighbour scheme. After a decade of GRAPE computers which speeded up the force calculation further, we are now in the era of GPUs where relatively small hardware systems are highly cost-effective. A significant gain in efficiency is achieved by employing the GPU to obtain the so-called regular force which typically involves some 99 percent of the particles, while the remaining local forces are evaluated on the host. However, the latter operation is performed up to 20 times more frequently and may still account for a significant cost. This effort is reduced by parallel SSE/AVX procedures where each interaction term is calculated using mainly single precision. We also discuss further strategies connected with coordinate and velocity prediction required by the integration scheme. This leaves hard binaries and multiple close encounters which are treated by several regularization methods. The present nbody6-GPU code is well balanced for simulations in the particle range $10^4-2 \times 10^5$ for a dual GPU system attached to a standard PC.

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arXiv2007

Dancing with black holes

We describe efforts over the last six years to implement regularization methods suitable for studying one or more interacting black holes by direct N-body simulations. Three different methods have been adapted to large-N systems: (i) Time-Transformed Leapfrog, (ii) Wheel-Spoke, and (iii) Algorithmic Regularization. These methods have been tried out with some success on GRAPE-type computers. Special emphasis has also been devoted to including post-Newtonian terms, with application to moderately massive black holes in stellar clusters. Some examples of simulations leading to coalescence by gravitational radiation will be presented to illustrate the practical usefulness of such methods.

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arXiv2007

The core binary fractions of star clusters from realistic simulations

We investigate the evolution of binary fractions in star clusters using N-body models of up to 100000 stars. Primordial binary frequencies in these models range from 5% to 50%. Simulations are performed with the NBODY4 code and include a full mass spectrum of stars, stellar evolution, binary evolution and the tidal field of the Galaxy. We find that the overall binary fraction of a cluster almost always remains close to the primordial value, except at late times when a cluster is near dissolution. A critical exception occurs in the central regions where we observe a marked increase in binary fraction with time -- a simulation starting with 100000 stars and 5% binaries reached a core binary frequency as high as 40% at the end of the core-collapse phase (occurring at 16 Gyr with ~20000 stars remaining). Binaries are destroyed in the core by a variety of processes as a cluster evolves, but the combination of mass-segregation and creation of new binaries in exchange interactions produces the observed increase in relative number. We also find that binaries are cycled into and out of cluster cores in a manner that is analogous to convection in stars. For models of 100000 stars we show that the evolution of the core-radius up to the end of the initial phase of core-collapse is not affected by the exact value of the primordial binary frequency (for frequencies of 10% or less). We discuss the ramifications of our results for the likely primordial binary content of globular clusters.

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arXiv2007

Post-Newtonian N-body simulations

We report on the first fully consistent conventional cluster simulation which includes terms up to post^{5/2} Newtonian in the potential of the massive body. Numerical problems for treating extremely energetic binaries orbiting a single massive object are circumvented by employing the special ``wheel-spoke'' regularization method of Zare (1974) which has not been used in large-N simulations before. Idealized models containing N = 10^5 particles of mass 1 M_sun with a central black hole of 300 M_sun have been studied on GRAPE-type computers. An initial half-mass radius of r_h = 0.1 pc is sufficiently small to yield examples of relativistic coalescence. This is achieved by significant binary shrinkage within a density cusp environment, followed by the generation of extremely high eccentricities which are induced by Kozai (1962) cycles and/or resonant relaxation. More realistic models with white dwarfs and ten times larger half-mass radii also show evidence of GR effects before disruption. Experimentation with the post-Newtonian terms suggests that reducing the time-scales for activating the different orders progressively may be justified for obtaining qualitatively correct solutions without aiming for precise predictions of the final gravitational radiation wave form. The results obtained suggest that the standard loss-cone arguments underestimate the swallowing rate in globular clusters containing a central black hole.

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arXiv2005

A Complete N-body Model of the Old Open Cluster M67

The old open cluster M67 is an ideal testbed for current cluster evolution models because of its dynamically evolved structure and rich stellar populations that show clear signs of interaction between stellar, binary and cluster evolution. Here we present the first truly direct N-body model for M67, evolved from zero age to 4 Gyr taking full account of cluster dynamics as well as stellar and binary evolution. Our preferred model starts with 12000 single stars and 12000 binaries placed in a Galactic tidal field at 8.0 kpc from the Galactic Centre. Our choices for the initial conditions and for the primordial binary population are explained in detail. At 4 Gyr, the age of M67, the total mass has reduced by 90% as a result of mass loss and stellar escapes. The mass and half-mass radius of luminous stars in the cluster are a good match to observations although the model is more centrally concentrated than observations indicate. The stellar mass and luminosity functions are significantly flattened by preferential escape of low-mass stars. We find that M67 is dynamically old enough that information about the initial mass function is lost, both from the current luminosity function and from the current mass fraction in white dwarfs. The model contains 20 blue stragglers at 4 Gyr which is slightly less than the 28 observed in M67. Nine are in binaries. The blue stragglers were formed by a variety of means and we find formation paths for the whole variety observed in M67. Both the primordial binary population and the dynamical cluster environment play an essential role in shaping the population. A substantial population of short-period primordial binaries (with periods less than a few days) is needed to explain the observed number of blue stragglers in M67.

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arXiv2002

MODEST-1: Integrating Stellar Evolution and Stellar Dynamics

We summarize the main results from MODEST-1, the first workshop on MOdeling DEnse STellar systems. Our goal is to go beyond traditional population synthesis models, by introducing dynamical interactions between single stars, binaries, and multiple systems. The challenge is to define and develop a software framework to enable us to combine in one simulation existing computer codes in stellar evolution, stellar dynamics, and stellar hydrodynamics. With this objective, the workshop brought together experts in these three fields, as well as other interested astrophysicists and computer scientists. We report here our main conclusions, questions and suggestions for further steps toward integrating stellar evolution and stellar (hydro)dynamics.

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arXiv2001

Regularization Tools for Binary Interactions

We first discuss two-body and chain regularization methods for direct N-body simulations on HARP-2 and GRAPE-6. The former is used for accurate integration of perturbed binaries and hierarchies, whereas the latter deals with strong interactions involving binaries. Combined with a powerful stability criterion for hierarchical systems, this versatile treatment provides an efficient way of studying all dynamical processes in globular clusters containing a realistic population of primordial binaries. These algorithms are also ideal for modelling a variety of astrophysical effects, such as averaging over Kozai cycles, tidal circularization, spin-orbit coupling and stellar collisions, where well-defined elements are used to describe near-singular solutions. We also describe a new time-transformed leapfrog scheme which has been developed to deal with black-hole binaries in galactic centres. This formulation is valid for large mass ratios and dominant two-body motions in a compact subsystem can be treated accurately in the post-Newtonian approximation. This method has been combined with the existing regularization algorithms into a new simulation code NBODY7. Some preliminary results of a test problem illustrating possible applications are presented.

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arXiv2001

Nbody2: A Direct N-Body Integration Code

We give a full description of the code NBODY2 for direct integration of the gravitational N-body problem. The method of solution is based on the neighbour scheme of Ahmad & Cohen (1973) which speeds up the force calculation already for quite modest particle numbers. Derivations of all the relevant mathematical expressions are given, together with a detailed discussion of the algorithms. The code may be used to study a wide variety of self-consistent problems based on a small softening of the interaction potential.

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arXiv2000

Direct N-body Modelling of Stellar Populations: Blue Stragglers in M67

We present a state-of-the-art N-body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N-body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N-body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N = 10000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.

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arXiv2000

The Formation and Evolution of Multiple Star Systems

Multiple systems play an important role in the evolution of star clusters. First we discuss several formation mechanisms which depend on the presence of binaries, either primordial or of dynamical origin. Hierarchical configurations are often stable over long times and yet may experience evolution of the internal orbital parameters. We describe an attempt to model the eccentricity change induced by the outer component using an averaging method, together with the effects due to tidal dissipation and apsidal motion acting on the inner binary. This treatment is adopted for systems with high induced eccentricity which gives rise to some interesting outcomes of significant period shrinkage.

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arXiv1999

Star Cluster Simulations: The State of the Art

This paper concentrates on four key tools for performing star cluster simulations developed during the last decade which are sufficient to handle all the relevant dynamical aspects. First we discuss briefly the Hermite integration scheme which is simple to use and highly efficient for advancing the single particles. The main numerical challenge is in dealing with weakly and strongly perturbed hard binaries. A new treatment of the classical Kustaanheimo-Stiefel two-body regularization has proved to be more accurate for studying binaries than previous algorithms based on divided differences or Hermite integration. This formulation employs a Taylor series expansion combined with the Stumpff functions, still with one force evaluation per step, which gives exact solutions for unperturbed motion and is at least comparable to the polynomial methods for large perturbations. Strong interactions between hard binaries and single stars or other binaries are studied by chain regularization which ensures a non-biased outcome for chaotic motions. A new semi-analytical stability criterion for hierarchical systems has been adopted and the long-term effects on the inner binary are now treated by averaging techniques for cases of interest. These modifications describe consistent changes of the orbital variables due to large Kozai cycles and tidal dissipation. The range of astrophysical processes which can now be considered by N-body simulations include tidal capture, circularization, mass transfer by Roche-lobe overflow as well as physical collisions, where the masses and radii of individual stars are modelled by synthetic stellar evolution.

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arXiv1996

Direct collisional simulation of 10 000 particles past core collapse

A collisional $N$-body simulation using NBODY5 on a single CRAY YMP processor is followed well into the post-collapse regime. This is presently one of the largest particle numbers of all such models published, but some data for an even larger $N$ produced by using special-purpose computers have recently been presented. In contrast to previous ensemble-averaged $N$-body simulations the noise here is low enough to just compare this one single run with the expectations from statistical models based on the Fokker-Planck approximation. Agreement is as good as could be expected for the case of the evolution of the Lagrangian radii, radial and tangential velocity dispersions and various core quantities. We briefly discuss approximate models to understand number and energy of escapers and the question of gravothermal core oscillations; although the system exhibits post-collapse oscillations they turn out to be directly binary driven and we cannot prove the existence of a gravothermal expansion at this particle number. Finally in a detailed examination of the wandering of the density centre we find in contrast to some previous studies a clear long-time period of the order of about 14 half-mass crossing times.

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