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1
Aarseth, Sverre J. "N-body codes." Proceedings of the International Astronomical Union 2, no. 14 (August 2006): 428–29. http://dx.doi.org/10.1017/s1743921307011210.
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AbstractWe review some advances relating to direct N-body codes. In particular, there has been significant progress in dealing with large-N systems containing a few dominant members. The simulation of massive black holes also requires treatment of relativistic effects for strongly bound two-body orbits. Although somewhat costly, the addition of post-Newtonian terms is still straightforward when used in connection with regularization methods. Several versions of multiple regularization are especially well suited to studying black hole problems. We also report on a new stability criterion for the general three-body problem which will provide a robust test in systems where hierarchies are a troublesome feature, as in the case of star cluster simulations with primordial binaries.
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Hernandez, David M., Sam Hadden, and Junichiro Makino. "Are long-term N-body simulations reliable?" Monthly Notices of the Royal Astronomical Society 493, no. 2 (February 19, 2020): 1913–25. http://dx.doi.org/10.1093/mnras/staa388.
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ABSTRACT N-body integrations are used to model a wide range of astrophysical dynamics, but they suffer from errors which make their orbits diverge exponentially in time from the correct orbits. Over long time-scales, their reliability needs to be established. We address this reliability by running a three-body planetary system over about 200 e-folding times. Using nearby initial conditions, we can construct statistics of the long-term phase-space structure and compare to rough estimates of resonant widths of the system. We compared statistics for a wide range of numerical methods, including a Runge–Kutta method, Wisdom–Holman method, symplectic corrector methods, and a method by Laskar and Robutel. ‘Improving’ an integrator did not increase the phase-space accuracy, but simply increasing the number of initial conditions did. In fact, the statistics of a higher order symplectic corrector method were inconsistent with the other methods in one test.
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Murtagh, F. D. "Hierarchical trees in N-body simulations: Relations with cluster analysis methods." Computer Physics Communications 52, no. 1 (December 1988): 15–18. http://dx.doi.org/10.1016/0010-4655(88)90166-x.
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Mukherjee, Diptajyoti, Qirong Zhu, Hy Trac, and Carl L. Rodriguez. "Fast Multipole Methods for N-body Simulations of Collisional Star Systems." Astrophysical Journal 916, no. 1 (July 1, 2021): 9. http://dx.doi.org/10.3847/1538-4357/ac03b2.
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Bowers, Kevin J., Ron O. Dror, and David E. Shaw. "Zonal methods for the parallel execution of range-limited N-body simulations." Journal of Computational Physics 221, no. 1 (January 2007): 303–29. http://dx.doi.org/10.1016/j.jcp.2006.06.014.
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Wang, Long, Rainer Spurzem, Sverre Aarseth, Keigo Nitadori, Peter Berczik, M. B. N. Kouwenhoven, and Thorsten Naab. "Acceleration of hybrid MPI parallel NBODY6++ for large N-body globular cluster simulations." Proceedings of the International Astronomical Union 10, S312 (August 2014): 260–61. http://dx.doi.org/10.1017/s174392131500798x.
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AbstractPrevious research on globular clusters (GCs) dynamics is mostly based on semi-analytic, Fokker-Planck, Monte-Carlo methods and on direct N-body (NB) simulations. These works have great advantages but also limits since GCs are massive and compact and close encounters and binaries play very important roles in their dynamics. The former three methods make approximations and assumptions, while expensive computing time and number of stars limit the latter method. The current largest direct NB simulation has ~ 500k stars (Heggie 2014). Here, we accelerate the direct NB code NBODY6++ (which extends NBODY6 to supercomputers by using MPI) with new parallel computing technologies (GPU, OpenMP + SSE/AVX). Our aim is to handle large N (up to 106) direct NB simulations to obtain better understanding of the dynamical evolution of GCs.
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Geller, Aaron M., Jarrod R. Hurley, and Robert D. Mathieu. "The progeny of stellar dynamics and stellar evolution within an N-body model of NGC 188." Proceedings of the International Astronomical Union 5, S266 (August 2009): 258–63. http://dx.doi.org/10.1017/s1743921309991128.
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AbstractWe present a direct N-body simulation modeling the evolution of the old (7 Gyr) open cluster NGC 188. This is the first N-body open cluster simulation whose initial binary population is directly defined by observations of a specific open cluster: M35 (150 Myr). We compare the simulated color–magnitude diagram at 7 Gyr to that of NGC 188, and discuss the blue stragglers produced in the simulation. We compare the solar-type main-sequence binary period and eccentricity distributions of the simulation to detailed observations of similar binaries in NGC 188. These results demonstrate the importance of detailed observations in guiding N-body open cluster simulations. Finally, we discuss the implications of a few discrepancies between the NGC 188 model and observations and suggest a few methods for bringing N-body open cluster simulations into better agreement with observations.
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Korkidis, Giorgos, Vasiliki Pavlidou, Konstantinos Tassis, Evangelia Ntormousi, Theodore N. Tomaras, and Konstantinos Kovlakas. "Turnaround radius of galaxy clusters in N-body simulations." Astronomy & Astrophysics 639 (July 2020): A122. http://dx.doi.org/10.1051/0004-6361/201937337.
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Aims. We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a ΛCDM Universe, can be meaningfully identified for galaxy clusters in the presence of full three-dimensional effects. Methods. We use The Dark Sky Simulations and Illustris-TNG dark-matter-only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius R200. There, the turnaround radius can be unambiguously identified as the largest nonexpanding scale around a center of gravity. Results. We find that: (a) a single turnaround scale can meaningfully describe strongly nonspherical structures. (b) For halos of masses M200 > 1013 M⊙, the turnaround radius Rta scales with the enclosed mass Mta as Mta1/3, as predicted by the spherical collapse model. (c) The deviation of Rta in simulated halos from the spherical collapse model prediction is relatively insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when these are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters (Ωm ∼ 0.3; ΩΛ ∼ 0.7) turnaround structures exhibit a density contrast with the matter density of the background Universe of δ ∼ 11. Thus, Rta is equivalent to R11 – in a way that is analogous to defining the “virial” radius as R200 – with the advantage that R11 is shown in this work to correspond to a kinematically relevant scale in N-body simulations.
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Modi, Chirag, Shi-Fan Chen, and Martin White. "Simulations and symmetries." Monthly Notices of the Royal Astronomical Society 492, no. 4 (January 28, 2020): 5754–63. http://dx.doi.org/10.1093/mnras/staa251.
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ABSTRACT We investigate the range of applicability of a model for the real-space power spectrum based on N-body dynamics and a (quadratic) Lagrangian bias expansion. This combination uses the highly accurate particle displacements that can be efficiently achieved by modern N-body methods with a symmetries-based bias expansion which describes the clustering of any tracer on large scales. We show that at low redshifts, and for moderately biased tracers, the substitution of N-body-determined dynamics improves over an equivalent model using perturbation theory by more than a factor of two in scale, while at high redshifts and for highly biased tracers the gains are more modest. This hybrid approach lends itself well to emulation. By removing the need to identify haloes and subhaloes, and by not requiring any galaxy-formation-related parameters to be included, the emulation task is significantly simplified at the cost of modelling a more limited range in scale.
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Heggie, Douglas C. "The Gravitational Million-Body Problem." Symposium - International Astronomical Union 208 (2003): 81–92. http://dx.doi.org/10.1017/s0074180900207043.
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We review what has been learned recently using N-body simulations about the evolution of globular clusters. While simulations of star clusters have become more realistic, and now include the evolution of single and binary stars, the prospect of reaching large enough N is still a distant one. Nevertheless more restricted kinds of simulations have recently brought valuable progress for certain problems of current observational interest, including the origin and structure of tidal tails of globular clusters. In addition, such simulations have forced us to rethink some basic aspects of stellar dynamics, including, in particular, the process of escape. Finally we turn to faster, approximate methods for studying star cluster dynamics, where the role of N-body simulations is one of calibration.
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Blot, Linda, Martin Crocce, Emiliano Sefusatti, Martha Lippich, Ariel G. Sánchez, Manuel Colavincenzo, Pierluigi Monaco, et al. "Comparing approximate methods for mock catalogues and covariance matrices II: power spectrum multipoles." Monthly Notices of the Royal Astronomical Society 485, no. 2 (February 19, 2019): 2806–24. http://dx.doi.org/10.1093/mnras/stz507.
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ABSTRACT We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constraints related to growth rate of structure, Alcock–Paczynski distortions, and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE–COLA, pinocchio, and peakpatch), methods that rely on halo assignment schemes on to dark matter overdensities calibrated with a target N-body run (halogen, patchy), and two standard assumptions about the full density probability distribution function (Gaussian and lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5{{\ \rm per\ cent}}$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10{{\ \rm per\ cent}}$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10{{\ \rm per\ cent}}$ of those from the N-body-based covariance.
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Hernandez, David M. "Improving the accuracy of simulated chaotic N-body orbits using smoothness." Monthly Notices of the Royal Astronomical Society 490, no. 3 (September 27, 2019): 4175–82. http://dx.doi.org/10.1093/mnras/stz2662.
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ABSTRACT Symplectic integrators are a foundation to the study of dynamical N-body phenomena, at scales ranging from planetary to cosmological. These integrators preserve the Poincaré invariants of Hamiltonian dynamics. The N-body Hamiltonian has another, perhaps overlooked, symmetry: it is smooth, or, in other words, it has infinite differentiability class order (DCO) for particle separations greater than 0. Popular symplectic integrators, such as hybrid methods or block adaptive stepping methods do not come from smooth Hamiltonians and it is perhaps unclear whether they should. We investigate the importance of this symmetry by considering hybrid integrators, whose DCO can be tuned easily. Hybrid methods are smooth, except at a finite number of phase space points. We study chaotic planetary orbits in a test considered by Wisdom. We find that increasing smoothness, at negligible extra computational cost in particular tests, improves the Jacobi constant error of the orbits by about 5 orders of magnitude in long-term simulations. The results from this work suggest that smoothness of the N-body Hamiltonian is a property worth preserving in simulations.
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Wang, Long, Masaki Iwasawa, Keigo Nitadori, and Junichiro Makino. "petar: a high-performance N-body code for modelling massive collisional stellar systems." Monthly Notices of the Royal Astronomical Society 497, no. 1 (July 24, 2020): 536–55. http://dx.doi.org/10.1093/mnras/staa1915.
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ABSTRACT The numerical simulations of massive collisional stellar systems, such as globular clusters (GCs), are very time consuming. Until now, only a few realistic million-body simulations of GCs with a small fraction of binaries ($5{{\ \rm per\ cent}}$) have been performed by using the nbody6++gpu code. Such models took half a year computational time on a Graphic Processing Unit (GPU)-based supercomputer. In this work, we develop a new N-body code, petar, by combining the methods of Barnes–Hut tree, Hermite integrator and slow-down algorithmic regularization. The code can accurately handle an arbitrary fraction of multiple systems (e.g. binaries and triples) while keeping a high performance by using the hybrid parallelization methods with mpi, openmp, simd instructions and GPU. A few benchmarks indicate that petar and nbody6++gpu have a very good agreement on the long-term evolution of the global structure, binary orbits and escapers. On a highly configured GPU desktop computer, the performance of a million-body simulation with all stars in binaries by using petar is 11 times faster than that of nbody6++gpu. Moreover, on the Cray XC50 supercomputer, petar well scales when number of cores increase. The 10 million-body problem, which covers the region of ultracompact dwarfs and nuclear star clusters, becomes possible to be solved.
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Fortin, Pierre, and Maxime Touche. "Dual tree traversal on integrated GPUs for astrophysical N-body simulations." International Journal of High Performance Computing Applications 33, no. 5 (April 15, 2019): 960–72. http://dx.doi.org/10.1177/1094342019840806.
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In astrophysical N-body simulations, O( N) fast multipole methods (FMMs) with dual tree traversal (DTT) on multi-core CPUs are faster than O( N log N) CPU tree-codes but can still be outperformed by GPU ones. In this article, we aim at combining the best algorithm, namely FMM with DTT, with the most powerful hardware currently available, namely GPUs. In the astrophysical context requiring low accuracies and non-uniform particle distributions, we show that such combination can be achieved thanks to a hybrid CPU-GPU algorithm on integrated GPUs: while the DTT is performed on the CPU cores, the far- and near-field computations are all performed on the GPU cores. We show how to efficiently expose the interactions resulting from the DTT to the GPU cores, how to deploy both the far- and near-field computations on GPU, and how to overlap the parallel DTT on CPU with GPU computations. Based on the falcON code and using OpenCL on AMD Accelerated Processing Units and on Intel integrated GPUs, this first heterogeneous deployment of DTT for FMM outperforms standard multi-core CPUs and matches GPU and high-end CPU performance, being hence more cost- and power-efficient.
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Warren, Michael S. "2HOT: An Improved Parallel Hashed Oct-Tree N-Body Algorithm for Cosmological Simulation." Scientific Programming 22, no. 2 (2014): 109–24. http://dx.doi.org/10.1155/2014/802125.
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We report on improvements made over the past two decades to our adaptive treecode N-body method (HOT). A mathematical and computational approach to the cosmological N-body problem is described, with performance and scalability measured up to 256k (218) processors. We present error analysis and scientific application results from a series of more than ten 69 billion (40963) particle cosmological simulations, accounting for 4×1020floating point operations. These results include the first simulations using the new constraints on the standard model of cosmology from the Planck satellite. Our simulations set a new standard for accuracy and scientific throughput, while meeting or exceeding the computational efficiency of the latest generation of hybrid TreePM N-body methods.
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Dugaro, A., G. C. de Elía, and L. A. Darriba. "Water worlds in N-body simulations with fragmentation in systems without gaseous giants." Astronomy & Astrophysics 641 (September 2020): A139. http://dx.doi.org/10.1051/0004-6361/202037619.
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Aims. We analyze the formation and evolution of terrestrial-like planets around solar-type stars in the absence of gaseous giants. In particular, we focus on the physical and dynamical properties of those that survive in the system’s habitable zone (HZ). This investigation is based on a comparative study between N-body simulations that include fragmentation and others that consider all collisions as perfect mergers. Methods. We use an N-body code, presented in a previous paper, that allows planetary fragmentation. We carry out three sets of 24 simulations for 400 Myr. Two sets are developed adopting a model that includes hit-and-run collisions and planetary fragmentation, each one with different values of the individual minimum mass allowed for the fragments. For the third set, we considered that all collisions lead to perfect mergers. Results. The planetary systems produced in N-body simulations with and without fragmentation are broadly similar, though with some differences. In simulations with fragmentation, the formed planets have lower masses since part of them is distributed among collisional fragments. Additionally, those planets presented lower eccentricities, presumably due to dynamical friction with the generated fragments. Lastly, perfect mergers and hit-and-run collisions are the most common outcome. Regardless of the collisional treatment adopted, most of the planets that survive in the HZ start the simulation beyond the snow line, having very high final water contents. Such planets are called water worlds. The fragments’ contribution to their final mass and water content is negligible. Finally, the individual minimum mass for fragments may play an important role in the planets’ collisional history. Conclusions. Collisional models that incorporate fragmentation and hit-and-run collisions lead to a more detailed description of the physical properties of the terrestrial-like planets formed. We conclude that planetary fragmentation is not a barrier to the formation of water worlds in the HZ. The results shown in this work suggest that further refinement is necessary to have a more realistic model of planetary formation.
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Vraštil, Michal, and Salman Habib. "Fast approximate methods for modified gravity cosmological simulations." Monthly Notices of the Royal Astronomical Society 493, no. 2 (February 11, 2020): 2085–100. http://dx.doi.org/10.1093/mnras/staa333.
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ABSTRACT The accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives. Predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly non-linear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we find that these methods can indeed be used to explore the region around the baryon acoustic oscillation scale, $k\sim 0.1~h\, \text{Mpc}^{-1}$ but not much further.
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Martí, Jordi, and Bernat Diaz. "Efficient recursive Adams–Bashforth methods in molecular dynamics simulations of N-body systems interacting through pairwise potentials." Molecular Simulation 46, no. 16 (September 9, 2020): 1248–54. http://dx.doi.org/10.1080/08927022.2020.1815730.
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Pelupessy, Inti, Vincent Icke, and Paul van der Werf. "Supernova Feedback in SPH Simulations of Galaxies." Symposium - International Astronomical Union 208 (2003): 439–40. http://dx.doi.org/10.1017/s0074180900207651.
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We report on the development of a N-body/SPH code for galaxy interactions, with particular emphasis on SN feedback implementations. We show that current methods of SN feedback probably need simulations with > 105– 106gas particles per galactic disk to be able to realistically describe galactic fountains and superwinds.
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Umbreit, Stefan, John M. Fregeau, and Frederic A. Rasio. "The Imprints of IMBHs on the Structure of Globular Clusters: Monte-Carlo Simulations." Proceedings of the International Astronomical Union 3, S246 (September 2007): 351–55. http://dx.doi.org/10.1017/s1743921308015913.
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AbstractWe present the first results of a series of Monte-Carlo simulations investigating the imprints of a central black hole on the core structure of globular clusters. We investigate the three-dimensional and the projected density profile of the inner regions of idealized as well as more realistic globular cluster models, taking into account a stellar mass spectrum, stellar evolution and allowing for a larger, more realistic, number of stars than was previously possible with direct N-body methods. We compare our results to other N-body simulations published previously in the literature.
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Schmittfull, Marcel. "Large-scale structure non-Gaussianities with modal methods." Proceedings of the International Astronomical Union 11, S308 (June 2014): 67–68. http://dx.doi.org/10.1017/s1743921316009649.
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AbstractRelying on a separable modal expansion of the bispectrum, the implementation of a fast estimator for the full bispectrum of a 3d particle distribution is presented. The computational cost of accurate bispectrum estimation is negligible relative to simulation evolution, so the bispectrum can be used as a standard diagnostic whenever the power spectrum is evaluated. As an application, the time evolution of gravitational and primordial dark matter bispectra was measured in a large suite of N-body simulations. The bispectrum shape changes characteristically when the cosmic web becomes dominated by filaments and halos, therefore providing a quantitative probe of 3d structure formation. Our measured bispectra are determined by ∼ 50 coefficients, which can be used as fitting formulae in the nonlinear regime and for non-Gaussian initial conditions. We also compare the measured bispectra with predictions from the Effective Field Theory of Large Scale Structures (EFTofLSS).
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Aarseth, S. J. "Dancing with Black Holes." Proceedings of the International Astronomical Union 3, S246 (September 2007): 437–46. http://dx.doi.org/10.1017/s1743921308016141.
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AbstractWe 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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Yang, B., J. Hanuš, M. Brož, O. Chrenko, M. Willman, P. Ševeček, J. Masiero, and H. Kaluna. "Physical and dynamical characterization of the Euphrosyne asteroid family." Astronomy & Astrophysics 643 (October 29, 2020): A38. http://dx.doi.org/10.1051/0004-6361/202038567.
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Aims. The Euphrosyne asteroid family occupies a unique zone in orbital element space around 3.15 au and may be an important source of the low-albedo near-Earth objects. The parent body of this family may have been one of the planetesimals that delivered water and organic materials onto the growing terrestrial planets. We aim to characterize the compositional properties as well as the dynamical properties of the family. Methods. We performed a systematic study to characterize the physical properties of the Euphrosyne family members via low-resolution spectroscopy using the NASA Infrared Telescope Facility. In addition, we performed smoothed-particle hydrodynamics (SPH) simulations and N-body simulations to investigate the collisional origin, determine a realistic velocity field, study the orbital evolution, and constrain the age of the Euphrosyne family. Results. Our spectroscopy survey shows that the family members exhibit a tight taxonomic distribution, suggesting a homogeneous composition of the parent body. Our SPH simulations are consistent with the Euphrosyne family having formed via a reaccumulation process instead of a cratering event. Finally, our N-body simulations indicate that the age of the family is 280−80+180 Myr, which is younger than previous estimates.
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Breen, Philip G., Simon Rozier, Douglas C. Heggie, and Anna Lisa Varri. "The kinematic richness of star clusters – II. Stability of spherical anisotropic models with rotation." Monthly Notices of the Royal Astronomical Society 502, no. 4 (February 9, 2021): 4762–78. http://dx.doi.org/10.1093/mnras/stab365.
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ABSTRACT We study the bar instability in collisionless, rotating, anisotropic, stellar systems, using N-body simulations and also the matrix technique for calculation of modes with the perturbed collisionless Boltzmann equation. These methods are applied to spherical systems with an initial Plummer density distribution, but modified kinematically in two ways: the velocity distribution is tangentially anisotropic, using results of Dejonghe, and the system is set in rotation by reversing the velocities of a fraction of stars in various regions of phase space, à la Lynden-Bell. The aim of the N-body simulations is first to survey the parameter space, and, using those results, to identify regions of phase space (by radius and orbital inclination) that have the most important influence on the bar instability. The matrix method is then used to identify the resonant interactions in the system that have the greatest effect on the growth rate of a bar. Complementary series of N-body simulations examine these processes in relation to the evolving frequency distribution and the pattern speed. Finally, the results are synthesized with an existing theoretical framework, and used to consider the old question of constructing a stability criterion.
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Antoniadou, Kyriaki I., and Dimitri Veras. "Driving white dwarf metal pollution through unstable eccentric periodic orbits." Astronomy & Astrophysics 629 (September 2019): A126. http://dx.doi.org/10.1051/0004-6361/201935996.
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Context. Planetary debris is observed in the atmospheres of over 1000 white dwarfs, and two white dwarfs are now observed to contain orbiting minor planets. Exoasteroids and planetary core fragments achieve orbits close to the white dwarf through scattering with major planets. However, the architectures that allow for this scattering to take place are time-consuming to explore with N-body simulations lasting ∼1010 yr; these long-running simulations restrict the amount of phase space that can be investigated. Aims. Here we use planar and three-dimensional (spatial) elliptic periodic orbits, as well as chaotic indicators through dynamical stability maps, as quick scale-free analytic alternatives to N-body simulations in order to locate and predict instability in white dwarf planetary systems that consist of one major and one minor planet on very long timescales. We then classify the instability according to ejection versus collisional events. Methods. We generalized our previous work by allowing eccentricity and inclination of the periodic orbits to increase, thereby adding more realism but also significantly more degrees of freedom to our architectures. We also carried out a suite of computationally expensive 10 Gyr N-body simulations to provide comparisons with chaotic indicators in a limited region of phase space. Results. We compute dynamical stability maps that are specific to white dwarf planetary systems and that can be used as tools in future studies to quickly estimate pollution prospects and timescales for one-planet architectures. We find that these maps also agree well with the outcomes of our N-body simulations. Conclusions. As observations of metal-polluted white dwarfs mount exponentially, particularly in the era of Gaia, tools such as periodic orbits can help infer dynamical histories for ensembles of systems.
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Pellejero-Ibañez, Marcos, Andres Balaguera-Antolínez, Francisco-Shu Kitaura, Raúl E. Angulo, Gustavo Yepes, Chia-Hsun Chuang, Guillermo Reyes-Peraza, Mathieu Autefage, Mohammadjavad Vakili, and Cheng Zhao. "The bias of dark matter tracers: assessing the accuracy of mapping techniques." Monthly Notices of the Royal Astronomical Society 493, no. 1 (January 29, 2020): 586–93. http://dx.doi.org/10.1093/mnras/staa270.
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ABSTRACT We present a comparison between approximated methods for the construction of mock catalogues based on the halo-bias mapping technique. To this end, we use as reference a high-resolution N-body simulation of 38403 dark matter particles on a 400 h−1 Mpc cube box from the Multidark suite. In particular, we explore parametric versus non-parametric bias mapping approaches and compare them at reproducing the halo distribution in terms of the two- and three-point statistics down to $\sim 10^8\, {\rm M}_{\odot }\, h^{-1}$ halo masses. Our findings demonstrate that the parametric approach remains inaccurate even including complex deterministic and stochastic components. On the contrary, the non-parametric one is indistinguishable from the reference N-body calculation in the power spectrum beyond $k=1\, h\, {\rm Mpc}^{-1}$, and in the bispectrum for typical configurations relevant to baryon acoustic oscillation analysis. We conclude that approaches which extract the full bias information from N-body simulations in a non-parametric fashion are ready for the analysis of the new generation of large-scale structure surveys.
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Ishiyama, Tomoaki, and Shin’ichiro Ando. "The abundance and structure of subhaloes near the free streaming scale and their impact on indirect dark matter searches." Monthly Notices of the Royal Astronomical Society 492, no. 3 (January 23, 2020): 3662–71. http://dx.doi.org/10.1093/mnras/staa069.
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ABSTRACT The free streaming motion of dark matter particles imprints a cutoff in the matter power spectrum and set the scale of the smallest dark matter halo. Recent cosmological N-body simulations have shown that the central density cusp is much steeper in haloes near the free streaming scale than in more massive haloes. Here, we study the abundance and structure of subhaloes near the free streaming scale at very high redshift using a suite of unprecedentedly large cosmological N-body simulations, over a wide range of the host halo mass. The subhalo abundance is suppressed strongly below the free streaming scale, but the ratio between the subhalo mass function in the cutoff and no cutoff simulations is well fitted by a single correction function regardless of the host halo mass and the redshift. In subhaloes, the central slopes are considerably shallower than in field haloes, however, are still steeper than that of the NFW profile. Contrary, the concentrations are significantly larger in subhaloes than haloes and depend on the subhalo mass. We compare two methods to extrapolate the mass–concentration relation of haloes and subhaloes to z = 0 and provide a new simple fitting function for subhaloes, based on a suite of large cosmological N-body simulations. Finally, we estimate the annihilation boost factor of a Milky-Way-sized halo to be between 1.8 and 6.2.
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MACKAPLOW, MICHAEL B., and ERIC S. G. SHAQFEH. "A numerical study of the sedimentation of fibre suspensions." Journal of Fluid Mechanics 376 (December 10, 1998): 149–82. http://dx.doi.org/10.1017/s0022112098002663.
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The sedimentation of fibre suspensions at low Reynolds number is studied using two different, but complementary, numerical simulation methods: (1) Monte Carlo simulations, which consider interparticle hydrodynamic interactions at all orders within the slender-body theory approximation (Mackaplow & Shaqfeh 1996), and (ii) dynamic simulations, which consider point–particle interactions and are accurate for suspension concentrations of nl3=1, where n and l are the number density and characteristic half-length of the fibres, respectively. For homogeneous, isotropic suspensions, the Monte Carlo simulations show that the hindrance of the mean sedimentation speed is linear in particle concentration up to at least nl3=7. The speed is well predicted by a new dilute theory that includes the effect of two-body interactions. Our dynamic simulations of dilute suspensions, however, show that interfibre hydrodynamic interactions cause the spatial and orientational distributions to become inhomogeneous and anisotropic. Most of the fibres migrate into narrow streamers aligned in the direction of gravity. This drives a downward convective flow within the streamers which serves to increase the mean fibre sedimentation speed. A steady-state orientation distribution develops which strongly favours fibre alignment with gravity. Although the distribution reaches a steady state, individual fibres continue to rotate in a manner that can be qualitatively described as a flipping between the two orientations aligned with gravity. The simulation results are in good agreement with published experimental data.
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Bhatt, Sandeep, Marina Chen, James Cowie, Cheng-Yee Lin, and Pangfeng Liu. "Object-Oriented Support for Adaptive Methods on Paranel Machines." Scientific Programming 2, no. 4 (1993): 179–92. http://dx.doi.org/10.1155/1993/474972.
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This article reports on experiments from our ongoing project whose goal is to develop a C++ library which supports adaptive and irregular data structures on distributed memory supercomputers. We demonstrate the use of our abstractions in implementing "tree codes" for large-scale N-body simulations. These algorithms require dynamically evolving treelike data structures, as well as load-balancing, both of which are widely believed to make the application difficult and cumbersome to program for distributed-memory machines. The ease of writing the application code on top of our C++ library abstractions (which themselves are application independent), and the low overhead of the resulting C++ code (over hand-crafted C code) supports our belief that object-oriented approaches are eminently suited to programming distributed-memory machines in a manner that (to the applications programmer) is architecture-independent. Our contribution in parallel programming methodology is to identify and encapsulate general classes of communication and load-balancing strategies useful across applications and MIMD architectures. This article reports experimental results from simulations of half a million particles using multiple methods.
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Rein, Hanno, Daniel Tamayo, and Garett Brown. "High-order symplectic integrators for planetary dynamics and their implementation in rebound." Monthly Notices of the Royal Astronomical Society 489, no. 4 (September 7, 2019): 4632–40. http://dx.doi.org/10.1093/mnras/stz2503.
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ABSTRACT Direct N-body simulations and symplectic integrators are effective tools to study the long-term evolution of planetary systems. The Wisdom–Holman (WH) integrator in particular has been used extensively in planetary dynamics as it allows for large time-steps at good accuracy. One can extend the WH method to achieve even higher accuracy using several different approaches. In this paper, we survey integrators developed by Wisdom et al., Laskar & Robutel, and Blanes et al. Since some of these methods are harder to implement and not as readily available to astronomers compared to the standard WH method, they are not used as often. This is somewhat unfortunate given that in typical simulations it is possible to improve the accuracy by up to six orders of magnitude (!) compared to the standard WH method without the need for any additional force evaluations. To change this, we implement a variety of high-order symplectic methods in the freely available N-body integrator rebound. In this paper, we catalogue these methods, discuss their differences, describe their error scalings, and benchmark their speed using our implementations.
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Di Cintio, Pierfrancesco, Mario Pasquato, Hyunwoo Kim, and Suk-Jin Yoon. "Introducing a new multi-particle collision method for the evolution of dense stellar systems." Astronomy & Astrophysics 649 (May 2021): A24. http://dx.doi.org/10.1051/0004-6361/202038784.
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Context. Stellar systems are broadly divided into collisional and non-collisional categories. While the latter are large-N systems with long relaxation timescales and can be simulated disregarding two-body interactions, either computationally expensive direct N-body simulations or approximate schemes are required to properly model the former. Large globular clusters and nuclear star clusters, with relaxation timescales of the order of a Hubble time, are small enough to display some collisional behaviour and big enough to be impossible to simulate with direct N-body codes and current hardware. Aims. We aim to introduce a new method to simulate collisional stellar systems and validate it by comparison with direct N-body codes on small-N simulations. Methods. The Multi-Particle Collision for Dense Stellar Systems (MPCDSS) code is a new code for evolving stellar systems with the multi-particle collision method. Such a method amounts to a stochastic collision rule that makes it possible to conserve the exact energy and momentum over a cluster of particles experiencing the collision. The code complexity scales with N log N in the number of particles. Unlike Monte Carlo codes, MPCDSS can easily model asymmetric, non-homogeneous, unrelaxed, and rotating systems, while allowing us to follow the orbits of individual stars. Results. We evolved small (N = 3.2 × 104) star clusters with MPCDSS and with the direct-summation code NBODY6, finding a similar evolution of key indicators. We then simulated different initial conditions in the 104 − 106 star range. Conclusions. MPCDSS bridges the gap between small collisional systems that can be simulated with direct N-body codes and large non-collisional systems. In principle, MPCDSS allows us to simulate globular clusters such as Ω Centauri and M 54, and even nuclear star clusters, which is beyond the limits of current direct N-body codes in terms of the number of particles.
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Sánchez, Mariana B., Gonzalo C. de Elía, and Juan José Downes. "Tidal and general relativistic effects in rocky planet formation at the substellar mass limit using N-body simulations." Astronomy & Astrophysics 637 (May 2020): A78. http://dx.doi.org/10.1051/0004-6361/201937317.
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Context. Recent observational results show that very low mass stars and brown dwarfs are able to host close-in rocky planets. Low-mass stars are the most abundant stars in the Galaxy, and the formation efficiency of their planetary systems is relevant in the computation of a global probability of finding Earth-like planets inside habitable zones. Tidal forces and relativistic effects are relevant in the latest dynamical evolution of planets around low-mass stars, and their effect on the planetary formation efficiency still needs to be addressed. Aims. Our goal is to evaluate the impact of tidal forces and relativistic effects on the formation of rocky planets around a star close to the substellar mass limit in terms of the resulting planetary architectures and its distribution according to the corresponding evolving habitable zone. Methods. We performed a set of N-body simulations spanning the first 100 Myr of the evolution of two systems composed of 224 embryos with a total mass 0.25 M⊕ and 74 embryos with a total mass 3 M⊕ around a central object of 0.08 M⊙. For these two scenarios we compared the planetary architectures that result from simulations that are purely gravitational with those from simulations that include the early contraction and spin-up of the central object, the distortions and dissipation tidal terms, and general relativistic effects. Results. We found that including these effects allows the formation and survival of a close-in (r < 0.07 au) population of rocky planets with masses in the range 0.001 < m∕M⊕ < 0.02 in all the simulations of the less massive scenario, and a close-in population with masses m ~ 0.35 M⊕ in just a few of the simulations of the more massive scenario. The surviving close-in bodies suffered more collisions during the integration time of the simulations. These collisions play an important role in their final masses. However, all of these bodies conserved their initial amount of water in mass throughout the integration time. Conclusions. The incorporation of tidal and general relativistic effects allows the formation of an in situ close-in population located in the habitable zone of the system. This means that both effects are relevant during the formation of rocky planets and their early evolution around stars close to the substellar mass limit, in particular when low-mass planetary embryos are involved.
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SCHÄFER, BJÖRN MALTE. "GALACTIC ANGULAR MOMENTA AND ANGULAR MOMENTUM CORRELATIONS IN THE COSMOLOGICAL LARGE-SCALE STRUCTURE." International Journal of Modern Physics D 18, no. 02 (February 2009): 173–222. http://dx.doi.org/10.1142/s0218271809014388.
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I review the theory of angular momentum acquisition of galaxies by tidal torquing, the resulting angular momentum distribution and the angular momentum correlation function, and discuss the implications of angular momentum alignments for weak lensing measurements. Starting from linear models for tidal torquing, I summarize perturbative approaches and the results from n-body simulations of cosmic structure formation. Then I discuss the validity of decompositions of the tidal shear and inertia fields, the effects of angular momentum biasing, the applicability of parametrized angular momentum correlation models and the consequences of angular momentum correlations for shape alignments. I compile the results of observations of shape alignments in recent galaxy surveys as well as in n-body simulations. Finally, I review the contamination of weak lensing surveys by spin-induced shape alignments and methods for suppressing this contamination.
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Meiron, Yohai. "Expansion techniques for collisionless stellar dynamical simulations." Proceedings of the International Astronomical Union 10, S312 (August 2014): 227–30. http://dx.doi.org/10.1017/s1743921315007851.
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AbstractWe present ETICS, a collisionless N-body code based on two kinds of series expansions of the Poisson equation, implemented for graphics processing units (GPUs). The code is publicly available and can be used as a standalone program or as a library (an AMUSE plugin is included). One of the two expansion methods available is the self-consistent field (SCF) method, which is a Fourier-like expansion of the density field in some basis set; the other is the multipole expansion (MEX) method, which is a Taylor-like expansion of the Green's function. MEX, which has been advocated in the past, has not gained as much popularity as SCF. Both are particle-field methods and optimized for collisionless galactic dynamics, but while SCF is a “pure” expansion, MEX is an expansion in just the angular part; thus, MEX is capable of capturing radial structure easily, while SCF needs a large number of radial terms.
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Bertschinger, Edmund, and James M. Gelb. "Path Integral Methods for Primordial Density Perturbations." Symposium - International Astronomical Union 130 (1988): 593. http://dx.doi.org/10.1017/s0074180900137192.
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Path integrals may be used to describe the statistical properties of a random field such as the primordial density perturbation field. In this framework the probability distribution is given for a Gaussian random field subjected to constraints such as the presence of a peak of given curvature at a specific location in the initial conditions. An algorithm has been constructed for generating samples of a constrained Gaussian random field on a lattice using Monte Carlo techniques. The algorithm is equivalent to, but much faster than, generating unconstrained random samples repeatedly until a sample is found satisfying the desired constraints to arbitrary precision. The method makes possible a systematic study of the density field around peaks or other constrained regions in the biased galaxy formation scenario and it is effective for generating initial conditions for N-body simulations with rare objects in the computational volume.
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Funato, Yoko, D. C. Heggie, P. Hut, and Jun Makino. "Test of the Accuracy of Approximate Methods to Handle Distant Binary-Single Star Encounters." Proceedings of the International Astronomical Union 3, S246 (September 2007): 469–70. http://dx.doi.org/10.1017/s1743921308016189.
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AbstractIn the numerical simulations of evolution of star clusters, binary-single star interactions frequently take place. Since the direct integration of them is time consuming, distant interactions between binaries and field stars are often integrated by using some approximations. Traditionally the effect of the error caused by the approximated treatment is regarded as small enough to be ignored. However, if we have a binary-dominated core, the energy drift is large. In this study, we perform numerical experiments to evaluate the effect of neglecting the weak perturbation from distant single particles. We developed an N-body integrator which can manipulate multiple precision floating point numbers.
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Martinez-Valpuesta, Inma, and E. Athanassoula. "Boxy/peanut bulges, vertical buckling and galactic bars." Proceedings of the International Astronomical Union 3, S245 (July 2007): 103–6. http://dx.doi.org/10.1017/s1743921308017390.
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AbstractBoxy/peanut bulges in disk galaxies have been associated to stellar bars. In this talk, we discuss the different properties of such bulges and their relation with the corresponding bar, using a very large sample of a few hundred numerical N-body simulations. We present and inter-compare various methods of measuring the boxy/peanut bulge properties, namely its strength, shape and possible asymmetry. Some of these methods can be applied to both simulations and observations. Our final goal is to get correlations that will allow us to obtain information on the boxy/peanut bulge for a galaxy viewed face-on as well as information on the bars of galaxies viewed edge-on.
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Spurzem, Rainer. "Fluid Techniques and Evolution of Anisotropy." Symposium - International Astronomical Union 174 (1996): 111–20. http://dx.doi.org/10.1017/s0074180900001443.
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Fluid dynamical techniques to model the dynamical evolution of star clusters, and their successors, gaseous models using an equation of heat conductivity to model relaxation effects, including anisotropy, are presented. The historical merits of such models are reviewed as well as the current status of their credibility, based on quantitative comparisons with other methods, like orbit-averaged Fokker-Planck solutions and direct N-body simulations.
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Dugaro, A., G. C. de Elía, and L. A. Darriba. "Physical properties of terrestrial planets and water delivery in the habitable zone using N-body simulations with fragmentation." Astronomy & Astrophysics 632 (November 22, 2019): A14. http://dx.doi.org/10.1051/0004-6361/201936061.
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Aims. The goal of this research is to study how the fragmentation of planetary embryos can affect the physical and dynamical properties of terrestrial planets around solar-type stars. Our study focuses on the formation and evolution of planets and water delivery in the habitable zone (HZ). We distinguish class A and class B HZ planets, which have an accretion seed initially located inside and beyond the snow line, respectively. Methods. We developed an N-body integrator that incorporates fragmentation and hit-and-run collisions, which is called D3 N-body code. From this, we performed 46 numerical simulations of planetary accretion in systems that host two gaseous giants similar to Jupiter and Saturn. We compared two sets of 23 N-body simulations, one of which includes a realistic collisional treatment and the other one models all impacts as perfect mergers. Results. The final masses of the HZ planets formed in runs with fragmentation are about 15–20% lower than those obtained without fragmentation. As for the class A HZ planets, those formed in simulations without fragmentation experience very significant increases in mass with respect to their initial values, while the growth of those produced in runs with fragmentation is less relevant. We remark that the fragments play a secondary role in the masses of the class A HZ planets, providing less than 30% of their final values. In runs without fragmentation, the final fraction of water of the class A HZ planets keeps the initial value since they do not accrete water-rich embryos. In runs with fragmentation, the final fraction of water of such planets strongly depends on the model used to distribute the water after each collision. The class B HZ planets do not show significant differences concerning their final water contents in runs with and without fragmentation. From this, we find that the collisional fragmentation is not a barrier to the survival of water worlds in the HZ.
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Giocoli, Carlo, Pierluigi Monaco, Lauro Moscardini, Tiago Castro, Massimo Meneghetti, R. Benton Metcalf, and Marco Baldi. "Testing the reliability of fast methods for weak lensing simulations: wl-moka on pinocchio." Monthly Notices of the Royal Astronomical Society 496, no. 2 (June 3, 2020): 1307–24. http://dx.doi.org/10.1093/mnras/staa1538.
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ABSTRACT The generation of simulated convergence maps is of key importance in fully exploiting weak lensing by large-scale structure (LSS) from which cosmological parameters can be derived. In this paper, we present an extension of the pinocchio code that produces catalogues of dark matter haloes so that it is capable of simulating weak lensing by Modify LSS into Large Scale Structures (LSS). Like wl-moka, the method starts with a random realization of cosmological initial conditions, creates a halo catalogue and projects it on to the past light-cone, and paints in haloes assuming parametric models for the mass density distribution within them. Large-scale modes that are not accounted for by the haloes are constructed using linear theory. We discuss the systematic errors affecting the convergence power spectra when Lagrangian perturbation theory at increasing order is used to displace the haloes within pinocchio, and how they depend on the grid resolution. Our approximate method is shown to be very fast when compared to full ray-tracing simulations from an N-body run and able to recover the weak lensing signal, at different redshifts, with a few percent accuracy. It also allows for quickly constructing weak lensing covariance matrices, complementing pinocchio’s ability of generating the cluster mass function and galaxy clustering covariances and thus paving the way for calculating cross-covariances between the different probes. This work advances these approximate methods as tools for simulating and analysing survey data for cosmological purposes.
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List, Florian, Nikolas Iwanus, Pascal J. Elahi, and Geraint F. Lewis. "A novel scheme for Dark Matter Annihilation Feedback in cosmological simulations." Monthly Notices of the Royal Astronomical Society 489, no. 3 (August 19, 2019): 4217–32. http://dx.doi.org/10.1093/mnras/stz2287.
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ABSTRACT We present a new self-consistent method for incorporating Dark Matter Annihilation Feedback (DMAF) in cosmological N-body simulations. The power generated by DMAF is evaluated at each dark matter (DM) particle which allows for flexible energy injection into the surrounding gas based on the specific DM annihilation model under consideration. Adaptive, individual time-steps for gas and DM particles are supported and a new time-step limiter, derived from the propagation of a Sedov–Taylor blast wave, is introduced. We compare this donor-based approach with a receiver-based approach used in recent studies and illustrate the differences by means of a toy example. Furthermore, we consider an isolated halo and a cosmological simulation and show that for these realistic cases, both methods agree well with each other. The extension of our implementation to scenarios such as non-local energy injection, velocity-dependent annihilation cross-sections, and DM decay is straightforward.
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Aarseth, Sverre J. "Star Cluster Simulations: The State of The Art." International Astronomical Union Colloquium 172 (1999): 127–37. http://dx.doi.org/10.1017/s0252921100072481.
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AbstractThis 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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Rantala, Antti, Pauli Pihajoki, Matias Mannerkoski, Peter H. Johansson, and Thorsten Naab. "mstar – a fast parallelized algorithmically regularized integrator with minimum spanning tree coordinates." Monthly Notices of the Royal Astronomical Society 492, no. 3 (January 15, 2020): 4131–48. http://dx.doi.org/10.1093/mnras/staa084.
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ABSTRACT We present the novel algorithmically regularized integration method mstar for high-accuracy (|ΔE/E| ≳ 10−14) integrations of N-body systems using minimum spanning tree coordinates. The twofold parallelization of the $\mathcal {O}(N_\mathrm{part}^2)$ force loops and the substep divisions of the extrapolation method allow for a parallel scaling up to NCPU = 0.2 × Npart. The efficient parallel scaling of mstar makes the accurate integration of much larger particle numbers possible compared to the traditional algorithmic regularization chain (ar-chain) methods, e.g. Npart = 5000 particles on 400 CPUs for 1 Gyr in a few weeks of wall-clock time. We present applications of mstar on few particle systems, studying the Kozai mechanism and N-body systems like star clusters with up to Npart = 104 particles. Combined with a tree or fast multipole-based integrator, the high performance of mstar removes a major computational bottleneck in simulations with regularized subsystems. It will enable the next-generation galactic-scale simulations with up to 109 stellar particles (e.g. $m_\star = 100 \, \mathrm{M}_\odot$ for an $M_\star = 10^{11} \, \mathrm{M}_\odot$ galaxy), including accurate collisional dynamics in the vicinity of nuclear supermassive black holes.
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de Elía, G. C., M. Zanardi, A. Dugaro, and S. Naoz. "Inverse Lidov-Kozai resonance for an outer test particle due to an eccentric perturber." Astronomy & Astrophysics 627 (June 25, 2019): A17. http://dx.doi.org/10.1051/0004-6361/201935220.
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Aims. We analyze the behavior of the argument of pericenter ω2 of an outer particle in the elliptical restricted three-body problem, focusing on the ω2 resonance or inverse Lidov-Kozai resonance. Methods. First, we calculated the contribution of the terms of quadrupole, octupole, and hexadecapolar order of the secular approximation of the potential to the outer particle’s ω2 precession rate (dω2∕dτ). Then, we derived analytical criteria that determine the vanishing of the ω2 quadrupole precession rate (dω2/dτ)quad for different values of the inner perturber’s eccentricity e1. Finally, we used such analytical considerations and described the behavior of ω2 of outer particles extracted from N-body simulations developed in a previous work. Results. Our analytical study indicates that the values of the inclination i2 and the ascending node longitude Ω2 associated with the outer particle that vanish (dω2/dτ)quad strongly depend on the eccentricity e1 of the inner perturber. In fact, if e1 < 0.25 (>0.40825), (dω2/dτ)quad is only vanished for particles whose Ω2 circulates (librates). For e1 between 0.25 and 0.40825, (dω2/dτ)quad can be vanished for any particle for a suitable selection of pairs (Ω2, i2). Our analysis of the N-body simulations shows that the inverse Lidov-Kozai resonance is possible for small, moderate, and high values of e1. Moreover, such a resonance produces distinctive features in the evolution of a particle in the (Ω2, i2) plane. In fact, if ω2 librates and Ω2 circulates, the extremes of i2 at Ω2 = 90° and 270° do not reach the same value, while if ω2 and Ω2 librate, the evolutionary trajectory of the particle in the (Ω2, i2) plane shows evidence of an asymmetry with respect to i2 = 90°. The evolution of ω2 associated with the outer particles of the N-body simulations can be very well explained by the analytical criteria derived in our investigation.
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Aarseth, Sverre J. "Regularization tools for binary interactions." Symposium - International Astronomical Union 208 (2003): 295–304. http://dx.doi.org/10.1017/s0074180900207249.
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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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Ogihara, Masahiro, Eiichiro Kokubo, Takeru K. Suzuki, and Alessandro Morbidelli. "Formation of close-in super-Earths in evolving protoplanetary disks due to disk winds." Astronomy & Astrophysics 615 (July 2018): A63. http://dx.doi.org/10.1051/0004-6361/201832720.
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Context. Planets with masses larger than about 0.1 M⊕ undergo rapid inward migration (type I migration) in a standard protoplanetary disk. Recent magnetohydrodynamical simulations revealed the presence of magnetically driven disk winds, which would alter the disk profile and the type I migration in the close-in region. Aims. We investigate orbital evolution of planetary embryos in disks that viscously evolve under the effects of disk winds. The aim is to discuss effects of altered disk profiles on type I migration. In addition, we aim to examine whether observed distributions of close-in super-Earths can be reproduced by simulations that include effects of disk winds. Methods. We perform N-body simulations of super-Earth formation from planetary embryos, in which a recent model for disk evolution is used. We explore a wide range of parameters and draw general trends. We also carry out N-body simulations of close-in super-Earth formation from embryos in such disks under various conditions. Results. We find that the type I migration is significantly suppressed in many cases. Even in cases in which inward migration occurs, the migration timescale is lengthened to 1 Myr, which mitigates the type I migration problem. This is because the gas surface density is decreased and has a flatter profile in the close-in region due to disk winds. We find that when the type I migration is significantly suppressed, planets undergo late orbital instability during the gas depletion, leading to a non-resonant configuration. We also find that observed distributions of close-in super-Earths (e.g., period ratio, mass ratio) can be reproduced. In addition, we show that in some results of simulations, systems with a chain of resonant planets, like the TRAPPIST-1 system, form.
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Theis, Christian. "Measuring Dark Matter Halos by Modeling Interacting Galaxies." Symposium - International Astronomical Union 220 (2004): 461–62. http://dx.doi.org/10.1017/s0074180900183822.
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The richness of tidal features seen in interacting galaxies allows for the determination of their characteristic parameters, provided one can deal with the extended parameter space. Genetic algorithm based methods – like our code minga – have proven to be such a tool. Here I discuss the implementation of dark matter halo descriptions in the restricted N-body simulations of minga. I show that the final morphology of a galaxy encounter strongly depends on the halo properties. Thus, modeling tidal features of interacting galaxies might allow also for conclusions on the galactic dark matter content.
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Ataiee, S., and W. Kley. "Pushing planets into an inner cavity by a resonant chain." Astronomy & Astrophysics 648 (April 2021): A69. http://dx.doi.org/10.1051/0004-6361/202038772.
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Context. The orbital distribution of exoplanets indicates an accumulation of super-Earth sized planets close to their host stars in compact systems. When an inward disc-driven migration scenario is assumed for their formation, these planets could have been stopped and might have been parked at an inner edge of the disc, or be pushed through the inner disc cavity by a resonant chain. This topic has not been properly and extensively studied. Aims. Using numerical simulations, we investigate the possibility that the inner planets in a resonant chain can be pushed into the disc inner cavity by outer planets. Methods. We performed hydrodynamical and N-body simulations of planetary systems embedded in their nascent disc. The inner edge of the disc was represented in two different ways, resembling either a dead zone inner edge (DZ) or a disc inner boundary (IB). The main difference lies in the steepness of the surface density profile. The innermost planet always has a mass of 10 MEarth, with additional outer planets of equal or higher mass. Results. A steeper profile is able to stop a chain of planets more efficiently than a shallower profile. The final configurations in our DZ models are usually tighter than in their IB counterparts, and therefore more prone to instability. We derive analytical expressions for the stopping conditions based on power equilibrium, and show that the final eccentricities result from torque equilibrium. For planets in thinner discs, we found, for the first time, clear signs for over-stable librations in the hydrodynamical simulations, leading to very compact systems. We also found that the popular N-body simulations may overestimate the number of planets in the disc inner cavity.
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Kalligiannaki, Evangelia, Vagelis Harmandaris, and Markos Katsoulakis. "Systematic Coarse-Grained Models for Molecular Systems Using Entropy." Proceedings 46, no. 1 (April 8, 2020): 27. http://dx.doi.org/10.3390/ecea-5-06710.
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The development of systematic coarse-grained mesoscopic models for complex molecular systems is an intense research area. Here we first give an overview of different methods for obtaining optimal parametrized coarse-grained models, starting from detailed atomistic representation for high dimensional molecular systems. We focus on methods based on information theory, such as relative entropy, showing that they provide parameterizations of coarse-grained models at equilibrium by minimizing a fitting functional over a parameter space. We also connect them with structural-based (inverse Boltzmann) and force matching methods. All the methods mentioned in principle are employed to approximate a many-body potential, the (n-body) potential of mean force, describing the equilibrium distribution of coarse-grained sites observed in simulations of atomically detailed models. We also present in a mathematically consistent way the entropy and force matching methods and their equivalence, which we derive for general nonlinear coarse-graining maps. We apply, and compare, the above-described methodologies in several molecular systems: A simple fluid (methane), water and a polymer (polyethylene) bulk system. Finally, for the latter we also provide reliable confidence intervals using a statistical analysis resampling technique, the bootstrap method.
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Price, M. A., J. D. McEwen, X. Cai, and T. D. Kitching (for the LSST Dark Energy Science Collaboration). "Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations." Monthly Notices of the Royal Astronomical Society 489, no. 3 (August 26, 2019): 3236–50. http://dx.doi.org/10.1093/mnras/stz2373.
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ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.