共查询到20条相似文献，搜索用时 343 毫秒
1.
2.
3.
《New Astronomy》2021
We present an N-body code called Taichi for galactic dynamics and controlled numerical experiments. The code includes two high-order hierarchical multipole expansion methods: the Barnes-Hut (BH) tree and the fast multipole method (FMM). For the time integration, the code can use either a conventional adaptive KDK or a Hamiltonian splitting integrator. The combination of FMM and the Hamiltonian splitting integrator leads to a momentum-conserving N-body scheme with individual time steps. We find Taichi performs well in the typical applications in galactic dynamics. In the isolated and interacting galaxies tests, the momentum conserving scheme produces the same result as a conventional BH tree code. But for similar force accuracies, FMM significantly speeds up the simulations compared to the monopole BH tree. In the cold collapse test, we find the inner structure after relaxation can be sensitive to the force accuracies. Taichi is ready to incorporate special treatment of close encounters thanks to the Hamiltonian splitting integrator, suitable for studying dynamics around central massive bodies. 相似文献
4.
An iterative approach is used to construct spherically symmetric equilibrium models with an anisotropic velocity distribution. The potentialities of the method have been tested on models with known distribution functions, the Osipkov-Merritt models. It is shown that models that differ significantly from the Osipkov-Merritt models can be constructed. An N-body model of a dark halo with a density distribution that approximates the results of cosmological simulations (the Navarro-Frenk-White model) has been constructed. The anisotropy profile has been taken to be similar to that yielded by cosmological simulations. The constructed models can serve as direct input data for investigating the dynamics and stability of such systems in N-body simulations. 相似文献
5.
Dany Vanbeveren Houria Belkus Joris Van Bever Nicki Mennekens 《Astrophysics and Space Science》2009,324(2-4):271-276
In the present paper we combine an N-body code that simulates the dynamics of young dense stellar systems with a massive star evolution handler that accounts in a realistic way for the effects of stellar wind mass loss. We discuss two topics.
- The formation and the evolution of very massive stars (with masses >120 M⊙) is followed in detail. These very massive stars are formed in the cluster core as a consequence of the successive (physical) collisions of the 10–20 most massive stars in the cluster (this process is known as ‘runaway merging’). The further evolution is governed by stellar wind mass loss during core hydrogen and core helium burning (the WR phase of very massive stars). Our simulations reveal that, as a consequence of runaway merging in clusters with solar and supersolar values, massive black holes can be formed, but with a maximum mass ≈70 M⊙. In low-metallicity clusters, however, it cannot be excluded that the runaway-merging process is responsible for pair-instability supernovae or for the formation of intermediate-mass black holes with a mass of several 100 M⊙.
- Massive runaways can be formed via the supernova explosion of one of the components in a binary system (the Blaauw scenario), or via dynamical interaction of a single star and a binary or between two binaries in a star cluster. We explore the possibility that the most massive runaways (e.g. ζ Pup, λ Cep, BD+43°3654) are the product of the collision and merger of two or three massive stars.
6.
7.
The saturation conditions for bending modes in inhomogeneous thin stellar disks that follow from an analysis of the dispersion relation are compared with those derived from N-body simulations. In the central regions of inhomogeneous disks, the reserve of disk strength against the growth of bending instability is smaller than that for a homogeneous layer. The spheroidal component (a dark halo, a bulge) is shown to have a stabilizing effect. The latter turns out to depend not only on the total mass of the spherical component, but also on the degree of mass concentration toward the center. We conclude that the presence of a compact (not necessarily massive) bulge in spiral galaxies may prove to be enough to suppress the bending perturbations that increase the disk thickness. This conclusion is corroborated by our N-body simulations in which we simulated the evolution of near-equilibrium, but unstable finite-thickness disks in the presence of spheroidal components. The final disk thickness at the same total mass of the spherical component (dark halo + bulge) was found to be much smaller than that in the simulations where a concentrated bulge is present. 相似文献
8.
We present a high-performance N-body code for self-gravitating collisional systems accelerated with the aid of a new SIMD instruction set extension of the x86 architecture: Advanced Vector eXtensions (AVX), an enhanced version of the Streaming SIMD Extensions (SSE). With one processor core of Intel Core i7-2600 processor (8 MB cache and 3.40 GHz) based on Sandy Bridge micro-architecture, we implemented a fourth-order Hermite scheme with individual timestep scheme (Makino and Aarseth, 1992), and achieved the performance of ∼20 giga floating point number operations per second (GFLOPS) for double-precision accuracy, which is two times and five times higher than that of the previously developed code implemented with the SSE instructions (Nitadori et al., 2006b), and that of a code implemented without any explicit use of SIMD instructions with the same processor core, respectively. We have parallelized the code by using so-called NINJA scheme (Nitadori et al., 2006a), and achieved ∼90 GFLOPS for a system containing more than N = 8192 particles with 8 MPI processes on four cores. We expect to achieve about 10 tera FLOPS (TFLOPS) for a self-gravitating collisional system with N ∼ 105 on massively parallel systems with at most 800 cores with Sandy Bridge micro-architecture. This performance will be comparable to that of Graphic Processing Unit (GPU) cluster systems, such as the one with about 200 Tesla C1070 GPUs (Spurzem et al., 2010). This paper offers an alternative to collisional N-body simulations with GRAPEs and GPUs. 相似文献
9.
The dynamical evolution of small stellar groups composed of N=6 components was numerically simulated within the framework of a gravitational N-body problem. The effects of stellar mass loss in the form of stellar wind, dynamical friction against the interstellar medium, and star mergers on the dynamical evolution of the groups were investigated. A comparison with a purely gravitational N-body problem was made. The state distributions at the time of 300 initial system crossing times were analyzed. The parameters of the forming binary and stable triple systems as well as the escaping single and binary stars were studied. The star-merger and dynamical-friction effects are more pronounced in close systems, while the stellar wind effects are more pronounced in wide systems. Star-mergers and stellar wind slow down the dynamical evolution. These factors cause the mean and median semimajor axes of the final binaries as well as the semimajor axes of the internal and external binaries in stable triple systems to increase. Star mergers and dynamical friction in close systems decrease the fraction of binary systems with highly eccentric orbits and the mean component mass ratios for the final binaries and the internal and external binaries in stable triple systems. Star mergers and dynamical friction in close systems increase the fraction of stable triple systems with prograde motions. Dynamical friction in close systems can both increase and decrease the mean velocities of the escaping single stars, depending on the density of the interstellar medium and the mean velocity of the stars in the system. 相似文献
10.
Generalized Jacobian coordinates can be used to decompose anN-body dynamical system intoN-1 2-body systems coupled by perturbations. Hierarchical stability is defined as the property of preserving the hierarchical arrangement of these 2-body subsystems in such a way that orbit crossing is avoided. ForN=3 hierarchical stability can be ensured for an arbitrary span of time depending on the integralz=c 2 h (angular momentum squared times energy): if it is smaller than a critical value, defined by theL 2 collinear equilibrium configuration, then the three possible hierarchical arrangements correspond to three disconnected subsets of the invariant manifold in the phase space (and in the configuration space as well; see Milani and Nobili, 1983a). The same definitions can be extended, with the Jacobian formalism, to an arbitrary hierarchical arrangement ofN≥4 bodies, and the main confinement condition, the Easton inequality, can also be extended but it no longer provides separate regions of trapped motion, whatever is the value ofz for the wholeN-body system,N≥4. However, thez criterion of hierarchical stability applies to every 3-body subsystem, whosez ‘integral’ will of course vary in time because of the perturbations from the other bodies. In theN=4 case we decompose the system into two 3-body subsystems whosec 2 h ‘integrals’,z 23 andz 34, att=0 are assumed to be smaller than the corresponding critical values \(\tilde z_{23} \) and \(\tilde z_{34} \) , so that both the subsystems are initially hierarchically stable. Then the hierarchical arrangement of the 4 bodies cannot be broken until eitherz 23 orz 34 is changed by an amount \(\tilde z_{ij} - z_{ij} \left( 0 \right)\) ; that is the whole system is hierarchically stable for a time spain not shorter than the minimum between \(\Delta t_{23} = {{\left( {\tilde z_{23} - z_{23} \left( 0 \right)} \right)} \mathord{\left/ {\vphantom {{\left( {\tilde z_{23} - z_{23} \left( 0 \right)} \right)} {\dot z_{23} }}} \right. \kern-0em} {\dot z_{23} }}\) and \(\Delta t_{34} = {{\left( {\tilde z_{34} - z_{34} \left( 0 \right)} \right)} \mathord{\left/ {\vphantom {{\left( {\tilde z_{34} - z_{34} \left( 0 \right)} \right)} {\dot z_{34} }}} \right. \kern-0em} {\dot z_{34} }}\) . To estimate how long is this stability time, two main steps are required. First the perturbing potentials have to be developed in series; the relevant small parameters are some combinations of mass ratios and length ratios, the? ij of Roy and Walker. When an appropriate perturbation theory is based on the? ij , the asymptotic expansions are much more rapidly decreasing than the usual expansions in powers of the mass ratios (as in the classical Lagrange perturbation theory) and can be extended also to cases such as lunar theory or double binaries. The second step is the computation of the time derivatives \(\dot z_{ij} \) (we limit ourselves to the planar case). To assess the long term behaviour of the system, we can neglect the short-periodic perturbations and discuss only the long-periodic and the secular perturbations. By using a Poisson bracket formalism, a generalization of Lagrange theorem for semimajor axes and a generalization of the classical first order theories for eccentricities and pericenters, we prove that thez ij do not undergo any secular perturbation, because of the interaction with the other subsystem, at the first order in the? ik . After the long-periodic perturbations have been accounted for, and apart from the small divisors problems that could arise both from ordinary and secular resonances, only the second order terms have to be considered in the computation of Δt 23, Δt 34. A full second order perturbative theory is beyond the scope of this paper; however an order-of-magnitude lower estimate of the Δt ij can be obtained with the very pessimistic assumption that essentially all the second order terms affect in a secular way thez ij . The same method could be applied also toN≥5 body systems. Since almost everyN-body system existing in nature is strongly hierarchical, the product of two? ij is very small for almost all the real astronomical problems. As an example, the hierarchical stability of the 4-body system Sun, Mercury, Venus, and Jupiter is investigated; this system turns out to be stable for at least 110 million years. Although this hierarchical stability time is ～10 times less than the real age of the Solar System, taking into account that many pessimistic assumptions have been done we can conclude that the stability of the Solar System is no more a forbidden problem for Celestial Mechanics. 相似文献
11.
We present results about the stability of vertical motion and its bifurcations into families of 3-dimensional (3D) periodic orbits in the Sitnikov restricted N-body problem. In particular, we consider ν = N ? 1 equal mass primary bodies which rotate on a circle, while the Nth body (of negligible mass) moves perpendicularly to the plane of the primaries. Thus, we extend previous work on the 4-body Sitnikov problem to the N-body case, with N = 5, 9, 15, 25 and beyond. We find, for all cases we have considered with N ≥ 4, that the Sitnikov family has only one stability interval (on the z-axis), unlike the N = 3 case where there is an infinity of such intervals. We also show that for N = 5, 9, 15, 25 there are, respectively, 14, 16, 18, 20 critical Sitnikov periodic orbits from which 3D families (no longer rectilinear) bifurcate. We have also studied the physically interesting question of the extent of bounded dynamics away from the z-axis, taking initial conditions on x, y planes, at constant z(0) = z 0 values, where z 0 lies within the interval of stable rectilinear motions. We performed a similar study of the dynamics near some members of 3D families of periodic solutions and found, on suitably chosen Poincaré surfaces of section, “islands” of ordered motion, while away from them most orbits become chaotic and eventually escape to infinity. Finally, we solve the equations of motion of a small mass in the presence of a uniform rotating ring. Studying the stability of the vertical orbits in that case, we again discover a single stability interval, which, as N grows, tends to coincide with the stability interval of the N-body problem, when the values of the density and radius of the ring equal those of the corresponding system of N ? 1 primary masses. 相似文献
12.
Here is a selection of applications of what is now called theory of dynamical systems in galactic dynamics and N-body systems. The study of chaotic motions in potentials used as a model for elliptical galaxies is a first example of these applications. The interest in this problem stems from the fact that there are now many theoretical and observational evidences that the overall potentials of galaxies are indeed non-integrable. There are classes of objects, for example small and intermediate luminosity elliptical galaxies, for which the presence of the famous third integral is not necessary or others in which we observe peculiarities in their photometry or kinematics. We address here some of these issues and their implications in modifying our current understanding of the structure and evolution of galaxies.More in general, there is the natural question of how the systems we see have settled to their present status and what would happen if some external cause perturbs it. This issue is related to the question of the stochasticity involved in the general N-body dynamics, especially when N is very large. An N-body dynamical system is definitely chaotic, as shown by several numerical investigations, at least for N not very large. However, this statement must be reconciled with the picture of non-collisional equilibrium of big systems. The second part of this review presents a survey of numerical experiments and an interpretation of the results obtained using standard chaoticity indicators. 相似文献
13.
Thierry Combot 《Celestial Mechanics and Dynamical Astronomy》2012,114(4):319-340
We prove an integrability criterion and a partial integrability criterion for homogeneous potentials of degree ?1 which are invariant by rotation. We then apply it to the proof of the meromorphic non-integrability of the n-body problem with Newtonian interaction in the plane on a surface of equation (H, C) = (H 0, C 0) with (H 0, C 0) ?? (0, 0) where C is the total angular momentum and H the Hamiltonian, in the case where the n masses are equal. Several other cases in the 3-body problem are also proved to be non integrable in the same way, and some examples displaying partial integrability are provided. 相似文献
14.
We present a time-transformed leapfrog scheme combined with the extrapolation method to construct an integrator for orbits in N-body systems with large mass ratios. The basic idea can be used to transform any second-order differential equation into a form which may allow more efficient numerical integration. When applied to gravitating few-body systems this formulation permits extremely close two-body encounters to be considered without significant loss of accuracy. The new scheme has been implemented in a direct N-body code for simulations of super-massive binaries in galactic nuclei. In this context relativistic effects may also be included. 相似文献
15.
16.
《New Astronomy》2007,12(3):169-181
The main performance bottleneck of gravitational N-body codes is the force calculation between two particles. We have succeeded in speeding up this pair-wise force calculation by factors between 2 and 10, depending on the code and the processor on which the code is run. These speed-ups were obtained by writing highly fine-tuned code for x86_64 microprocessors. Any existing N-body code, running on these chips, can easily incorporate our assembly code programs.In the current paper, we present an outline of our overall approach, which we illustrate with one specific example: the use of a Hermite scheme for a direct N2 type integration on a single 2.0 GHz Athlon 64 processor, for which we obtain an effective performance of 4.05 Gflops, for double-precision accuracy. In subsequent papers, we will discuss other variations, including the combinations of N log N codes, single-precision implementations, and performance on other microprocessors. 相似文献
17.
Antonio Pasqua 《Astrophysics and Space Science》2013,346(2):531-543
In this work, I consider the logarithmic-corrected and the power-law corrected versions of the holographic dark energy (HDE) model in the non-flat FRW universe filled with a viscous Dark Energy (DE) interacting with Dark Matter (DM). I propose to replace the infra-red cut-off with the inverse of the Ricci scalar curvature R. I obtain the equation of state (EoS) parameter ω Λ , the deceleration parameter q and the evolution of energy density parameter $\varOmega_{D}'$ in the presence of interaction between DE and DM for both corrections. I study the correspondence of the logarithmic entropy corrected Ricci Dark Dnergy (LECRDE) and power-law entropy corrected Ricci Dark Energy (PLECRDE) models with the the Modified Chaplygin Gas (MCG) and some scalar fields including tachyon, K-essence, dilaton and quintessence. I also make comparisons with previous results. 相似文献
18.
Will M. Farr Jeff AmesPiet Hut Junichiro MakinoSteve McMillan Takayuki MuranushiKoichi Nakamura Keigo NitadoriSimon Portegies Zwart 《New Astronomy》2012,17(5):520-523
We present a data format for the output of general N-body simulations, allowing the presence of individual time steps. By specifying a standard, different N-body integrators and different visualization and analysis programs can all share the simulation data, independent of the type of programs used to produce the data. Our Particle Stream Data Format, PSDF, is specified in YAML, based on the same approach as XML but with a simpler syntax. Together with a specification of PSDF, we provide background and motivation, as well as specific examples in a variety of computer languages. We also offer a web site from which these examples can be retrieved, in order to make it easy to augment existing codes in order to give them the option to produce PSDF output. 相似文献
19.
Christoph Lhotka 《Celestial Mechanics and Dynamical Astronomy》2017,127(4):397-428
In this paper, we consider the elliptic collinear solutions of the classical n-body problem, where the n bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion is called an elliptic Euler–Moulton collinear solution. Here we prove that the corresponding linearized Hamiltonian system at such an elliptic Euler–Moulton collinear solution of n-bodies splits into \((n-1)\) independent linear Hamiltonian systems, the first one is the linearized Hamiltonian system of the Kepler 2-body problem at Kepler elliptic orbit, and each of the other \((n-2)\) systems is the essential part of the linearized Hamiltonian system at an elliptic Euler collinear solution of a 3-body problem whose mass parameter is modified. Then the linear stability of such a solution in the n-body problem is reduced to those of the corresponding elliptic Euler collinear solutions of the 3-body problems, which for example then can be further understood using numerical results of Martínez et al. on 3-body Euler solutions in 2004–2006. As an example, we carry out the detailed derivation of the linear stability for an elliptic Euler–Moulton solution of the 4-body problem with two small masses in the middle. 相似文献
20.
We present a new method for fast numerical integration of close binaries inN-body systems. The basic idea is to slow down the motion of the binary artificially, which makes a faster numerical integration possible but still maintains correct treatment of secular and long-period effects on the motion. We discuss the general principle, with application to close binaries inN-body codes and in the chain regularization. 相似文献