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1.
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2.
We compare orbits in a thin axisymmetric disc potential in Modified Newtonian Dynamics (MOND) with those in a thin disc plus near-spherical dark matter halo predicted by a ΛCDM cosmology. Remarkably, the amount of orbital precession in MOND is nearly identical to that which occurs in a mildly oblate CDM Galactic halo (potential flattening   q = 0.9  ), consistent with recent constraints from the Sagittarius stream. Since very flattened mass distributions in MOND produce rounder potentials than in standard Newtonian mechanics, we show that it will be very difficult to use the tidal debris from streams to distinguish between a MOND galaxy and a standard CDM galaxy with a mildly oblate halo.
If a galaxy can be found with either a prolate halo or one that is more oblate than   q ∼ 0.9  this would rule out MOND as a viable theory. Improved data from the leading arm of the Sagittarius dwarf – which samples the Galactic potential at large radii – could rule out MOND if the orbital pole precession can be determined to an accuracy of the order of  ±1°  .  相似文献   

3.
We present a general recipe for constructing N -body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N -body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.  相似文献   

4.
Potential–density pair basis sets can be used for highly efficient N -body simulation codes, but they suffer from a lack of versatility, i.e. a basis set has to be constructed for each different class of stellar system. We present numerical techniques for generating a biorthonormal potential–density pair basis set that has a general specified pair as its lowest-order member. We go on to demonstrate how the set can be used to construct N -body equilibria, which we then evolve using an N -body code that calculates forces using the basis set.  相似文献   

5.
We used the star counts in 21 BATC fields obtained with the National Astronomical Observatories (NAOC) 60/90 cm Schmidt Telescope to study the structure of the Galactic halo.Adopting a de Vaucouleurs γ/4 law halo,we found that the halo is somewhat flatter (c/a～0.4) towards the Galactic center than in the anticentre and antirotation direction (c/a ＞ 0.4).We also notice that the axial ratios are smaller (flatter) towards the low latitude fields than the high latitude fields,except for a few fields.We provide robust limits on the large-scale flattening of the halo.Our analysis shows that the axial ratio of the halo may vary with distance and the observation direction.At large Galactocentric radii,the halo may not have a smooth density distribution,but rather,it may be largely composed of overlapping streams or substructures,which provides a support for the hybrid formation model.  相似文献   

6.
The evolution of substructure embedded in non-dissipative dark haloes is studied through N -body simulations of isolated systems, both in and out of initial equilibrium, complementing cosmological simulations of the growth of structure. We determine by both analytic calculations and direct analysis of the N -body simulations the relative importance of various dynamical processes acting on the clumps, such as the removal of material by global tides, clump–clump heating, clump–clump merging and dynamical friction. The ratio of the internal clump velocity dispersion to that of the dark halo is an important parameter; as this ratio approaches a value of unity, heating by close encounters between clumps becomes less important, while the other dynamical processes continue to increase in importance. Our comparison between merging and disruption processes implies that spiral galaxies cannot be formed in a protosystem that contains a few large clumps, but can be formed through the accretion of many small clumps; elliptical galaxies form in a more clumpy environment than do spiral galaxies. Our results support the idea that the central cusp in the density profiles of dark haloes is the consequence of self-limiting merging of small, dense haloes. This implies that the collapse of a system of clumps/substructure is not sufficient to form a cD galaxy, with an extended envelope; plausibly, subsequent accretion of large galaxies is required. The post-collapse system is in general triaxial, with rounder systems resulting from fewer, but more massive, clumps. Persistent streams of material from disrupted clumps can be found in the outer regions of the final system, and at an overdensity of around 0.75, can cover 10 to 30 per cent of the sky.  相似文献   

7.
We describe a novel N -body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkola's 'algorithmic' chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite- N gravitational fluctuations on the orbits of the S-stars, and inspiral of an intermediate-mass black hole into the Galactic Centre.  相似文献   

8.
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9.
We run numerical simulations of the disruption of satellite galaxies in a Galactic potential to build up the entire stellar halo, in order to investigate what the next generation of astrometric satellites will reveal by observing the halo of the Milky Way. We generate artificial DIVA , FAME and GAIA halo catalogues, in which we look for the signatures left by the accreted satellites. We develop a method based on the standard Friends-of-Friends algorithm applied to the space of integrals of motion. We find this simple method can recover about 50 per cent of the different accretion events, when the observational uncertainties expected for GAIA are taken into account, even when the exact form of the Galactic potential is unknown. The recovery rate for DIVA and FAME is much smaller, but these missions, like GAIA , should be able to test the hierarchical formation paradigm on our Galaxy by measuring the amount of halo substructure in the form of nearby kinematically cold streams with, for example, a two-point correlation function in velocity space.  相似文献   

10.
We derive analytic merger rates for dark matter haloes within the framework of the extended Press–Schechter (EPS) formalism. These rates become self-consistent within EPS once we realize that the typical merger in the limit of a small time-step involves more than two progenitors, contrary to the assumption of binary mergers adopted in earlier studies. We present a general method for computing merger rates that span the range of solutions permitted by the EPS conditional mass function, and focus on a specific solution that attempts to match the merger rates in N -body simulations. The corrected EPS merger rates are more accurate than the earlier estimates of Lacey & Cole by ∼20 per cent for major mergers and by up to a factor of ∼3 for minor mergers of mass ratio 1:104. Based on the revised merger rates, we provide a new algorithm for constructing Monte Carlo EPS merger trees, which could be useful in semi-analytic modelling. We provide analytic expressions and plot numerical results for several quantities that are very useful in studies of galaxy formation. This includes (i) the rate of mergers of a given mass ratio per given final halo, (ii) the fraction of mass added by mergers to a halo and (iii) the rate of mergers per given main progenitor. The creation and destruction rates of haloes serve for a self-consistency check. Our method for computing merger rates can be applied to conditional mass functions beyond EPS, such as those obtained by the ellipsoidal collapse model or extracted from N -body simulations.  相似文献   

11.
We present a state-of-the-art N -body code which includes a detailed treatment of stellar and binary evolution as well as the cluster dynamics. This code is ideal for investigating all aspects relating to the evolution of star clusters and their stellar populations. It is applicable to open and globular clusters of any age. We use the N -body code to model the blue straggler population of the old open cluster M67. Preliminary calculations with our binary population synthesis code show that binary evolution alone cannot explain the observed numbers or properties of the blue stragglers. On the other hand, our N -body model of M67 generates the required number of blue stragglers and provides formation paths for all the various types found in M67. This demonstrates the effectiveness of the cluster environment in modifying the nature of the stars it contains, and highlights the importance of combining dynamics with stellar evolution. We also perform a series of N =10 000 simulations in order to quantify the rate of escape of stars from a cluster subject to the Galactic tidal field.  相似文献   

12.
Dynamics of an interacting luminous disc, dark halo and satellite companion   总被引：1，自引：0，他引：1  
This paper describes a method, based on linear perturbation theory, to determine the dynamical interaction between extended halo and spheroid components and an environmental disturbance. One finds that resonant interaction between a galaxy and passing interlopers or satellite companions can carry the disturbance inward, deep inside the halo, where it can perturb the disc.    Applied to the Milky Way for example, the LMC and SMC appear to be sufficient to cause the observed Galactic warp and possibly seed other asymmetries. This is a multi-scale interaction in which the halo wake has a feature at roughly half the satellite orbital radius owing to a 2:1 orbital resonance. The rotating disturbance then excites an m  = 1 vertical disc mode which has the classic integral-sign morphology. A polar satellite orbit produces the largest warp and therefore the inferred LMC orbit is nearly optimal for maximum warp production.   Both the magnitude and morphology of the response depend on the details of the disc and halo models. Most critically, a change in the halo profile will shift the resonant frequencies and response location and consequently alter the coupling to the bending disc. Increasing the halo support relative to the disc, a sub-maximal disc model, decreases the warp amplitude.   Finally, the results and prognosis for N -body simulations are discussed. Discreteness noise in the halo, similar to that arising from a population of 106-M⊙ black holes, can produce observable warping.  相似文献   

13.
The stellar streams originated from the Galactic halo may be detected when they pass by the solar neighborhood, and they still keep some information at their birth times. Thus, the investigation of halo streams in the solar neighborhood is very important for understanding the formation and evolution of our Galaxy. In this paper, the researches of halo streams in the solar neighborhood are briefly reviewed. We have introduced the methods how to detect the halo streams and identify their member stars, summarized the progresses in the observation of member stars of halo streams and in the study of their origins, introduced in detail how to analyze the origins of halo streams in the solar neighborhood by means of numerical simulation and chemical abundance, and finally discussed the prospects of the LAMOST and GAIA in the research of halo streams in the solar neighborhood.  相似文献   

14.
We apply the joint lensing and dynamics code for the analysis of early-type galaxies, 'Combined Algorithm for Unified Lensing and Dynamics ReconstructiON ( cauldron )', to a rotating N -body stellar system with dark matter halo which significantly violates the two major assumptions of the method, i.e. axial symmetry supported by a two-integral distribution function. The goal is to study how cauldron performs in an extreme case, and to determine which galaxy properties can still be robustly recovered. Three data sets, corresponding to orthogonal lines of sight, are generated from the N -body system and analysed with the identical procedure followed in the study of real lens galaxies, adopting an axisymmetric power-law total density distribution. We find that several global properties of the N -body system are recovered with remarkable accuracy, despite the fact that the adopted power-law model is too simple to account for the lack of symmetry of the true density distribution. In particular, the logarithmic slope of the total density distribution is robustly recovered to within less than 10 per cent (with the exception of the ill-constrained very inner regions), the inferred angle-averaged radial profile of the total mass closely follows the true distribution, and the dark matter fraction of the system (inside the effective radius) is correctly determined within ∼10 per cent of the total mass. Unless the line-of-sight direction is almost parallel to the total angular momentum vector of the system, reliably recovered quantities also include the angular momentum, the   V /σ  ratio and the anisotropy parameter δ. We conclude that the cauldron code can be safely and effectively applied to real early-type lens galaxies, also providing reliable information for the systems that depart significantly from the method's assumptions.  相似文献   

15.
We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f 0. Our method uses importance sampling to find the sampling DF f s that minimizes the mean-square formal errors in a given set of projections of the DF f 0. The result is a multimass N -body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal.  相似文献   

16.
A recent observation with the Hipparcos satellite and some numerical simulations imply that the interaction between an oblate halo and a disc is inappropriate for the persistence of galactic warps. Following on from this , we have compared the time evolution of galactic warps in a prolate halo with that in an oblate halo. The haloes were approximated as fixed potentials, while the discs were represented by N -body particles. We have found that the warping in the oblate halo continues to wind up, and finally disappears. On the other hand, for the prolate halo model, the precession rate of the outer disc increases when the precession of the outer disc recedes from that of the inner disc, and vice versa. Consequently, the warping in the prolate halo persisted to the end of the simulation by retaining the alignment of the line of nodes of the warped disc. Therefore, our results suggest that prolate haloes could sustain galactic warps. The physical mechanism of the persistence of warp is discussed on the basis of the torque between a halo and a disc and that between the inner and outer regions of the disc.  相似文献   

17.
The evolution of a stellar bar transforms not only the galactic disc, but also the host dark matter halo. We present high-resolution, fully self-consistent N -body simulations that clearly demonstrate that dark matter halo central density cusps flatten as the bar torques the halo. This effect is independent of the bar formation mode and occurs even for rather short bars. The halo and bar evolution is mediated by resonant interactions between orbits in the halo and the bar pattern speed, as predicted by linear Hamiltonian perturbation theory. The bar lengthens and slows as it loses angular momentum, a process that occurs even in rather warm discs. We demonstrate that the bar and halo response can be critically underestimated for experiments that are unable to resolve the relevant resonant dynamics; this occurs when the phase space in the resonant region is undersampled or plagued by noise.  相似文献   

18.
The formation of galaxy clusters in hierarchically clustering universes is investigated by means of high-resolution N -body simulations. The simulations are performed using a newly developed multimass scheme which combines a PM code with a high-resolution N -body code. Numerical effects resulting from time-stepping and gravitational softening are investigated, as well as the influence of the simulation box size and of the assumed boundary conditions. Special emphasis is laid on the formation process and the influence of various cosmological parameters. Cosmogonies with massive neutrinos are also considered. Differences between clusters in the same cosmological model seem to dominate over differences caused by differing background cosmogony. The cosmological model can alter the time evolution of cluster collapse, but the merging pattern remains fairly similar, e.g. the number of mergers and the mass ratio of mergers. The gross properties of a halo, such as its size and total angular momentum, also evolve in a similar manner for all cosmogonies, and can be described using analytical models. It is shown that the density distribution of a halo shows a characteristic radial dependence which follows a power law with a slope of =1 at small radii and =3 at large radii, independent of the background cosmogony or the considered redshift. The shape of the density profiles follows the generic form proposed by Navarro et al. for all hierarchically clustering scenarios, and retains very little information about the formation process or the cosmological model. Only the central matter concentration of a halo is correlated with the formation time and therefore the corresponding cosmogony. We emphasize the role of non-radial motions of the halo particles in the evolution of the density profile.  相似文献   

19.
Recent surveys have identified seven hypervelocity stars (HVSs) in the halo of the Milky Way. Most of these stars may have originated from the breakup of binary star systems by the nuclear black hole SgrA*. In some instances, the breakup of the binary may lead to a collision between its member stars. We examine the dynamical properties of these collisions by simulating thousands of different binary orbits around SgrA* with a direct N -body integration code. For some orbital parameters, the two stars collide with an impact velocity lower than their escape velocity and may therefore coalesce. It is possible for a coalescing binary to have sufficient velocity to escape the galaxy. Furthermore, some of the massive S-stars near Sgr A* might be the merger remnants of binary systems, however this production method can not account for most of the S-stars.  相似文献   

20.
We present a computer code written in c that is designed to simulate structure formation from collisionless matter. The code is purely grid-based and uses a recursively refined Cartesian grid to solve Poisson's equation for the potential, rather than obtaining the potential from a Green's function. Refinements can have arbitrary shapes and in practice closely follow the complex morphology of the density field that evolves. The time-step shortens by a factor of 2 with each successive refinement.
Competing approaches to N -body simulation are discussed from the point of view of the basic theory of N -body simulation. It is argued that an appropriate choice of softening length ε is of great importance and that ε should be at all points an appropriate multiple of the local interparticle separation. Unlike tree and P3M codes, multigrid codes automatically satisfy this requirement. We show that at early times and low densities in cosmological simulations, ε needs to be significantly smaller relative to the interparticle separation than in virialized regions. Tests of the ability of the code's Poisson solver to recover the gravitational fields of both virialized haloes and Zel'dovich waves are presented, as are tests of the code's ability to reproduce analytic solutions for plane-wave evolution. The times required to conduct a ΛCDM cosmological simulation for various configurations are compared with the times required to complete the same simulation with the ART, AP3M and GADGET codes. The power spectra, halo mass functions and halo–halo correlation functions of simulations conducted with different codes are compared.
The code is available from http://www-thphys.physics.ox.ac.uk/users/MLAPM .  相似文献   

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