How to simulate the Universe in a Computer

In this contribution a broad overview of the methodologies of cosmological N-body simulations and a short introduction explaining the general idea behind such simulations is presented. After explaining how to set up the initial conditions using a set of N particles two (diverse) techniques are presented for evolving these particles forward in time under the influence of their self-gravity. One technique (tree codes) is solely based upon a sophistication of the direct particle-particle summation whereas the other method relies on the continuous (de-)construction of arbitrarily shaped grids and is realized in adaptive mesh refinement codes.Comment: 8 pages, 4 figures, accepted for publication in PASA (refereed proceedings contribution for the meeting "Gravity 2004" held in Sydney, April 15-16, 2004

The sense of rotation of subhaloes in cosmological dark matter haloes

We present a detailed analysis of the velocity distribution and orientation of orbits of subhaloes in high resolution cosmological simulations of dark matter haloes. We find a trend for substructure to preferentially revolve in the same direction as the sense of rotation of the host halo: there is an excess of prograde satellite haloes. Throughout our suite of nine host haloes (eight cluster sized objects and one galactic halo) there are on average 59% of the satellites corotating with the host. Even when including satellites out to five virial radii of the host, the signal still remains pointing out the relation of the signal with the infall pattern of subhaloes. However, the fraction of prograde satellites weakens to about 53% when observing the data along a (random) line-of-sight and deriving the distributions in a way an observer would infer them. This decrease in the observed prograde fraction has its origin in the technique used by the observer to determine the sense of rotation, which results in a possible misclassification of non-circular orbits. We conclude that the existence of satellites on corotating orbits is another prediction of the cold dark matter structure formation scenario, although there will be difficulties to verify it observationally. Since the galactic halo simulation gave the same result as the cluster-sized simulations, we assume that the fraction of prograde orbits is independent of the scale of the system, though more galactic simulations would be necessary to confirm this.Comment: 16 pages, 9 figures, accepted by MNRAS; extended comparison with previous work (mistake corrected) and observations, typos correcte

Comment on ''On the problem of initial conditions in cosmological N-body simulations'' (Europhys. Lett. 57, 322)

In astro-ph/0109199, the initial conditions (IC's) of cosmological N-body simulations by the Virgo Consortium are analyzed and it is concluded that the density fluctuations are rather different from the desired ones. We have repeated the analysis of the IC's using our own code and the code provided by the authors of astro-ph/0109199, obtaining results that disprove the criticisms.Comment: 2 pages, 4 eps figures, epl.cls style fil

MLAPM - a C code for cosmological simulations

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 timestep shortens by a factor two with each successive refinement. It is argued that an appropriate choice of softening length is of great importance and that the softening should be at all points an appropriate multiple of the local inter-particle separation. Unlike tree and P3M codes, multigrid codes automatically satisfy this requirement. We show that at early times and low densities in cosmological simulations, the softening needs to be significantly smaller relative to the inter-particle separation than in virialized regions. Tests of the ability of the code's Poisson solver to recover the gravitational fields of both virialized halos 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 LCDM 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.Comment: 20 pages, 20 figures, MNRAS in press, the code can be downloaded at http://www-thphys.physics.ox.ac.uk/users/MLAPM