We present a new high-resolution N-body algorithm for cosmological simulations. The algorithm employs a traditional particle-mesh technique on a cubic grid and successive multilevel relaxations on the Ðner meshes, introduced recursively in a fully adaptive manner in the regions where the density exceeds a predeÐned threshold. The mesh is generated to e †ectively match an arbitrary geometry of the underlying density ÐeldÈa property particularly important for cosmological simulations. In a simulation the mesh structure is not created at every time step but is properly adjusted to the evolving particle distribution. The algorithm is fast and e †ectively parallel : the gravitational relaxation solver is approximately half as fast as the fast Fourier transform solver on the same number of mesh cells. The required CPU time scales with the number of cells, as The code allows us to improve considerably N c , DO(N c ). the spatial resolution of the particle-mesh code without loss in mass resolution. We present a detailed description of the methodology, implementation, and tests of the code.We further use the code to study the structure of dark matter halos in high-resolution (D2 h~1 kpc) simulations of standard CDM () \ 1, h \ 0.5, and.0) models. We Ðnd that halo density proÐles in both CDM and "CDM models are well Ðtted by the analytical model presented recently by Navarro et al., which predicts a singular [o(r) P r~1] behavior of the halo density proÐles at small radii. We therefore conclude that halos formed in the "CDM model have structure similar to that of CDM halos and thus cannot explain the dynamics of the central parts of dwarf spiral galaxies, as inferred from the galaxiesÏ rotation curves.

We present analysis of the evolution of dark matter halos in dense environments of groups and clusters in dissipationless cosmological simulations. The premature destruction of halos in such environments, known as "" the overmerging, ÏÏ reduces the predictive power of N-body simulations and makes difficult any comparison between models and observations. We analyze the possible processes that cause the overmerging and assess the extent to which this problem can be cured with current computer resources and codes. Using both analytic estimates and high-resolution numerical simulations, we argue that the overmerging is mainly due to the lack of numerical resolution. We Ðnd that the force and mass resolution required for a simulated halo to survive in galaxy groups and clusters is extremely high and was almost never reached before : D1È3 kpc and 108È109 respectively. We use the high-resolution M _ , Adaptive ReÐnement Tree (ART) N-body code to run cosmological simulations with particle mass B2 ] 108 h~1 and spatial resolution B1È2 h~1 kpc and show that in these simulations the halos M _ do survive in regions that would appear overmerged with lower force resolution. Nevertheless, the halo identiÐcation in very dense environments remains a challenge even with resolution this high. We present two new halo-Ðnding algorithms developed to identify both isolated and satellite halos that are stable (existed at previous moments) and gravitationally bound. To illustrate the use of the satellite halos that survive the overmerging, we present a series of halo statistics, which can be compared with those of observed galaxies. Particularly, we Ðnd that, on average, halos in groups have the same velocity dispersion as the dark matter particles ; i.e., they do not exhibit signiÐcant velocity bias. The small-scale (100 kpc to 1 Mpc) halo correlation function in both models is well described by the power law m P r~1.7 and is in good agreement with observations. It is slightly antibiased (b B 0.7È0.9) relative to the dark matter. To test other galaxy statistics, we use the maximum of the halo rotation velocity and the Tully-Fisher relation to assign luminosity to the halos. For two cosmological models, a Ñat model with the cosmological constant and and a model with a mixture of cold and hot dark ) 0 \ 1 [ ) " \ 0.3, h \ 0.7 matter and we construct luminosity functions and evaluate mass-to-light ) 0 \ 1.0, ) l \ 0.2, h \ 0.5, ratios in groups. Both models produce luminosity functions and mass-to-light ratios (D200È400) that are in reasonable agreement with observations. The latter implies that the mass-to-light ratio in galaxy groups (at least for h~1 analyzed here) is not a good indicator of M vir[ 3 ] 1013 M _ ) 0 .

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including SPH and grid methods with fixed, deformable or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gas dynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be non-radiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of two. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to about 10%, and the ratio of specific kinetic to thermal energies of the gas agree to about 5%. Various factors contribute to the spread in calculated cluster properties, including differences in the internal timing of the simulations. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modelled.

We numerically studied the explosion of a supernova caused by supersonic jets present in its center. The jets are assumed to be generated by a magneto-rotational mechanism when a stellar core collapses into a neutron star. We simulated the process of the jet propagation through the star, jet breakthrough, and the ejection of the supernova envelope by the lateral shocks generated during jet propagation. The end result of the interaction is a highly nonspherical supernova explosion with two high-velocity jets of material moving in polar directions, and a slower moving, oblate, highly distorted ejecta containing most of the supernova material.

Large-scale three-dimensional numerical simulations of the deflagration stage of a thermonuclear supernova explosion show the formation and evolution of a highly convoluted turbulent flame in a gravitational field of an expanding carbon-oxygen white dwarf. The flame dynamics is dominated by the gravity-induced Rayleigh-Taylor instability that controls the burning rate. The thermonuclear deflagration releases enough energy to produce a healthy explosion. The turbulent flame, however, leaves large amounts of unburnt and partially burnt material near the star center, whereas observations imply these materials only in outer layers. This disagreement could be resolved if the deflagration triggers a detonation.

High-quality spectropolarimetry (range 417-860 nm; spectral resolution 1.27 nm and 0.265 nm/pixel) of the SN Ia 2001el were obtained with the ESO Very Large Telescope Melipal (+ FORS1) at 5 epochs. The spectra a week before maximum and around maximum indicate photospheric expansion velocities of about 10,000 km s −1 . Prior to optical maximum, the linear polarization of the continuum was ≈ 0.2 − 0.3% with a constant position angle, showing that SN 2001el has a well-defined axis of symmetry. The polarization was nearly undetectable a week after optical maximum.The spectra are similar to those of the normally-bright SN 1994D with the exception of a strong double-troughed absorption feature seen around 800 nm (FWHM about 22 nm). The 800 nm feature is probably due to the Ca II IR triplet at very high velocities (20,000 -26,000 km s −1 ) involving ∼ 0.004 M ⊙ of calcium and perhaps 0.1 M ⊙ total mass. The 800 nm feature is distinct in velocity space from the photospheric Ca II IR triplet and has a significantly higher

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