Alexei M. Khokhlov

Adaptive refinement tree: A New high resolution N body code for cosmological simulations

Abstract : 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 finer meshes, introduced recursively in a fully adaptive manner in the regions where the density exceeds a predefined threshold. The mesh is generated to effectively match an arbitrary geometry of the underlying density field-a property particularly important for cosmological simulations. In a simulation the mesh structure is not created at every time step but properly adjusted to the evolving particle distribution. The algorithm is fast and effectively parallel: the gravitational relaxation solver is approximately two times slower than the FFT solver on the same number of mesh cells. The required CPU time scales with number of cells, N suc c, as ^O(Nc). It allows us to improve considerably 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 (^2/h kpc) simulations of standard CDM (Omega = 1, h = 0.5, sigma sub g = 0.63) and (Lambda)CDM (0A = 1 -Omega sub O = 0.7, h = 0.7, sigma sub g = 1.0) models. We find that halo density profiles in both CDM and ACDM models are well fit by the analytical model presented recently by Navarro et al. (1966) which predicts a singular (rho(r) oc 1/r) behavior of the halo density profiles at small radii. We therefore conclude that halos formed in the (Lambda)CDM model have structure similar to the CDM halos, and thus cannot explain dynamics of the central parts of dwarf spiral galaxies infrerred from their rotation curves.

Galaxies in N-Body Simulations: Overcoming the Overmerging Problem

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, 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 find 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: ~1-3 kpc and 108-109 M☉, respectively. We use the high-resolution Adaptive Refinement Tree (ART) N-body code to run cosmological simulations with particle mass ≈2 × 108 h-1 M☉ and spatial resolution ≈1-2 h-1 kpc and show that in these simulations the halos do survive in regions that would appear overmerged with lower force resolution. Nevertheless, the halo identification in very dense environments remains a challenge even with resolution this high. We present two new halo-finding 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 find that, on average, halos in groups have the same velocity dispersion as the dark matter particles; i.e., they do not exhibit significant velocity bias. The small-scale (100 kpc to 1 Mpc) halo correlation function in both models is well described by the power law ξ r-1.7 and is in good agreement with observations. It is slightly antibiased (b≈0.7-0.9) 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 flat model with the cosmological constant and Ω0=1-ΩΛ=0.3,h=0.7 and a model with a mixture of cold and hot dark matter and Ω0=1.0,Ων=0.2,h=0.5, we construct luminosity functions and evaluate mass-to-light ratios in groups. Both models produce luminosity functions and mass-to-light ratios ( ~200-400) that are in reasonable agreement with observations. The latter implies that the mass-to-light ratio in galaxy groups (at least for Mvir 3 × 1013 h-1 M☉ analyzed here) is not a good indicator of Ω0.

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions

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 smoothed particle hydrodynamics (SPH) and grid methods with fixed, deformable, or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gasdynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be nonradiative. 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 2. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to within about 10%, and the ratio of specific dark matter kinetic to gas thermal energies agree to within about 5%. Various factors, including differences in the internal timing of the simulations, contribute to the spread in calculated cluster properties. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modeled.

Thermonuclear Supernovae: Simulations of the Deflagration Stage and Their Implications

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 the gravitational field of an expanding carbon-oxygen white dwarf. The flame dynamics are 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 unburned and partially burned material near the star center, whereas observations that imply these materials are present only in outer layers. This disagreement could be resolved if the deflagration triggers a detonation.

Three-dimensional delayed-detonation model of type ia supernovae

We study a Type Ia supernova explosion using large-scale three-dimensional numerical simulations based on reactive fluid dynamics with a simplified mechanism for nuclear reactions and energy release. The initial deflagration stage of the explosion involves a subsonic turbulent thermonuclear flame propagating in the gravitational field of an expanding white dwarf. The deflagration produces an inhomogeneous mixture of unburned carbon and oxygen with intermediate-mass and iron-group elements in central parts of the star. During the subsequent detonation stage, a supersonic detonation wave propagates through the material unburned by the deflagration. The total energy released in this delayed-detonation process, (1.3-1.6) × 1051 ergs, is consistent with a typical range of kinetic energies obtained from observations. In contrast to the deflagration model, which releases only about 0.6 × 1051 ergs, the delayed-detonation model does not leave carbon, oxygen, and intermediate-mass elements in central parts of a white dwarf. This removes the key disagreement between three-dimensional simulations and observations, and makes a delayed detonation the mostly likely mechanism for Type Ia supernova explosions.

Jet-induced Explosions of Core Collapse Supernovae

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 magnetorotational 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 slower moving, oblate, highly distorted ejecta containing most of the supernova material. The jet-induced explosion is entirely due to the action of the jets on the surrounding star and does not depend on neutrino transport or reacceleration of a stalled shock. The jet mechanism can explain the observed high polarization of Types Ib, Ic, and IIsupernovae, pulsar kicks, very high velocity material observed in supernova remnants, indications that radioactive material was carried to the hydrogen-rich layers in SN 1987A, and other observations that are very difficult or impossible to explain by the neutrino energy deposition mechanism. The breakout of the jet from a compact, hydrogen-deficient core may account for the γ-ray burst and radio outburst associated with SN 1998bw/GRB 980425.

Numerical simulation of deflagration-to-detonation transition : The role of shock-flame interactions in turbulent flames

Abstract Two-dimensional reactive Navier-Stokes equations for an acetylene–air mixture are solved numerically to simulate the interaction of a shock wave and an expanding flame front, the formation of a flame brush, and deflagration-to-detonation transition (DDT). The effects of viscosity, thermal conduction, molecular diffusion, and chemical reactions are included. A new method for adaptive mesh refinement was used to ensure that the structure of the flame front was resolved. The shock–flame interactions, through the Richtmyer-Meshkov instability, create and maintain a highly turbulent flame brush. The turbulence is not Kolmogorov turbulence, but it is driven at all scales by repeated shock–flame interactions. Pressure fluctuations generated in the region of the turbulent flame brush create, in turn, hot spots in unreacted material. These hot spots may then transition to DDT through the gradient mechanism. Repeated shock–flame interactions and merging shocks in unreacted material lead to the development of a high-speed shock that moves out in front of the turbulent flame. The region between this shock and the flame is subject to intense fluctuations generated in the flame. The simulations show that the interactions of shocks and flames create the conditions under which deflagration-to-detonation transition may occur.

Hydrodynamical simulations of galaxy formation: effects of supernova feedback

We numerically simulate some of the most critical physical processes in galaxy formation: The supernova feedback, in conjunction with gasdynamics and gravity, plays a crucial role in determining how galaxies arise within the context of a model for large-scale structure. Our treatment incorporates a multi-phase model of the interstellar medium and includes the effects of cooling, heating and metal enrichment by supernovae, and evaporation of cold clouds. The star formation happens inside the clouds of cold gas, which are produced via thermal instability. We simulate the galaxy formation in standard biased CDM model for a variety of parameters and for several resolutions in the range 2--20

Deflagration to Detonation Transition in Thermonuclear Supernovae.

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Evolution of bias in different cosmological models

kpc. In our picture, supernova feedback regulates the evolution of the gas components and star formation. The efficiency of cloud evaporation by supernova strongly influences star formation rates. This feedback results in a steady rate of star formation in large galaxies (mass larger than