Parallelization of a treecode

I describe here the performance of a parallel treecode with individual particle timesteps. The code is based on the Barnes-Hut algorithm and runs cosmological N-body simulations on parallel machines with a distributed memory architecture using the MPI message-passing library. For a configuration with a constant number of particles per processor the scalability of the code was tested up to P=128 processors on an IBM SP4 machine. In the large $P$ limit the average CPU time per processor necessary for solving the gravitational interactions is $\sim 10$ higher than that expected from the ideal scaling relation. The processor domains are determined every large timestep according to a recursive orthogonal bisection, using a weighting scheme which takes into account the total particle computational load within the timestep. The results of the numerical tests show that the load balancing efficiency $L$ of the code is high ($>=90$) up to P=32, and decreases to $L\sim 80$ when P=128. In the latter case it is found that some aspects of the code performance are affected by machine hardware, while the proposed weighting scheme can achieve a load balance as high as $L\sim 90$ even in the large $P$ limit.Comment: 30 pages, 3 tables, 9 figures, accepted for publication in New Astronom

Iron abundances and heating of the ICM in hydrodynamical simulations of galaxy clusters

Results from a large set of hydrodynamical SPH simulations of galaxy clusters in a flat LCDM cosmology are used to investigate the metal enrichment and heating of the ICM. The physical modeling of the gas includes radiative cooling, star formation, energy feedback and metal enrichment that follow from the explosions of SNe of type II and Ia. The metallicity dependence of the cooling function is also taken into account. For a fiducial set of model prescriptions the results indicate radial iron profiles in broad agreement with observations; global iron abundances are also consistent with data. It is found that the iron distribution in the ICM is critically dependent on the shape of the metal deposition profile. For low temperatu re clusters simulations yield iron abundances below the allowed observational range, unless it is introduced a minimum diffusion length of metals in the ICM. The simulated emission-weighted radial temperature profiles are in good agreement with data for cooling flow clusters, but at very small distances from the cluster centres ($\sim 2$ of the virial radii) the temperatures are a factor $\sim$ two higher than the measured spectral values. The luminosity-temperature relation is in excellent agreement with the data, cool clusters ($T_X\sim 1keV$) have a core excess entropy of $\sim 200 keVcm^2$ and their X-ray properties are unaffected by the amount of feedback energy that has heated the ICM. The fraction of hot gas $f_g$ at the virial radius increases with $T_X$ and the distribution obtained from the simulated cluster sample is consistent with the observational ranges.Comment: 29 pages, 5 tables, 8 figures, accepted for publication in MNRAS new version with small corrections to the values of M_200 in Table

Global cluster morphology and its evolution: X-ray data vs CDM, LCDM and mixed models

The global structure of galaxy clusters and its evolution are tested within a large set of TREESPH simulations, so to allow a fair statistical comparison with available X-ray data. Structure tests are based on the "power ratios", introduced by Buote & Tsai. Cosmological models considered are CDM, LCDM (Omega_L=0.7) and CHDM (1 mass.neu., Omega_h = 0.2). All models are normalized to provide a fair number density of clusters. For each model we run a P3M simulation in a large box, where we select the most massive 40 clusters. Going back to the initial redshift we run a hydro-TREESPH simulation for each of them. In this way we perform a statistical comparison of the global morphology of clusters, for each cosmological model, with ROSAT data, using Student t-test, F-test and K-S test. The last test and its generalization to 2--D distributions are also used to compare the joint distributions of 2 or 3 power ratios. We find that, using DM distribution, instead of gas, as done by some authors, leads to biased results, as baryons are distributed in a less structured way than DM. We also find that the cosmological models considered have different behaviours in these tests: LCDM has the worst performance. CDM and our CHDM have similar scores. The general trend of power ratio distributions is already fit by these models, but a further improvement is expected either from a different DM mix or a non-flat CDM model.Comment: 29 pages (LaTeX,macros included), 9 figure.ps & 3 tables included. To appear on New Astronom

Improved Performances in Subsonic Flows of an SPH Scheme with Gradients Estimated using an Integral Approach

In this paper, we present results from a series of hydrodynamical tests aimed at validating the performance of a smoothed particle hydrodynamics (SPH) formulation in which gradients are derived from an integral approach. We specifically investigate the code behavior with subsonic flows, where it is well known that zeroth-order inconsistencies present in standard SPH make it particularly problematic to correctly model the fluid dynamics. In particular, we consider the Gresho-Chan vortex problem, the growth of Kelvin-Helmholtz instabilities, the statistics of driven subsonic turbulence and the cold Keplerian disk problem. We compare simulation results for the different tests with those obtained, for the same initial conditions, using standard SPH. We also compare the results with the corresponding ones obtained previously with other numerical methods, such as codes based on a moving-mesh scheme or Godunov-type Lagrangian meshless methods. We quantify code performances by introducing error norms and spectral properties of the particle distribution, in a way similar to what was done in other works. We find that the new SPH formulation exhibits strongly reduced gradient errors and outperforms standard SPH in all of the tests considered. In fact, in terms of accuracy, we find good agreement between the simulation results of the new scheme and those produced using other recently proposed numerical schemes. These findings suggest that the proposed method can be successfully applied for many astrophysical problems in which the presence of subsonic flows previously limited the use of SPH, with the new scheme now being competitive in these regimes with other numerical methods