# NUMERICAL SIMULATIONS

N-body simulations have been widely used over the last decade as a standard tool to study the birth and growth of large scale structure, clusters and galaxies. This approach has dealt, until recently, with the forward integration in time of a set of collisionless particles. Although what we observe directly is the luminous matter distribution , a proper hydrodynamical treatment of the baryonic component has not received much attention in the past, most because of the lack of computing power.

The situation has began to change in the last few years. Several techniques have been used to simulate the evolution  of the gaseous component. The classical approach is the Eulerian one. An alternative scheme is the smoothed - particle - hydrodynamics ( SPH ), which is a Lagrangian method with each particle carrying information about the fluid element. The code that I use  is based on the SPH technique. In this code the gravitational N-body system is solved using a hierarchical tree algorithm. The TREESPH has been used in a range of astrophysical problems, like formation and evolution of cluster of galaxies, formation of galaxies,and the formation of damped Lyman- systems.

A  parallel version of the code has been developed recently [5], that will allow to model with highly improved dynamical range the evolution of cosmologically relevant structure.

A long-term research project is  in progress in which large sets of TREESPH simulations  are used to  investigate the
dependence of cluster X-ray properties of the simulated samples on the background cosmological model, as well as
the numerical resolution of the simulations and the assumed model for the physical gas processes.
Using the numerical samples the global morphology of galaxy clusters and its evolution can be compared against X-ray data.

The internal dynamical state of galaxy clusters   is a function of the global cosmological density parameter  m and is connected to the amount of observed substructures. Therefore a promising way to constrain the cosmological models arises from the study of substructures in the inner mass distribution [1]. This approach has observational support both from internal galaxy distribution and from X--ray image brightness.

Another issue, which is closely related to the amount of substructure in clusters,  is the evolution of cluster
morphology with redshit.  For three different cosmological models,   a simulation sample of 40 clusters was
generated  from hydrodynamical SPH simulations and used to investigate the cluster
morpho
logical
evolution out to z=0.4 [2].

In order to quantify the cluster morphology  we used  Minkowski functionals, which are  defined in terms of 2+1 measures applied to cluster X-ray maps. The cluster dynamical state is described using global cluster parameters which obey fundamental plane relations such as $M_vr_h^{\alpha}T_v^{\beta}=const$.

Works in progress  on X-ray clusters are :

1. 1) The ensemble of N-body/hydrodynamical simulations which was used in [1] and [2]  is currently to be rerun with enlarged mass and spatial resolution. The hydrodynamics includes radiative cooling an SN energy feedback in the ICM medium. The new simulation ensemble will allow to test the reliability of the cluster X-ray temperature function and luminosity function, which have been used to draw conclusions about the consistency of the cosmological models  with observations, in particular for clusters with cooling flows.
2. 2) Analysis of spatially resolved X-ray spectra of the ICM has confirmed the existence of metallicity gradients, increasing towards the center. The metal abundance of galaxy clusters can be used to constrain the formation and evolution of clusters and of their galaxies. Numerical simulations of galaxy clusters have not yet produced until now informations about the metallicity content of the simulated clusters. With the simulations of point 1) this issue will be addressed, with interesting informations about the ICM metallicity in cosmologies with different  0, the preheating of the ICM due to SNe and the global metallicity of the universe at high redshift.

These arguments can be studied using hydrodynamics simulations which must model the non-gravitational
physical
processes of the gas component.  Therefore, a TREESPH code which includes radiative cooling,
star formation, energy feedback and metal enrichment that follow from the explosions of supernovae of
type II and Ia was developed in order to investigate the quoted issues.

In a first paper it was studied  the dependence of the final cluster X-ray properties on the simulation numerical
resolution and on the  models used to describe the effects  of radiative cooling and star formation [3] of the gas.

In [4] it was investigated how the  heating of the ICM and the final metal abudance of the simulated clusters
are affected by the choice of different  stellar IMF and metal ejection parameters that are designed to
model the corresponding physical processes.

Related Publications:

[1] Valdarnini, R., Ghizzardi, S. & Bonometto, S., 1999, Global Cluster Morphology and its Evolution: X--ray data vs CDM ,  CDM and CHDM models , New Astr., 4, 79
[2] Beisbart, C., Valdarnini, R. & Buchert, T., 2001, The morphological and dynamical evolution of simulated galaxy
clusters,
Astr. & Astrophys., 379 , 412
[3] Valdarnini, R., 2002, Numerical convergence of physical variables in hydrodynamical simulations of cooling
clusters,
ApJ, 567, 741
[4] Valdarnini, R., 2003, Iron abundances and heating of the ICM in hydrodynamical simulations of galaxy clusters,
MNRAS, 339, 1117
[5] Valdarnini, R., 2003, Parallelization of a treecode , New Astr., 8, 691
[6] Valdarnini, R., 2006, X-ray temperature spectroscopy of simulated cooling clusters, New Astr., 12, 71