Properties of galaxy halos in Clusters and Voids

We use the results of a high resolution N-body simulation to investigate the role of the environment on the formation and evolution of galaxy-sized halos. Starting from a set of constrained initial conditions, we have produced a final configuration hosting a double cluster in one octant and a large void extending over two octants of the simulation box. In this paper we concentrate on {\em gravitationally bound} galaxy-sized halos extracted from the two regions. Exploiting the high mass resolution of our simulation ($m_{body} = 2.1\times 10^{9} h^{-1} M_{\odot}$), we focus on halos with a relatively small mass: $5\times 10^{10} \leq M \leq 2\times 10^{12} M_{\odot}$. We present results for two statistics: the relationship between 1-D velocity dispersion and mass and the probability distribution of the spin parameter $P(\lambda)$. We do find a clear difference between halos lying in overdense regions and in voids. The \svm relationship is well described by the Truncated Isothermal Sphere (TIS) model introduced by Shapiro et al. (1999), but the slope of the relationship is larger in voids. We study in more detail the TIS model, and we find new relationships between the truncation radius and other structural parameters. After a comparison with the simulation, we conclude that the structural properties of our halos are well described by the TIS model, although not by the minimum energy solution. We show also that the dependence of the statistical properties on environment can be quantitatively accounted for within this model by a different dependence of the dimensionless truncation radius on mass in clustered and void regions.