Properties of galaxy haloes 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 haloes. 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 gravitationally bound galaxy-sized haloes extracted from these two regions and from a third region hosting a single, relaxed cluster without substructure. Exploiting the high mass resolution of our simulation (m(body) =2.1x10(9) h(-1) M-circle dot), we construct halo samples probing more than two decades in mass, starting from a rather small mass threshold: 5x10(10) h(-1) M-circle dot less than or equal to M. We present results for two statistics: the relationship between one-dimensional velocity dispersion sigma(v) and mass M-0 and the probability distribution of the spin parameter P(lambda), and for three different group finders. The sigma(v)-M-0 relationship is well reproduced by the truncated isothermal sphere (TIS) model introduced by Shapiro et al., although the slope is different from the original prediction. A series of sigma(v)-M (0) relationships for different values of the anisotropy parameter beta, obtained using the theoretical predictions by Lokas & Mamon for Navarro et al. density profiles, are found to be only marginally consistent with the data. Using some properties of the equilibrium TIS models, we construct subsamples of fiducial equilibrium TIS haloes from each of the three subregions, and we study their properties. For these haloes, we do find an environmental dependence of their properties, in particular of the spin parameter distribution P(lambda). We study the TIS model in more detail, and we find new relationships between the truncation radius and other structural parameters. No gravitationally bound halo is found having a radius larger than the critical value for gravithermal instability for TIS haloes (r(t) greater than or equal to34.2r(0), where r(0) is the core radius of the TIS solution). We do, however, find a dependence of this relationship on the environment, like for the P(lambda) statistics. These facts hint at a possible role of tidal fields in determining the statistical properties of haloes.