Concentration, Spin and Shape of Dark Matter Haloes: Scatter and the Dependence on Mass and Environment

We use a series of cosmological N-body simulations for a flat LCDM cosmology to investigate the properties of dark matter haloes in the mass range 3.0e9-3.0e13 Msun. These properties include the concentration parameter (c), the spin parameter (lambda) and the mean axis ratio (q). For the concentration-mass relation we find c~M^(-0.11) in agreement with the model proposed by Bullock et al. even if we find a lower normalization (15%). The results for lambda and q are in good agreement with previous studies, while c and lambda are anti-correlated. In an attempt to remove unrelaxed haloes, we use the offset parameter (xoff), defined as the distance between the most bound particle and the center of mass. Removing haloes with large xoff increases the c by ~10%, lowers the lambda by ~15%, and removes the most prolate haloes. In addition, it largely removes the anti-correlation between c and lambda though not entirely. We also investigate the effects of the large-scale environment. We find that more concentrated haloes live in denser environments. Note, however, that the trend is weak compared to the scatter. For the spin parameters we find no environment dependence, while there is a weak indication that the most spherical haloes reside in denser region. Finally, using a simple model for disk galaxy formation we show that haloes that host low surface brightness galaxies are expected to be hosted by a biased sub-set of haloes. Not only do these haloes have spin parameters that are larger than average, they also have c that are 15% percent lower than the average at a given halo mass. We discuss the implications of all these findings for the claimed disagreement between halo concentrations inferred from LSB rotation curves, and those expected for a LCDM cosmology. (abridged)