Estimating the intergalactic medium ionization level of a region needs proper treatment of the reionization process for a large representative volume of the universe. The clumping factor, a parameter which accounts for the effect of recombinations in
unresolved, small-scale structures, aids in achieving the required accuracy for the reionization history even in simulations with low spatial resolution. In this paper, we study for the first time the redshift evolution of clumping factors of different ionized species of H and He in a small but very high resolution simulation of the reionization process. We investigate the dependence of the value and redshift evolution of clumping factors on their definition, the ionization level of the gas, the grid resolution, box size and mean dimensionless density of the simulations.
We investigate the correlation between nine different dark matter halo properties using a rank correlation analysis and a Principal Component Analysis for a sample of haloes spanning five orders of magnitude in mass. We consider mass and dimensionles
s measures of concentration, age, relaxedness, sphericity, triaxiality, substructure, spin, and environment, where the latter is defined in a way that makes it insensitive to mass. We find that concentration is the most fundamental property. Except for environment, all parameters are strongly correlated with concentration. Concentration, age, substructure, mass, sphericity and relaxedness can be considered a single family of parameters, albeit with substantial scatter. In contrast, spin, environment, and triaxiality are more independent, although spin does correlate strongly with substructure and both spin and triaxiality correlate substantially with concentration. Although mass sets the scale of a halo, all other properties are more sensitive to concentration.
