Ellipsoidal collapse of dark matter haloes in cosmological simulations

Nowadays different observational campaigns agree on the standard cosmological model to explain and describe the formation and evolution of large scale structures in our Universe. In this scenario, almost 95% of the energy content of the Universe is in unknown forms of energy and matter, generally called dark energy and dark matter. The structures observed today are assumed to have grown gravitationally from small and initially Gaussian density fluctuations. As the universe expands, sufficiently overdense regions expand until they reach a maximum size and then collapse under the action of their own gravity: since dark matter is believed to be the dominant matter component of the universe, it leads the gravitational collapse process, forming structures called dark matter haloes. It is within the potential wells of these haloes that gas can shock, cool and eventually form stars and galaxies. The main theoretical models on the gravitational collapse of dark matter haloes are the spherical collapse and the ellipsoidal collapse (EC) models. The former describes haloes as spherical overdense regions embedded in an uniform background, while the latter allows more possible shapes, defining haloes as homogeneous ellipsoids. Moreover, the ellipsoidal collapse model predicts that there is a direct connection between the evolution of an halo and the properties of the corresponding region in the initial conditions. Despite the fact that a triaxial modelling is obviously more realistic, the spherical approximation is still the most common choice. In this work we analysed the results of several cosmological simulations (the GIF2 , Le SBARBINE - designed and run in Padova by our group - and the Millennium XXL simulations), with the aim of study the triaxiality of dark matter haloes in detail. In particular, we developed a new halo finder, called ``Ellipsoidal Overdensity Halo Finder'' (EO), which identifies dark matter haloes as triaxial ellipsoids at all times, thus following the prescription of the EC model. Using its results, we studied the properties of protohaloes in the initial conditions and their evolution through the whole history of the Universe: this is crucial to understand the role of the initial density peaks, which are believed to be the seeds of all the observed structures. Our results help to understand the dynamics of halo collapse, confirming many predictions of the EC model, but also provide hints for a more realistic modelling. As the issue of halo triaxiality is still not completely solved in theory and simulations, it started to be considered very recently in observational studies. Galaxy clusters are the largest virialized systems in the Universe and, following hierarchical clustering, also the last to form; almost 80% of their mass is attributed to dark matter, while the rest to baryons. The estimate of mass of clusters is still an open problem and the uncertainties are also related to the triaxiality of the haloes that surrounds them. For example, the estimated mass is on average biased to be lower than the true one, due to the fact that the haloes are embedded are typically prolate and so the spherical modelling is not able to capture their real structure. We studied the shape distributions of dark matter haloes at all times and for different cosmologies, using Le SBARBINE and the MXXL simulations. In this way, we derived some universal relations between the shape parameters and the mass of haloes, independent from the cosmological model and redshift. These results will be useful to generate mock halo catalogues with given triaxial properties and can be used in triaxial mass reconstruction methods that require priors for the axial ratio distributions. Then, we concentrated on very massive haloes to provide more accurate predictions for cluster-size haloes. Finally, we studied the halo mass function and tested its universality. With this purpose, we identified dark matter haloes at six different density thresholds (the virial one and other multiples of the background and the critical densities, which are commonly used in literature). Our results confirm the universality of the halo mass function, when measured with virialized haloes, while it does not hold for other halo identifications. We provide the fitting formulae for all the overdensity, believing that they could be useful for observers, and a method to rescale from one to the others.