Cosmological shock waves: clues to the formation history of haloes
  Shock waves developed during the formation and evolution of cosmic structures
encode crucial information on the hierarchical formation of the Universe. We
analyze an Eulerian AMR hydro + N-body simulation in a $\Lambda$CDM cosmology
focused on the study of cosmological shock waves. The combination of a
shock-capturing algorithm together with the use of a halo finder allows us to
study the morphological structures of the shock patterns, the statistical
properties of shocked cells, and the correlations between the cosmological
shock waves appearing at different scales and the properties of the haloes
harbouring them. The shocks in the simulation can be split into two broad
classes: internal weak shocks related with evolutionary events within haloes,
and external strong shocks associated with large-scale events. The shock
distribution function contains information on the abundances and strength of
the different shocks, and it can be fitted by a double power law with a break
in the slope around a Mach number of 20. We introduce a generalised scaling
relation that correlates the average Mach numbers within the virial radius of
haloes and their virial masses. In this plane, haloes occupy different areas
according to their early evolutionary histories: those with a quiet evolution
have an almost constant Mach number independently of their masses, whereas
haloes undergoing significant merger events very early in their evolution show
a linear dependence with their masses. At high redshift, the halo distribution
in this scaling relation forms a L-like pattern that changes due to the
evolution of the haloes. The analysis of the propagation speed and size of the
shock waves around haloes could give some hints on the formation time and main
features of the haloes. (Abridged)
