in these past years. Details of the code and some results can be found, for instance, in the papers by Filloux et al. (2010, 2011) or Durier & de Freitas Pacheco (2011). For the sake of completeness, a short summary of the main features of the code will be presented here.

All the simulations were performed in the context of the $\Lambda$CDM cosmology, using the parallel TreePM-SPH code GADGET-2 in a formulation, despite the use of fully adaptive smoothed particle hydrodynamics (SPH), that conserves energy and entropy (Springel 2005). Initial conditions are established according to the algorithm COSMICS (Bertschinger 1995) and the evolution of the structures are followed in the redshift range $60 \geq z \geq 0$. Ionization equilibrium taking into account collisional and radiative processes were included following Katz, Weinberg & Hernquist (1996), as well as the contribution of the ionizing radiation background. The contribution of cooling processes such as collisional excitation of HI, HeI and HeII levels, radiative recombination, free-free emission and inverse Compton were also included, using the results by Sutherland & Dopita (1993). An interpolation procedure was adopted to take into account the enhancement of the cooling as the medium is enriched by metals. The cooling 