2012MNRAS.423.2325A

We explore the possibility of detecting radio emission in the cosmic web by analysing shock waves in the MareNostrum cosmological simulation. This requires a careful calibration of shock finding algorithms in smoothed particle hydrodynamics simulations, which we present here. Moreover, we identify the elements of the cosmic web, namely voids, walls, filaments and clusters with the use of the SpineWeb technique, a procedure that classifies the structure in terms of its topology. Thus, we are able to study the Mach number distribution as a function of its environment. We find that the median Mach number for clusters is M_clusters ≈ 1.8, for filaments is M_filaments ≈ 6.2, for walls is Mwalls_ ≈ 7.5 and for voids is M_voids ≈ 18. We then estimate the radio emission in the cosmic web using the formalism derived in Hoeft & Brüggen. We also find that in order to match our simulations with observational data [e.g. NRAO VLA Sky Survey (NVSS) radio relic luminosity function], a fraction of energy dissipated at the shock of ξ_e= 0.0005 is needed, in contrast with the ξ_e= 0.005 proposed by Hoeft et al. We find that 41 per cent of clusters with M ≥ 10¹⁴ M_☉ host diffuse radio emission in the form of radio relics. Moreover, we predict that the radio flux from filaments should be S_150MHz ∼ 0.12µJy at a frequency of 150 MHz.