We explore the possibility of detecting radio emission in the \emph{ cosmic web} by analyzing 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 $\mathcal{ M}_{ \mathrm{ clusters}}\approx1.8$, for filaments is $\mathcal{ M}_{ \mathrm{ filaments}}\approx 6.2$, for walls is $\mathcal{ M}_{ \mathrm{ walls}}\approx 7.5$, and for voids is $\mathcal{ M}_{ \mathrm{ voids}}\approx 18$. We then estimate the radio emission in the cosmic web using the formalism derived in Hoeft & Br\"{ u}ggen (2007). We also find that in order to match our simulations with observational data (e.g., NVSS radio relic luminosity function), a fraction of energy dissipated at the shock of $\xi_{ \mathrm{ e}}=0.0005$ is needed, in contrast with the $\xi_{ \mathrm{ e}}=0.005$ proposed by Hoeft et al. (2008). We find that 41% of clusters with $M \ge 10^{ 14} M_{ \odot}$ host diffuse radio emission in the form of radio relics. Moreover, we predict that the radio flux from filaments should be $S_{ 150 MHz}\sim 0.12$ $\mu$Jy at a frequency of 150 MHz.
Categories: astro-ph.CO