We explore the possibility of detecting radio emission in the 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 } } \approx 1.8 , 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 & Brüggen ( 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 \geq 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 .