Radio Emission in the Cosmic Web
  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.
