Filamentary Baryons and Where to Find Them: A forecast of synchrotron radiation from merger and accretion shocks in the local Cosmic Web

We generate probabilistic predictions of the low-redshift ($z < 0.2$) synchrotron Cosmic Web for half of the Northern Sky. In particular, we predict the contribution to the specific intensity function at $\nu_\mathrm{obs} = 150\ \mathrm{MHz}$ from merger shocks in clusters and accretion shocks in filaments, both of which arise during large-scale structure formation. We assume a primordial magnetogenesis scenario, but our method is general enough to allow for an exploration of alternative magnetogenesis scenarios - and even alternative radiation mechanisms and spectral windows. In the future, by comparing different predictions, one could infer the most plausible physical model from a synchrotron Cosmic Web detection. Our method combines Bayesian large-scale structure reconstructions, snapshots of an MHD cosmological simulation, a Gaussian random field, and a ray tracing approach. The results help to select targets for deep observations and can be used in actual detection experiments. We highlight predictions for the Hercules Cluster, the Coma Cluster, Abell 2199, Abell 2255, the Lockman Hole and the Ursa Major Supercluster. At degree-scale resolution, the median specific intensity reaches $m_{I_\nu} \sim 10^{-1}\ \xi_e\ \mathrm{Jy\ deg^{-2}}$, where $\xi_e$ is the electron acceleration efficiency.