Low Frequency Radio Constraints on the Synchrotron Cosmic Web

We present a search for the synchrotron emission from the synchrotron cosmic web by cross correlating 180MHz radio images from the Murchison Widefield Array with tracers of large scale structure (LSS). We use two versions of the radio image covering $21.76\times 21.76$ degrees with point sources brighter than 0.05 Jy subtracted, with and without filtering of Galactic emission. As tracers of the LSS we use the Two-Micron-All-Sky-Survey (2MASS) and the Widefield InfraRed Explorer (WISE) redshift catalogues to produce galaxy number density maps. The cross correlation functions all show peak amplitudes at zero degrees, decreasing with varying slopes towards zero correlation over a range of one degree. The cross correlation signals include components from point source, Galactic, and extragalactic diffuse emission. We use models of the diffuse emission from smoothing the density maps with Gaussians of sizes 1-4 Mpc to find limits on the cosmic web components. From these models we find surface brightness 99.7 per cent upper limits in the range of 0.09-2.20 mJy beam$^{-1}$ (average beam size of 2.6 arcmin), corresponding to 0.01-0.30 mJy arcmin$^{-2}$. Assuming equipartition between energy densities of cosmic rays and the magnetic field, the flux density limits translate to magnetic field strength limits of 0.03-1.98 $\mu$G, depending heavily on the spectral index. We conclude that for a 3$\sigma$ detection of 0.1 $\mu$G magnetic field strengths via cross correlations, image depths of sub-mJy to sub-$\mu$Jy are necessary. We include discussion on the treatment and effect of extragalactic point sources and Galactic emission, and next steps for building on this work.