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.
