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 \degr \times 21.76 \degr 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 .