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 180-MHz radio images from the Murchison Widefield Array with tracers of large-scale structure (LSS). We use two versions of the radio image covering 21.degrees 76 x 21.degrees 76 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 and the Wide-field InfraRed Explorer redshift catalogues to produce galaxy number density maps. The cross-correlation functions all show peak amplitudes at 0 degrees, decreasing with varying slopes towards zero correlation over a range of 1 degrees. 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.