Cross-correlation of diffuse synchrotron and large-scale structures

We explore for the first time the method of cross-correlation of radio synchrotron emission and tracers of large-scale structure in order to detect the warm-hot intergalactic medium (WHIM). We performed a cross-correlation of a 34° × 34° area of Two-Micron All-Sky Survey (2MASS) galaxies for two redshift slices (0.03 < z < 0.04 and 0.06 < z < 0.07) with the corresponding region of the 1.4 GHz Bonn survey. For this analysis, we assumed that the synchrotron surface brightness is linearly proportional to surface density of galaxies. We also sampled the cross-correlation function (CCF) using 24 distant fields of the same size from the Bonn survey, to better assess the noise properties. Though we obtained a null result, we found that by adding a signal weighted by the 2MASS image with a filament (peak) surface brightness of 1 (7) and 7(49) mK would produce a 3σ positive correlation for the 0.03 < z < 0.04 and 0.06 < z < 0.07 redshift slices, respectively. These detection thresholds correspond to minimum energy magnetic fields as low as 0.2 μG, close to some theoretical expectations for filament field values. This injected signal is also below the rms noise of the Bonn survey, and demonstrates the power of this technique and its utility for upcoming sensitive continuum surveys such as those planned with the Murchison Widefield Array.