Fluctuations in the Radio Background from Intergalactic Synchrotron Emission

The shocks produced in the intergalactic medium during large-scale structure formation accelerate a population of highly relativistic electrons which emit synchrotron radiation due to intergalactic magnetic fields. In a previous paper (Loeb & Waxman 2000) we have shown that these electrons cool primarily by inverse-Compton scattering of the microwave background photons and can thereby produce the observed intensity and spectrum of the diffuse gamma-ray background. Here we calculate the intensity and angular fluctuations of the radio synchrotron background that results from the same high-energy electrons, as well as the expected angular fluctuations in the gamma-ray background. On angular scales smaller than a degree, the predicted fluctuations in the microwave background temperature are of order 40micro-K*(xi_B/0.01)(nu/10 GHz)^{-3}, where xi_B is the magnetic fraction of the post-shock energy density. This foreground might have already dominated the anisotropy signal detected in existing low-frequency CMB experiments, and can be identified with confidence through multi-frequency observations. Detection of the synchrotron fluctuations would allow to determine the strength of the intergalactic magnetic field. We predict a strong correlation between high-resolution maps taken at low-frequency radio waves and at high-energy gamma-rays. Young X-ray clusters may also appear as radio or gamma-ray clusters. The detailed study of this correlation will become easily accessible with the future launch of GLAST.