Signature of excess radio background in the 21-cm global signal and power spectrum

The recent tentative detection by the Experiment to Detect the Global EoR Signature (EDGES) low band of the hydrogen 21-cm line from cosmic dawn, if confirmed, is the first ever signature observed from the epoch of primordial star formation. However, the magnitude and the shape of this signal are incompatible with standard astrophysical predictions, requiring either colder than expected gas, or an excess radio background above the cosmic microwave background (CMB) radiation. In this paper, we explore the latter option, investigating possible 21-cm signals in models with standard astrophysics to which a phenomenological excess radio background was added. Assuming uniform radiation with a synchrotron-like spectrum and redshift-independent amplitude existing throughout cosmic history, we show that such a radio background, in addition to explaining the EDGES detection, enhances the cosmic dawn power spectrum. The signal during cosmic dawn and re-ionization strongly depends on both the intensity of the background and the astrophysical parameters. We verify the broad agreement of our models with the detected feature, including additional constraints from the EDGES high-band, high-redshift quasars, and observational limits on the extra-Galactic radio background. The data imply a lower limit on the star formation efficiency of 2.8 per cent, an upper limit on the minimum mass of star-forming haloes of Mh = 109 M⊙ at z = 17, and a lower limit on the excess background of 1.9 times the CMB at 78 MHz. The properties of X-ray sources are unconstrained by the data. We also show that during the dark ages, such a radio background leaves smoking gun signature in the 21-cm signal.