Tight Constraints on the Excess Radio Background at $z = 9.1$ from LOFAR

The ARCADE2 and LWA1 experiments have claimed an excess over the Cosmic Microwave Background (CMB) at low radio frequencies. If the cosmological high-redshift contribution to this radio background is between 0.1% and 22% of the CMB at $1.42\,$GHz, it could explain the tentative EDGES Low-Band detection of the anomalously deep absorption in the 21-cm signal of neutral hydrogen (Fialkov & Barkana 2019). We use the upper limit on the 21-cm signal from the Epoch of Reionization ($z=9.1$) based on $141\,$hours of observations with LOFAR (Mertens et al. 2020) to evaluate the contribution of the high redshift Universe to the detected radio background. Marginalizing over astrophysical properties of star-forming halos, we find (at 68% C.L.) that the cosmological radio background can be at most 0.7% of the CMB at $1.42\,$GHz. This limit rules out strong contribution of the high-redshift Universe to the ARCADE2 and LWA1 measurements. Even though LOFAR places limit on the extra radio background, excess of $0.1-0.7$% over the CMB (at $1.42\,$GHz) is still allowed and could explain the EDGES Low-Band detection. We also constrain the thermal and ionization state of the gas at $z = 9.1$, and put limits on the properties of the first star-forming objects. We find that, in agreement with the limits from EDGES High-Band data, LOFAR data disfavour scenarios with inefficient X-ray sources and cases where the Universe was ionized by massive halos only.