Radio background and IGM heating due to Pop III supernovae explosions

We consider the synchrotron emission from high energy electrons accelerated in supernova explosions of massive Population III stars in high redshift minihaloes of mass $10^{5\hbox {--}7} \rm M_\odot$. We show the resulting intensity of radio background from this process can be substantial, which could potentially explain the recently reported EDGES result, if not for the associated heating of the IGM by CR protons which are also produced at the same time. The trade-off between the radio background and heating is such that the 21 cm brightness temperature cannot be larger than $\vert \Delta T_{21}\vert \sim 0.25$ K. The radio background and heating are both produced by energetic particles, although one by energetic electrons and the other by energetic protons. The two competing processes, production of radio background and heating of IGM by Pop III supernovae, determine the depth of the trough in the 21 cm brightness temperature which can be observed in future experiments and used as a test of this scenario.