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.
