Muon excess at sea level from solar flares in association with the Fermi GBM spacecraft detector

This paper presents results of an ongoing survey on the associations between muon excesses at ground level registered by the Tupi telescopes and transient solar events, two solar flares whose gamma-ray and X-ray emissions were reported by, respectively, the Fermi GBM and the GOES 14. We show that solar flares of small scale, those with prompt X-ray emission classified by GOES as C-Class (power $10^{-6}$ to $10^{-5}$ W m$^2$ at 1 AU) may give rise to muon excess probably associated with solar protons and ions emitted by the flare and arriving at the Earth as a coherent particle pulse. The Tupi telescopes are within the central region of the South Atlantic Anomaly (SAA), which allows particle detectors to achieve a low rigidity of response to primary and secondary charged particles ($\geq 0.1$ GV). Here we argue for the possibility of a "scale-free" energy distribution of particles accelerated by solar flares. Large and small scale flares have the same energy spectrum up to energies exceeding the pion production, the difference between them is only the intensity. If this hypothesis is correct, the Tupi telescope is registering muons produced by protons (ions) whose energy corresponds to the tail of the spectrum. Consequently the energy distribution of the emitted protons has to be a power law spectrum, since power law distributions are characterized as scale free distributions. The Tupi events give support to this conjecture.