Inferred cosmic-ray spectrum from $Fermi$-LAT $\gamma$-ray observations of the Earth's limb

Recent accurate measurements of cosmic-ray (CR) species by ATIC-2, CREAM, and PAMELA reveal an unexpected hardening in the proton and He spectra above a few hundred GeV, a gradual softening of the spectra just below a few hundred GeV, and a harder spectrum of He compared to that of protons. These newly-discovered features may offer a clue to the origin of high-energy CRs. We use the ${\it Fermi}$LargeAreaTelescopeobservationsofthe$\gamma$-ray emission from the Earth’s limb for an indirect measurement of the local spectrum of CR protons in the energy range $\sim 90$GeV-$6$TeV (derived from a photon energy range $15$GeV-$1$TeV). Our analysis shows that single power law and broken power law spectra fit the data equally well and yield a proton spectrum with index $2.68\pm 0.04$ and $2.61\pm 0.08$ above $\sim 200$GeV, respectively.