Method to extract the primary cosmic ray spectrum from very high energy gamma-ray data and its application to SNR RX J1713.7-3946

Abstract

Supernova remnants are likely to be the accelerators of the galactic cosmic rays. Assuming the correctness of this hypothesis, we develop a method to extract the parent cosmic ray spectrum from the VHE gamma ray flux emitted by supernova remnants (and other gamma transparent sources). Namely, we calculate semi-analytically the (inverse) operator which relates an arbitrary gamma ray flux to the parent cosmic ray spectrum, without relying on any theoretical assumption about the shape of the cosmic ray and/or photon spectrum. We illustrate the use of this technique by applying it to the young SNR RX J1713.7-3946 which has been observed by H.E.S.S. experiment during the last three years. Specific implementations of the method permit to use as an input either the parameterized VHE gamma ray flux or directly the raw data. The possibility to detect features in the cosmic rays spectrum and the error in the determination of the parent cosmic ray spectrum are also discussed.