Search for the Galactic accelerators of cosmic rays up to the knee with the Pevatron test statistic

The Pevatron test statistic (PTS) is applied to data from & gamma;-ray observatories to test for the origin of cosmic rays (CRs) at energies around the knee of the CR spectrum. Several sources are analysed within hadronic emission models. Previously derived results for RX J1713.7-3946, Vela Jr, and HESS J1745-290 are confirmed to demonstrate the concept, reliability, and advantages of the PTS. It is excluded with a significance more than 5 & sigma; that the sources RX J1713.7-3946 and Vela Jr are Pevatrons, while strong indications exceeding 4 & sigma; are found for excluding HESS J1745-290 as a Pevatron. The importance to resolve source confusion with high angular resolution observations for Pevatrons searches is demonstrated using PTS for the region containing the SNR G106.3+2.7 and the Boomerang nebula. No statistically significant conclusion with respect to Pevatron associations could be drawn from this region, for the diffuse & gamma;-ray emission around the Galactic Centre, and the unidentified & gamma;-ray sources LHAASO J2108+5157, HESS J1702-420A, and MGRO J1908+06. Assuming the entire & gamma;-ray emission from MGRO J1908+06 and the tail region of SNR G106.3+2.7 are hadronic, a statistical indication exceeding 3 & sigma; is found for the underlying proton spectrum to extend beyond 350-400 TeV as a power law. This result can indicate that these sources are proton and helium Pevatrons, in which the accelerated particles contribute to the knee of proton and helium spectra observed at Earth.