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Constraining Galactic $pγ$ Interactions with Cosmic Ray Electron and Positron Spectra

High energy protons produced by various sources of cosmic rays, {\it e.g.} supernova remnants, pulsar wind nebulae, active galactic nuclei and gamma-ray bursts participate in $pγ$ and $pp$ interactions. Although $pp$ interactions may be the dominant mechanism in our Galaxy, it is unclear how important $pγ$ process is. We show that the upper bound on the fraction of protons participating in $pγ$ interactions inside all Galactic astrophysical sources of cosmic rays is 10%.