  We examine the cosmic ray proton (CRp) population within the giant elliptical
galaxy M 87 using the TeV gamma-ray detection of the HEGRA collaboration. In
our scenario, the gamma-rays are produced by decaying pions which result from
hadronic CRp interactions with thermal gas of the interstellar medium of M 87.
By comparing the gamma-ray emission to upper limits of EGRET, we constrain the
spectral index of the CRp population to alpha(GeV,TeV) < 2.275 within our
scenario. Both the expected radial gamma-ray profile and the required amount of
CRp support this hadronic scenario. The accompanying radio mini-halo of
hadronically originating cosmic ray electrons is outshone by the synchrotron
emission of the relativistic jet of M 87 by one order of magnitude. According
to our predictions, the future GLAST mission should allow us to test this
hadronic scenario.
