  We consider axion-mediated dark matter models motivated by Fermi gamma ray
line at 130 GeV, where anomaly interactions of an axion-like scalar mediate a
singlet Dirac fermion dark matter (DM) to electroweak gauge bosons. In these
models, extra vector-like leptons generate anomaly interactions for the axion
and can also couple to the SM Higgs boson to modify the Higgs-to-diphoton rate.
We can distinguish models by the branching fraction of the DM annihilation into
a photon pair, favoring the model with a triplet fermion. From the condition
that the lighter charged extra lepton must be heavier than dark matter for no
tree-level DM annihilations, we also show that the ratio of Higgs-to-diphoton
rate to the SM value is constrained by vacuum stability to 1.4(1.5) for the
cutoff scale of 10(1) TeV.
