  In models of anapole dark matter (DM), the DM candidate is a Majorana fermion
whose primary interaction with standard model (SM) particles is through an
anapole coupling to off-shell photons. As such, at tree-level, anapole DM
undergoes p-wave annihilation into SM charged fermions via a virtual photon.
But, generally, Majorana fermions are polarizable, coupling to two real
photons. This fact admits the possibility that anapole DM can annihilate into
two photons in an s-wave process. Using an explicit model, we compute both the
tree-level and diphoton contributions to the anapole DM annihilation cross
section. Depending on model parameters, the s-wave process can either rival or
be dwarfed by the p-wave contribution to the total annihilation cross section.
Subjecting the model to astrophysical upper bounds on the s-wave annihilation
mode, we rule out the model with large s-wave annihilation.
