  The effective interactions of dark matter with photons are fairly restricted.
Yet both direct detection as well as monochromatic gamma ray signatures depend
sensitively on the presence of such interactions. For a Dirac fermion,
electromagnetic dipoles are possible, but are very constrained. For Majorana
fermions, no such terms are allowed. We consider signals of an effective theory
with a Majorana dark matter particle and its couplings to photons. In the
presence of a nearby excited state, there is the possibility of a magnetic
dipole transition (Magnetic inelastic Dark Matter or MiDM), which yields both
direct and indirect detection signals, and, intriguingly, yields essentially
the same size over a wide range of dipole strengths. Absent an excited state,
the leading interaction of WIMPs is similar to the Rayleigh scattering of low
energy photons from neutral atoms, which may be captured by an effective
operator of dimension 7 of the form $\bar{\chi}\chi F_{\mu\nu}F^{\mu\nu}$.
While it can be thought of as a phase of the Magnetic inelastic Dark Matter
scenario where the excited state is much heavier than the ground state, it can
arise from other theories as well. We study the resulting phenomenology of this
scenario: gamma ray lines from the annihilation of WIMPs; nuclear recoils in
direct detection; and direct production of the WIMP pair in high-energy
colliders. Considering recent evidence in particular for a 130 GeV line from
the galactic center, we discuss the detection prospects at upcoming
experiments.
