X-ray lines and self-interacting dark matter

We study the correlation between a monochromatic signal from annihilating dark matter and its self-interacting cross section. We apply our argument to a complex scalar dark sector, where the pseudo-scalar plays the role of a warm dark matter candidate while the scalar mediates its interaction with the Standard Model. We combine the recent observation of the cluster Abell 3827 for self-interacting dark matter and the constraints on the annihilation cross section for monochromatic X-ray lines. We also confront our model to a set of recent experimental analyses and find that such an extension can naturally produce a monochromatic keV signal corresponding to recent observations of Perseus or Andromeda while in the meantime predicts self-interacting cross section of the order of $\sigma / m\simeq0.1-1~\mathrm{cm^2/g}$ as recently claimed in the observation of the cluster Abell 3827. We also propose a way to distinguish such models by future direct detection techniques.