Astrophysical Implications of Self-interacting Dark Matter

In this thesis we study the astrophysical implication of self-interacting dark matter. Observations on different scales suggest the existence of an additional form of matter which interacts gravitationally. This dark matter is assumed to be cold and collisionless in the standard model of cosmology. Discrepancies between observations and predictions of the $\Lambda$CDM model on cosmologically small scales motivate us to think beyond the assumptions of the model.Relaxing the assumption on the collisionality of dark matter leads to the idea of self-interacting dark matter, which may be able to resolve the small-scale issues. Studying astrophysical observables is a very promising avenue to understand the nature and the interactions of dark matter. Some signatures have the potential to test the standard cold and collisionless dark matter paradigm and could rule out many popular dark matter candidates. Self-interacting dark matter has striking consequences for colliding dark matter haloes such as an observable offset between the luminous and dark matter of an infalling halo. We demonstrate how a detection of such an offset leads to direct constraints on the self-interaction cross section. We distinguish between rare and frequent self-interactions and observe that it may be possible to gain knowledge about the fundamentals of the interaction from observations of merging systems. We also discuss a limitation of simulations of merging galaxy clusters with dark matter self-interactions, namely that commonly the galaxies are treated as collisionless test particles. However, the fact that galaxies reside in dark matter haloes makes the galaxies themselves collisional if dark matter self-interactions are implemented. We demonstrate how this effect diminishes observable offsets. Finally, we present the first implementation of frequent self-interactions in $N$-body simulations. Using smoothed particle hydrodynamics we find an effective description of energy transfer for the case that the interactions are too frequent to be resolved explicitly. Simulations of an isolated dark matter halo of a dwarf galaxy show that we are able to reproduce dark matter density profiles with an isothermal core