Black holes, dark matter spikes, and constraints on simplified models with t-channel mediators

A possible density spike of dark matter (DM) in the subparsec region near the supermassive black hole at the Galactic center could have a significant effect on indirect signals of dark matter annihilation. Here we explore the impacts of the modeling of the dark matter distribution in the inner Galaxy on gamma-ray signals of dark matter annihilation. We consider a range of values for relevant astrophysical parameters that describe the dark matter profile, including a possible spike, and quantify the dependence of the gamma-ray flux on these choices. We consider both an idealized case where no depletion of the spike has occurred since its formation, as well as a case where the spike is significantly depleted over time due, e.g., to gravitational interactions with baryons. We also consider a range of power-law descriptions of the dark matter profile outside of the spike region. Taking Fermi-LAT data for the gamma-ray flux from the point source 3FGL J1745.6-2859c (Sgr A*), we calculate the resulting constraints on generic models of DM, allowing for the possibility of a non-negligible velocity-dependent component of the annihilation cross section. We find that for very depleted spikes, the spike itself would contribute insignificantly to a dark matter annihilation signal, though constraints on dark matter models are still possible depending on the power law behavior of the dark matter profile on larger scales. For idealized spikes, we quantify the influence of the spike, as well as the larger-scale dark matter profile, on the gamma-ray flux from dark matter annihilations and on the constraints on the properties of particle dark matter from observations of the Galactic center point source.