Novel method to trace the dark matter density profile around supermassive black holes with AGN reverberation mapping

We propose a new method to determine the dark matter density profile in the vicinity of distant supermassive black holes (SMBH) using reverberation mapping (RM) measurements of active galactic nuclei (AGN). The mapping of multiple emission lines allows the measurement of the enclosed mass within different radii from the central SMBH, which can be used to infer or constrain the dark matter density profile on sub-parsec scales. We apply a toy model based on this method to a sample of fourteen AGN to test its feasibility based on current measurements. We find that for five objects, the observed enclosed mass does grow with radii, hinting towards the presence of a dark matter component at the 1-2 $σ$ level. For these sources, we find global evidence for a universal dark matter profile with a preferred radial steepness of index $γ\sim 1.6$, consistent with the scenario expected for a dark matter spike mildly relaxed by stellar heating processes. The enclosed dark matter mass, however, is found to be significantly larger than expected. We show that the current RM based mass measurements suffer from large systematic uncertainties, that limit the effectiveness of our method. Our work emphasizes the importance of applying the recent developments in mass determination techniques to target multiple emission lines with future RM and interferometry campaigns. This provides the most direct way of constraining the dark matter density in the sub-parsec regions around extragalactic SMBHs, which is crucial to our understanding of the dynamics and nature of dark matter.