Iron K$α$ signatures from accretion disks around fermionic dark matter cores

Abstract

The fluorescent iron line and its broadening due to relativistic effects are excellent probes to study the inner part of an accretion disk and the space-time geometry near the compact object. We investigate the iron K$α$ line profile within the extended RAR model, which describes a fermionic dark matter distribution on galaxy scales. The most general solutions are characterized by a compact and highly degenerate core able to mimic the central black hole, transitioning into an extended halo composed of the same particles. We aim to contrast the resulting line morphologies in this scenario with those predicted by the standard Kerr black hole paradigm. Special attention will be given to MCG-06-30-15 galaxy. We compute the line profile using the numerical ray-tracing code, Skylight. We consider two distinct configurations for the emissivity of the cold accretion disk: an irradiation profile based on the lamp-post corona prescription, and a phenomenological power-law profile. The resulting profiles exhibit a diverse phenomenology. In particular, the most compact fermion cores produce a line broadening comparable to that observed in rapidly rotating black holes. The presence of emitting matter at radii smaller than a gravitational radius yields distinctive spectral features that are entirely absent in the black hole scenario. For MCG-06-30-15 galaxy, we find a good agreement with the observed broad features of the iron line profile, provided the compactness of the fermion core is close to critical. These results reinforce the need for independent black hole spin measurements. Combined with such constraints, iron-line spectroscopy may provide a powerful observational tool to distinguish black holes from alternative compact solutions, in particular compact fermionic dark-matter cores.