Iron K$\alpha$ line of Kerr black holes with Proca hair

We continue our study on the capabilities of present and future X-ray missions to test the nature of astrophysical black hole candidates via X-ray reflection spectroscopy and distinguish Kerr black holes from other solutions of 4-dimensional Einstein's gravity in the presence of a matter field. Here we investigate the case of Kerr black holes with Proca hair [1]. The analysis of a sample of these configurations suggests that even extremely hairy black holes can mimic the iron line profile of the standard Kerr black holes, and, at least for the configurations of our study, we find that current X-ray missions cannot distinguish these objects from Kerr black holes. This contrasts with our previous findings for the case of Kerr black holes with scalar (rather than Proca) hair [2], even though such comparison may be biased by the limited sample. Future X-ray missions can detect the presence of Proca hair, but a theoretical knowledge of the expected intensity profile (currently missing) can be crucial to obtain strong constraints.