  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.
