  The present paper is a sequel to our previous work [Y. Ni et al., JCAP 1607,
049 (2016)] in which we studied the iron K$\alpha$ line expected in the
reflection spectrum of Kerr black holes with scalar hair. These metrics are
solutions of Einstein's gravity minimally coupled to a massive, complex scalar
field. They form a continuous bridge between a subset of Kerr black holes and a
family of rotating boson stars depending on one extra parameter, the
dimensionless scalar hair parameter $q$, ranging from 0 (Kerr black holes) to 1
(boson stars). Here we study the limiting case $q=1$, corresponding to rotating
boson stars. For comparison, spherical boson stars are also considered. We
simulate observations with XIS/Suzaku. Using the fact that current observations
are well fit by the Kerr solution and thus requiring that acceptable
alternative compact objects must be compatible with a Kerr fit, we find that
some boson star solutions are relatively easy to rule out as potential
candidates to explain astrophysical black holes, while other solutions, which
are neither too dilute nor too compact are more elusive and we argue that they
cannot be distinguished from Kerr black holes by the analysis of the iron line
with current X-ray facilities.
