  Accretion disks play an important role in the evolution of their relativistic
inner compact objects. The emergence of a new generation of interferometers
will allow to resolve these accretion disks and provide more information about
the properties of the central gravitating object. Due to this instrumental leap
forward it is crucial to investigate the accretion disk physics near various
types of inner compact objects now to deduce later constraints on the central
objects from observations. A possible candidate for the inner object is the
boson star. Here, we will try to analyze the differences between accretion
structures surrounding boson stars and black holes. We aim at analysing the
physics of circular geodesics around boson stars and study simple thick
accretion tori (so-called Polish doughnuts) in the vicinity of these stars. We
realize a detailed study of the properties of circular geodesics around boson
stars. We then perform a parameter study of thick tori with constant angular
momentum surrounding boson stars. This is done using the boson star models
computed by a code constructed with the spectral solver library KADATH. We
demonstrate that all the circular stable orbits are bound. In the case of a
constant angular momentum torus, a cusp in the torus surface exists only for
boson stars with a strong gravitational scalar field. Moreover, for each inner
radius of the disk, the allowed specific angular momentum values lie within a
constrained range which depends on the boson star considered. We show that the
accretion tori around boson stars have different characteristics than in the
vicinity of a black hole. With future instruments it could be possible to use
these differences to constrain the nature of compact objects.
