  There may exist extended configurations in the dark matter sector that are
analogues of structures in the visible sector. In this work, we explore
non-topological solitonic configurations, specifically Q-balls, and study when
they may form macroscopic astrophysical structures and what their distinct
characteristics might be. We study in some detail theoretical bounds on their
sizes and constraints on the underlying parameters, based on criteria for an
astrophysical Q-ball's existence, gravitational stability and viability of
solutions. Following this path, one is able to obtain novel limits on
astrophysical Q-ball sizes and their underlying parameters. We also explore the
gravitational lensing features of different astrophysical Q-ball profiles,
which are more general than the simple thin-wall limit. It is seen that the
magnification characteristics may be very distinct, depending on the actual
details of the solution, even for astrophysical Q-balls having the same size
and mass. Assuming that such astrophysical Q-balls may form a small component
of the dark matter in the universe, we place limits on this fraction from the
gravitational microlensing surveys EROS-2, OGLE-IV, HSC-Subaru and the proposed
future survey WFIRST. Exploring various astrophysical Q-ball profiles and
sizes, it is found that while for most intermediate masses that we consider,
the dark matter fraction comprising astrophysical Q-balls is at most
sub-percent, for other masses it may be significantly higher.
