  LIGO and Virgo have recently observed a number of gravitational wave (GW)
signals that are fully consistent with being emitted by binary black holes
described by general relativity. However, there are theoretical proposals of
exotic objects that can be massive and compact enough to be easily confused
with black holes. Nevertheless, these objects differ from black holes in having
nonzero tidal deformabilities, which can allow one to distinguish binaries
containing such objects from binary black holes using GW observations. Using
full Bayesian parameter estimation, we investigate the possibility of
constraining the parameter space of such "black hole mimickers" with upcoming
GW observations. Employing perfect fluid stars with a polytropic equation of
state as a simple model that can encompass a variety of possible black hole
mimickers, we show how the observed masses and tidal deformabilities of a
binary constrain the equation of state. We also show how such constraints can
be used to rule out some simple models of boson stars.
