  The existence of black holes remains open to doubt until other conceivable
options are excluded. With this motivation, we consider a model of a compact
star in which most of the mass consists of dark particles of some kind, and a
small fraction of the mass is in the form of ordinary nucleonic gas. The gas
does not interact with the dark matter other than via gravity, but collects at
the center as a separate fermionic fluid component. Depending on whether the
dark mass is made of fermions or bosons, the objects may be called
fermion-fermion stars or boson-fermion stars, respectively. For appropriate
choices of the mass of the dark matter particles, these objects are viable
models of black hole candidates in X-ray binaries. We consider models with a
dark mass of 10 solar masses and a range of gas mass from 10^{-6} to nearly one
solar mass, and analyse the bursting properties of the models when they accrete
gas. We show that all the models would experience thermonuclear Type I X-ray
bursts at appropriate mass accretion rates. Since no Type I bursts have been
reported from black hole candidates, the models are ruled out. The case for
identifying black hole candidates in X-ray binaries as true black holes is thus
strengthened.
