  We study the Jeans-type gravitational instability for a self-gravitating
medium composed of two species, baryonic (bright) and dark matter particles,
using a hybrid quantum-classical fluid approach. Baryonic matter is treated
classically, which is appropriate for most astrophysical environments, e.g.,
Bok globules, while dark matter is treated through a quantum hydrodynamic
approach allowing for possible nonlinearities. These nonlinearities may arise
in bosonic dark matter due to attractive or repulsive short-range
self-interaction (attractive interaction being more relevant for axions) or
from the Pauli exclusion principle for fermionic dark matter, e.g., massive
neutrinos. This allows us to explore, in a very broad context, the impact of a
dark matter background on the Jeans process for different scenarios discussed
in the literature. In the simplest case, it is shown that the effect of a dark
matter background on the Jeans mass depends only on the ratio of densities and
velocity dispersions of baryonic and dark matter particles. Taking advantage of
that, we confront the established stability criterion with Bok globule
stability observations and show that the model adequately accounts for the data
with dark matter parameters close to those predicted independently from
numerical simulations.
