  We analyse perturbations of self-interacting, scalar field dark matter that
contains modes both in a coherent condensate state and an incoherent
particle-like state. Starting from the coupled equations for the condensate,
the particles' phase space distribution and their mutual gravitational
potential, first derived from first principles in earlier work by the authors,
we derive a hydrodynamic limit of two coupled fluids and study their linearized
density perturbations in an expanding universe, also including particle
pressure under an assumption for an equation of state consistent with the
dynamical equations. We find that away from the condensate-only or
particle-only limits, and for certain ranges of the parameters, such
self-interacting mixtures can significantly enhance the density power spectrum
above the standard linear $\Lambda$CDM value at localised wavenumbers, even
pushing structure formation into the non-linear regime earlier than expected in
$\Lambda$CDM for these scales. We also note that such mixtures can lead to
degeneracies between models with different boson masses and self-coupling
strengths, in particular between self-coupled models and non-coupled Fuzzy Dark
Matter made up of heavier bosons. These findings open up the possibility of a
richer phenomenology in scalar field dark matter models and could further
inform efforts to place observational limits on their parameters.
