  A previous work found that a nonminimally coupled theory of gravity can,
under appropriate conditions, give rise to an additional contribution to the
field equations interpreted as dark matter [1]: in particular, the density of
this dark matter component was found to scale as a power of the density of
visible matter. However, no explicit solution for the modified field equations
was provided, so that a direct computation of the specific density profile
followed by visible matter is missing.
  This question is now addressed: analytical solutions to the modified field
equations are derived in the appropriate perturbative regime and characterised,
with an emphasis on directly obtaining the visible matter profile in a
self-consistent way. We compare with known profiles for visible and dark matter
and obtain constraints on the parameters of the model.
