  Bosonic fields can give rise to self-gravitating structures. These are
interesting hypothetical new "dark matter stars" and good descriptions of dark
matter haloes if the fields are very light. We study the dynamical response of
Newtonian boson stars (NBS) when excited by external matter (stars, planets or
black holes) in their vicinities. Our setup can describe the interaction
between a massive black hole and the surrounding environment, shortly after the
massive body has undergone a "kick", due to the collapse of baryonic matter at
the galactic center, or dark matter depletion as a reaction to an inspiralling
binary. We perform the first self-consistent calculation of dynamical friction
acting on moving bodies in these backgrounds. Binaries close to coalescence
"stir" the NBS core, and backreaction affects gravitational waveforms at
leading $-6PN$ order with respect to the dominant quadrupolar term; the
coefficient is too small to allow detection by next-generation interferometers.
We also show that the gravitational collapse to a supermassive black hole at
the center of a NBS is accompanied by only a small change in the surrounding
core. The NBS eventually gets accreted, but for astrophysical parameters this
occurs only after several Hubble times.
