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

Stirred and shaken: dynamical behavior of boson stars and dark matter cores