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

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.