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Black Holes (BH) traversing a dark matter cloud made out of aself-interacting scalar soliton are slowed down by two complementary effects.At low subsonic speeds, the BH accretes dark matter and this is the only sourceof dragging along its motion, if we neglect the backreaction of the cloudself-gravity. The situation changes at larger supersonic speeds where a shockappears. This leads to the emergence of an additional friction term, associatedwith the gravitational and scalar pressure interactions and with the wakebehind the moving BH. This is a long distance effect that can be captured bythe hydrodynamical regime of the scalar flow far away from the BH. Thisdynamical friction term has the same form as the celebrated Chandrasekharcollisionless result, albeit with a well-defined Coulomb logarithm and aprefactor that is smaller by a factor 2/3. The infra-red cut-off is naturallyprovided by the size of the scalar cloud, which is set by the scalar mass andcoupling, whilst the ultra-violet behaviour corresponds to the distance fromthe BH where the velocity field is significantly perturbed by the BH, which isdetermined by pressure effects. As a result, supersonic BH are slowed down byboth the accretion drag and the dynamical friction. This effect will bepotentially detectable by future gravitational wave experiments as itinfluences the phase of the gravitational wave signal from inspirallingbinaries.

Supersonic friction of a black hole traversing a self-interacting scalar dark matter cloud