Black Holes' Dark Dress: On the merger rate of a subdominant population of primordial black holes

The formation of astrophysical and primordial black holes influences the distribution of dark matter surrounding them. Black holes are thus expected to carry a dark matter dress' whose properties depend on their formation mechanism and on the properties of the environment. Here we carry out a numerical and analytical study of the merger of dressed black holes, and show that the distribution of dark matter around them dramatically affects the dynamical evolution of the binaries. Although the final impact on the merger rate of primordial black holes is rather small with respect to the case of naked’ black holes, we argue that our analysis places the calculation of this rate on more solid ground, with LIGO-Virgo observations ruling out a dark matter fraction of ${10}^{-3}$ for primordial black holes of 100 solar masses, and it paves the way to more detailed analyses of environmental effects induced by dark matter on the gravitational wave emission of binary black holes.