Imprints of recoiling massive black holes on the hot gas of early-type galaxies

Anisotropic gravitational radiation from a coalescing black hole (BH) binary is known to impart recoil velocities of up to  ∼1000 km s⁻¹  to the remnant BH. In this context, we study the motion of a recoiling BH inside a galaxy modelled as a Hernquist sphere, and the signature that the hole imprints on the hot gas, using N -body/smoothed particle hydrodynamics simulations. Ejection of the BH results in a sudden expansion of the gas ending with the formation of a gaseous core, similarly to what is seen for the stars. A cometary tail of particles bound to the BH is initially released along its trail. As the BH moves on a return orbit, a nearly spherical swarm of hot gaseous particles forms at every apocentre: this feature can live up to ≈10⁸ years. If the recoil velocity exceeds the sound speed initially, the BH shocks the gas in the form of a Mach cone in density near each supersonic pericentric passage. We find that the X-ray fingerprint of a recoiling BH can be detected in Chandra X-ray maps out to a distance of Virgo. For exceptionally massive BHs, the Mach cone and the wakes can be observed out to a few hundred of milliparsec. The detection of the Mach cone is of twofold importance as it can be a probe of high-velocity recoils, and an assessment of the scatter of the   M _BH− M _bulge  relation at large BH masses.