Ring formation from an oscillating black hole

Massive black hole (BH) mergers can result in the merger remnant receiving a 'kick' of the order of 200 km s(-1) or more, which will cause the remnant to oscillate about the galaxy centre. Here, we analyse the case where the BH oscillates through the galaxy centre perpendicular or parallel to the plane of the galaxy for a model galaxy consisting of an exponential disc, a Plummer model bulge and an isothermal dark matter halo. For the perpendicular motion, we find that there is a strong resonant forcing of the disc radial motion near but somewhat less than the 'resonant radii' r(R) where the BH oscillation frequency is equal to one-half, one-fourth, one-sixth, etc. of the radial epicyclic frequency in the plane of the disc. Near the resonant radii, there can be a strong enhancement of the radial flow and disc density which can lead to shock formation. In turn, the shock may trigger the formation of a ring of stars near r(R). As an example, for a BH mass of 10(8)M(circle dot) and a kick velocity of 150 km s(-1), we find that the resonant radii lie between 0.2 and 1 kpc. For BH motion parallel to the plane of the galaxy, we find that the BH leaves behind it a supersonic wake where star formation may be triggered. The shape of the wake is calculated as well as the slow-down time of the BH. The differential rotation of the disc stretches the wake into ring-like segments.