Massive black hole ( BH ) mergers can result in the merger remnant receiving a “ kick , ” of order 200 km s ^ { -1 } or more , which will cause the remnant to oscillate about the galaxy centre .
Here we analyze 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 disk , 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 disk radial motion near but somewhat less than the “ resonant radii ” r _ { R } where the BH oscillation frequency is equal one-half , one-fourth , ( 1 / 6 , etc . )
of the radial epicyclic frequency in the plane of the disk .
Near the resonant radii there can be a strong enhancement of the radial flow and disk 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 _ { \odot } 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 disk stretches the wake into ring-like segments .