Resonant Dynamical Friction in Nuclear Star Clusters: Rapid Alignment of an Intermediate-mass Black Hole with a Stellar Disk

Abstract

We investigate the dynamical evolution of an intermediate-mass black hole (IMBH) in a nuclear star cluster hosting a supermassive black hole (SMBH) and both a spherical and a flattened disk-like distribution of stellar-mass objects. We use a direct N-body (phi GPU) and an orbit-averaged (N-ring) numerical integrator to simulate the orbital evolution of stars and the IMBH. We find that the IMBH's orbit gradually aligns with the stellar disk if their mutual initial inclination is less than 90 degrees. If it is larger than 90 degrees, i.e., counter-rotating, the IMBH does not align. Initially, the rate of orbital reorientation increases linearly with the ratio of the mass of the IMBH over the SMBH mass, and it is orders of magnitude faster than ordinary (i.e., Chandrasekhar) dynamical friction, particularly for high SMBH masses. The semimajor axes of the IMBH and the stars are approximately conserved. This suggests that the alignment is predominantly driven by orbit-averaged gravitational torques of the stars, a process that may be called resonant dynamical friction. The stellar disk is warped by the IMBH, and ultimately increases its thickness. This process may offer a test for the viability of IMBH candidates in the Galactic Center. Resonant dynamical friction is not limited to IMBHs; any object much more massive than disk particles may ultimately align with the disk. This may have implications for the formation and evolution of black hole disks in dense stellar systems and gravitational wave source populations for LIGO, VIRGO, KAGRA, and LISA.