Anisotropic Star Clusters around Recoiling Supermassive Black Holes

Gravitational-wave recoil kicks from merging supermassive black hole binaries can have a profound effect on the surrounding stellar population. In this work, we study the dynamic and kinematic properties of nuclear star clusters following a recoil kick. We show that these postkick structures present unique signatures that can provide key insight to observational searches for recoiling supermassive black holes. In our previous paper, we showed that an in-plane recoil kick turns a circular disk into a lopsided, eccentric disk such as the one we observe in the Andromeda nucleus. Building on this work, here we explore many recoil kick angles as well as initial stellar configurations. For a circular disk of stars, an in-plane kick causes strong apsidal alignment with a significant fraction of the disk becoming retrograde at large radii. If the initial orbits are highly eccentric, an in-plane kick forms a bar-like structure made up of two antialigned lopsided disks. An out-of-plane kick causes clustering in the argument of periapsis, omega, regardless of the initial eccentricity distribution. Initially, isotropic configurations form anisotropies in the form of a torus of eccentric orbits oriented perpendicular to the recoil kick. Postkick surface density and velocity maps are presented in each case to highlight the distinct, observable structures of these systems.