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 post-kick structures present unique signatures that can provide key insight to observational searches for recoiling supermassive black holes. In Akiba & Madigan (2021), 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 initial orbits are highly eccentric, an in-plane kick forms a bar-like structure made up of two anti-aligned 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. Post-kick surface density and velocity maps are presented in each case to highlight the distinct, observable structures of these systems.