Abstract

In a galactic nucleus, the gravitational potential is dominated by the SMBH , around which the stars are on nearly Keplerian orbits. The cluster of stars acts as a fluctuating perturbation to the potential, leading to a relaxation of the stars’ orbital planes in a process called Vector Resonant Relaxation (VRR). The equilibrium of VRR is a state in which the orbital planes of the massive stars self-align, forming a narrow stellar disk. We present a maximum entropy method to systematically and efficiently compute this long-term distribution. We use this algorithm to explore parameter space, and find two results relevant to astrophysics. First, the thickness of the disk is related to the stars’ and the BHs’ initial mass functions. This highlights a possible new (indirect) method to constrain the mass distribution of IMB Hs in galactic nuclei. Second, the thickness of the disk also depends on the geometry of star formation. This could help understand how stars form in galactic nuclei. Finally, the thermodynamics of VRR are also intriguing, with negative temperatures, negative specific heats, phase transitions and ensemble inequivalence.