The Role of Self-Gravity in Debris Disk Warp Formation: The Case of HD 110058

Abstract

We investigate the crucial role of self-gravity in the formation of warps in debris disks, focusing on the HD 110058 system as an example. Using advanced, GPU-accelerated $N$-body simulations, we model the gravitational dynamics of a massive planetesimal disk perturbed by an inclined, inner planet. Our simulations reveal that self-gravity fundamentally alters the disk's evolution compared to massless models. It enforces a coherent, semi-rigid precession of the disk and enables the rapid formation of a global warp structure within 0.5 Myr. The warp angle undergoes a damped oscillation, eventually settling into a quasi-equilibrium state. By generating synthetic scattered-light images, we demonstrate that our model successfully reproduces the observed S-shaped warp morphology of the debris disk in HD 110058, supporting the existence of an unseen planet. Furthermore, we derive an empirical relationship that connects the equilibrium warp angle to the physical parameters of the disk and the planet. Applying this relation to HD 110058, we constrain its disk mass to be likely less than 1,000 $M_\oplus$, offering a new dynamical perspective on the debris disk mass problem.