Resolving Oblique Star-Disk Collisions in Quasi-Periodic Eruptions: Numerical Requirements and the Importance of Geometry

Abstract

Star-disk collisions have been proposed as a promising mechanism for producing quasi-periodic eruptions (QPEs) in galactic nuclei. Because the stellar atmospheric scale height is orders of magnitude smaller than the stellar radius, studying the shock launching by stars poses a significant numerical challenge. We implement an immersed solid-boundary method in Athena++ to study bow-shock formation and ejecta launching when a solid sphere crosses an accretion disk at supersonic speed. After validating the method against experimental results for solid bodies in uniform flows, we perform two- and three-dimensional adiabatic simulations of star-disk collisions. We find that resolving the bow-shock stand-off distance during the compression phase is essential: under-resolved simulations severely underestimate the ejecta mass and energy. When adequately resolved, the ejecta properties agree well with analytical estimates. We further show that collision geometry plays a critical role. Oblique encounters, which arise naturally due to disk rotation, allow easier shock breakout from the disk's backside and substantially reduce the luminosity contrast between forward and backward ejecta compared to perpendicular collisions. These results emphasize the importance of both numerical resolution and three-dimensional geometry in modeling star-disk collisions and interpreting QPEs.

Figures (15)

• Figure 1: Schematic illustration of a star-disk collision producing quasi-periodic eruptions (QPEs). A star repeatedly intersects the accretion disk around the central supermassive black hole, generating episodic energy release. The lower portion of the figure shows representative three-dimensional renderings from our 3D simulations, included for illustrative purposes (see Section \ref{['subsec:result_3d']} for details). Note that, even if the star's orbital plane is perpendicular to the disk plane, the collision is oblique due to the disk's rotation.
• Figure 2: Density snapshots of a solid body in a uniform supersonic flow with different $\mathcal{M}$. From left to right, each column represents $\mathcal{M} = 1.5$, $2.0$, $2.5$, $3.0$, and $4.0$, respectively. The top row shows results from 2D simulations, and the bottom row shows the midplane ($z=0$) of 3D simulations. The cyan line in the third panel of the first row represents the shock standoff distance. The adiabatic index is $\gamma = 1.4$ for these plots.
• Figure 3: The snapshot of steady-state Mach number at midplane ($z=0$) for 3D simulation with $\mathcal{M} = 4$.
• Figure 4: Shock stand-off distance $R_{\rm sod}$ as a function of the Mach number $\mathcal{M}$. nes are the best fit for the experimental results from 1967Billig. The blue and red crosses represent results from 2D and 3D simulations, respectively. The blue and red lines are the best fit from the experiment for the cylinder wedge and spherical body (1967Billig), respectively.
• Figure 5: Density snapshots for the star-disk collision with different resolutions and SMR levels. Each column represents a different configuration: the first four columns correspond to a resolution of $1024\times 1600$ with SMR levels 0, 1, 2, and 3, respectively, while the fifth column shows results at a uniform resolution of $4096\times 6400$. Note that the effective highest resolution of the third column ($1024\times 1600$ with SMR level 2) around the star is equivalent to the resolution of the fifth column. Rows represent the simulation time at frames $-43.6\,{\rm s}$, $43.6\,{\rm s}$, $174.5\,{\rm s}$, and $327.2\,{\rm s}$, from top to bottom. The gray horizontal lines represent the disk's mid-plane, and the green lines represent $4H_{\rm d}$ from the mid-plane.