Quasi-periodic Eruptions from Stellar-mass Black Holes Impacting Accretion Disks in Galactic Nuclei

Abstract

We investigate the origins of quasi-periodic eruptions (QPEs) in galactic nuclei using global three-dimensional meshless finite-mass (MFM) simulations. By modeling stellar and black-hole impactors traversing accretion disks under various inclinations and surface densities, we evaluate their consistency with the observed properties of QPEs. Stellar impacts produce highly asymmetric bipolar ejecta with forward outbursts dominating by over an order of magnitude in energy and luminosity due to the star blocking downstream flow and creating a low-density wake. This shock-compression mechanism often renders backward events unobservable, implying one detectable burst per orbit, and challenging the standard assumption of two bursts. It also fails to explain alternating long-short recurrence patterns and places several sources near or within twice the tidal disruption radius for solar-mass stars, raising severe stability concerns. Whereas a stellar-mass black hole (sBH) gravitationally focuses and heats disk gas extending from its Bondi radius $R_{\rm B}$ to its Hill radius $R_{\rm H}$ during an impact, yielding nearly symmetric ejecta with mild contrasts. This gravitational-drag mechanism generates higher energy budgets at low inclinations due to enhanced mass accumulation. We suggest an ad hoc effective interaction radius $ R_{\rm eff} \simeq 0.5\, R_{\rm B}^{1/3} R_{\rm H}^{2/3} $ to quantify this trend. Our semi-analytical model confirms that sBH-disk collisions can power the full QPE energy range ($10^{44}$-$10^{48}$ erg), naturally accounting for periodicity, asymmetry, durations and diversity.

Figures (8)

• Figure 1: Schematic illustration of an extreme mass-ratio inspirals (EMRIs) system, where a stellar-mass black hole (sBH) moves along a low-inclination orbit and penetrates an optically thick accretion disk with a relative velocity below the local Keplerian speed. During each orbital period, the sBH impacts the disk twice, exciting nearly symmetric ejecta in the vertical directions. The ejecta subsequently expand and cool, evolving into optically thin bubbles through which radiation can escape. Meanwhile, strong gravitational perturbations induce local spiral-shaped density waves in the disk material.
• Figure 2: Upper panel: Energy budget estimated with the Linial's model for a surface density of $10^6~\mathrm{g\,cm^{-2}}$. The blue solid and red dashed curves correspond to shocked regions of radius $R_{\mathrm{B}}$ and $2R_{\mathrm{B}}$. The gray dotted line indicates the minimum energy budget observed for GSN 069, $\simeq 7\times10^{45}\,\mathrm{erg}$miniutti2023AA...670A..93MGuo2026ApJ...998...78G. Lower panel: Duration time as a function of inclination. The blue curve shows the prediction of the sBH-disk model, while the red dashed curve corresponds to the star-disk model.
• Figure 3: Global simulation of a full accretion disk impacted by an EMRI. The color scale shows the absolute velocity perturbation $|\Delta v|/c$ relative to the unperturbed disk. Regions outside of the Hill sphere remain essentially unaffected by the intruder. The white box outlines the simulation domain we adopted in our production runs. This sector has a radial width of $\sim 0.2~\mathrm{AU}$, and spans an azimuthal angle corresponding to $\sim 1/16$ of the local disk circumference, centered on the impact point. The upper-right panel displays a magnified view of the stellar EMRI resolved by $\sim10^5$ MFM particles in our simulations.
• Figure 4: Vertical slices through the disk along the azimuthal direction showing the density distribution and velocity field. Arrow lengths are not to scale. (a) The bow shock is generated by a star-disk collision, and downstream material fills the low-density cavity left by the star's passage, producing backward ejecta; (b) The perturbation induced by the sBH-disk interaction, exhibiting a bow-shock-like structure. The black hole attracts surrounding material along its path, producing a pronounced density enhancement and quickly generates backward ejecta. (The size of black-filled part is bondi radius of sBH.)
• Figure 5: Projected density plot for three simulations in Table \ref{['tab:table']}, which involve stellar or black hole impacts on the disk at inclinations of $\pi/10$ and $\pi/2$. In the first column, arrows mark the directions of motion of both the disk gas and the impactor. For each simulation, the snapshots are shown at 0.25, 0.5, and 1.0 hours after the initial contact.