Radiation-hydrodynamics of star-disc collisions for quasi-periodic eruptions

Quasi-periodic eruptions (QPEs) are recently discovered transients of unknown nature occurring near supermassive black holes, which feature bright X-ray bursts separated by hours to days. A promising model for QPEs is the star-disc collisions model, where a star repeatedly interacts with an accretion disc around a black hole, creating shocks that expel dense outflows of gas from which radiation emerges. We investigate the dynamics of the star-disc collisions, the properties of the outflows, and the resulting radiation signatures. Our study focuses on the generic case where the star remains unperturbed by the collision and the stellar crossing time through the disc is sufficiently long for shocked gas to flow around the star. We performed a three-dimensional (3D) radiation-hydrodynamics simulation of the star-disc collision. The star was modeled as a solid, spherical body, and the interaction was simulated for a small, local section of the accretion disc. We found that star-disc collisions generate a nearly paraboloidal bow shock. The heating of gas is not confined to the column of gas directly ahead of the star but also extends laterally as the shock front expands sideways while traveling with the star. As the star crosses the disc, it injects momentum preferentially along its direction of motion, leading to an asymmetric redistribution of energy and momentum. As a result, two outflows emerge on opposite sides of the disc with different properties: the forward outflow expands faster, contains more mass, carries more energy, and is about twice as luminous as the backward outflow. Our findings suggest that the asymmetry in outflow properties and luminosity arises naturally from the collision dynamics, offering a possible explanation for the alternating strong-weak flare patterns observed in several QPE sources.

💡 Research Summary

Quasi‑Periodic Eruptions (QPEs) are a recently discovered class of nuclear transients that show bright X‑ray flares recurring on timescales of hours to days. One of the most promising explanations is the star‑disc collision model, in which a star on an inclined orbit repeatedly pierces an accretion disc around a super‑massive black hole (SMBH). The impact generates strong shocks, expels dense, optically thick gas clouds, and the subsequent radiation from these outflows is observed as QPE flares. In this work the authors present the first fully three‑dimensional radiation‑hydrodynamics simulation of such a collision, focusing on the regime most relevant to observed QPEs: the disc vertical thickness is a few stellar radii, allowing shocked gas to flow around the star while the star itself remains essentially unperturbed.

The simulation uses the Smoothed‑Particle Hydrodynamics (SPH) code Phantom with a flux‑limited diffusion (FLD) treatment of radiation. The star is modeled as a rigid sphere of solar radius (R★ = R⊙) moving at v★ = 0.1 c perpendicular to a locally uniform disc segment. The disc parameters (height H = 3 R★, density ρd = 3.7 × 10⁻⁸ g cm⁻³) are chosen to match a radiation‑pressure‑dominated α‑disc around a 10⁶ M⊙ SMBH with a QPE period of ~4 h. The computational domain is a rectangular box (12 R★ × 12 R★ × 2H) filled with 1.5 million SPH particles. The star‑gas interaction is treated as elastic collisions; the star’s velocity is held fixed because its mass (≈ M⊙) exceeds the intercepted disc mass by a factor of ~10⁷.

The evolution proceeds through several distinct phases. As the star first contacts the disc (t ≈ 0.12 tcr, where tcr is the crossing time), a radiation‑pressure‑dominated bow shock forms, heating the gas and raising the radiation energy density. The shocked gas streams around the star; post‑shock velocities range from ~v★/7 up to the sound speed, comparable to v★. By t ≈ 0.25 tcr a quasi‑steady configuration is reached: inflow into the shock balances outflow around the star, and the shock front reaches the upper disc surface, producing a breakout. Gas that passes the star’s wake forms a secondary shock, reheating material and creating a distinct ejecta component.

When the bow shock reaches the lower disc surface (t ≈ 0.88 tcr) a second breakout occurs, launching a nearly spherical outflow in the forward direction (the direction of stellar motion). The outflows emerging from the upper and lower disc surfaces are markedly asymmetric. The forward (upper) outflow contains roughly twice the mass, has higher average velocity, and carries about twice the radiation energy compared with the backward (lower) outflow. Consequently, its bolometric luminosity is about a factor of two larger. This intrinsic asymmetry arises because the star injects momentum preferentially along its trajectory, leading to an uneven redistribution of kinetic and radiative energy.

The authors argue that this natural forward‑backward asymmetry can explain the alternating “strong–weak” flare pattern observed in several QPE sources: the brighter flare corresponds to the forward outflow, the dimmer to the backward one, and the observer’s line of sight determines which side is seen first. They also note that the shocked gas may be out of local thermodynamic equilibrium; photon production can be inefficient during rapid expansion, potentially yielding spectra with higher effective temperatures than a simple blackbody.

Several simplifying assumptions are discussed. Differential rotation (shear) of the disc is neglected because the crossing time is much shorter than the local shear time (tcr ≪ t shear). Gravitational forces from the SMBH, Coriolis, and centrifugal terms are omitted for the same reason. Self‑gravity of the gas and the star’s gravity are ignored because the kinetic energy imparted to the shocked gas dominates. The simulation does not include a low‑density ambient medium for radiation to escape once the gas becomes optically thin; tests in Appendix A show this omission has negligible impact on the main results. The star is treated as perfectly rigid; mass stripping or structural changes that could accumulate over many passages are not modeled.

The paper concludes that 3‑D radiation‑hydrodynamics simulations reveal a robust mechanism for producing asymmetric, luminous outflows from star‑disc collisions. The forward outflow’s higher mass, speed, and radiative energy naturally generate a flare roughly twice as bright as the backward one, offering a compelling physical explanation for the strong‑weak QPE phenomenology. The authors suggest future work should incorporate relativistic orbital dynamics, multi‑pass stellar evolution, and more realistic disc structures (including shear, magnetic fields, and vertical stratification) to fully capture the diversity of observed QPE behaviours.