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.