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

Technical Summary: Radiation Hydrodynamics of Star-Disc Collisions for Quasi-Periodic Eruptions

Problem Statement
Quasi-periodic eruptions (QPEs) are luminous X-ray transients occurring near supermassive black holes (SMBHs), characterized by bright bursts separated by hours to days. A leading theoretical model posits that these eruptions result from a star on an inclined orbit repeatedly colliding with an accretion disc. While previous studies have explored star-disc interactions, many lacked detailed radiation transport or focused on regimes where the star is significantly perturbed or the crossing time is too short for gas to flow around the star. Furthermore, the physical origin of the observed alternating "strong-weak" flare patterns in some QPE sources remains to be fully explained by collision dynamics. This study addresses the need for a three-dimensional (3D) radiation-hydrodynamics treatment of the collision in the regime where the star remains largely unperturbed and the shocked gas has sufficient time to flow around it.

Methodology
The authors performed a 3D radiation-hydrodynamics simulation using the smoothed particle hydrodynamics (SPH) code Phantom. The simulation was conducted in a reference frame co-moving with the accretion disc to isolate the local collision dynamics.

• Setup: A rigid, spherical star ($R_\star = R_\odot$) moves perpendicularly through a uniform, optically thick, radiation-pressure-dominated accretion disc ($H = 3R_\star$, $\rho_d = 3.7 \times 10^{-8}$ g cm$^{-3}$) at a velocity of $v_\star = 0.1c$. The system parameters correspond to an SMBH mass of $10^6 M_\odot$ and a QPE period of 4 hours.
• Physics: The gas follows an adiabatic equation of state ($\Gamma = 5/3$). Radiation transport is treated via the flux-limited diffusion approximation, assuming local thermodynamical equilibrium (LTE). The star is modeled as a rigid body interacting elastically with gas particles; gravitational forces from the SMBH and self-gravity are neglected as the collision timescale is much shorter than orbital timescales.
• Scope: The simulation focuses on a localized section of the disc ($12R_\star \times 2H$) to resolve the shock structure and outflow formation without the computational cost of a global simulation.

Key Contributions
This work presents the first 3D radiation-hydrodynamics simulation of a star-disc collision specifically targeting the parameter space relevant to most QPEs (where the disc is thick enough for gas to flow around the star). The study provides a detailed analysis of:

1. The formation and evolution of the bow shock and secondary shocks.
2. The asymmetric redistribution of momentum and energy injected by the star.
3. The distinct properties of the forward and backward outflows.
4. The resulting bolometric light curves and effective temperatures.

Results

• Shock Dynamics: The collision generates a nearly paraboloidal bow shock that travels with the star and expands laterally. A secondary shock forms in the star's wake as gas streams converge. The lateral expansion of the shock front follows a power-law scaling ($r_\perp \propto t^{0.4}$), slightly shallower than the steady-state $t^{0.5}$ prediction, indicating the system is still evolving toward a steady state.
• Asymmetric Outflows: The collision produces two distinct outflows on opposite sides of the disc:
  • Forward Outflow (direction of motion): This flow is driven by a quasi-spherical shock breakout as the star exits the disc. It expands faster, contains significantly more mass (approx. 10 times the backward flow), carries more energy and momentum, and is approximately twice as luminous as the backward outflow.
  • Backward Outflow: This flow lacks a quasi-spherical breakout component. It is formed by gas that flows around the star and is redirected by the secondary shock or escapes from the upper disc edge. It is less massive and less luminous.
• Luminosity and Light Curves: The forward outflow reaches a peak bolometric luminosity of $\sim 10^{41}$ erg s$^{-1}$, roughly double that of the backward outflow. The forward light curve exhibits a rapid rise followed by a break to a slower decline, interpreted as a shift from radiation emerging from the initial shock breakout ejecta to radiation from gas escaping the cavity after a longer delay. The effective temperatures peak at $\sim 29$ eV for the forward flow and slightly lower for the backward flow.
• Momentum Injection: The star injects momentum preferentially along its direction of motion. The total vertical momentum of the shocked gas asymptotes to $P_z \approx -0.45 M_d v_\star$, reflecting the anisotropic nature of the energy injection and the oblique angles of gas reflection.

Significance and Claims
The authors claim that the intrinsic asymmetry in the collision dynamics naturally explains the "strong-weak" flare patterns observed in several QPE sources (e.g., GSN 069). Because the forward outflow is significantly more luminous than the backward outflow, an observer viewing the system from a specific angle would see alternating bright and dim flares corresponding to the star's successive passages through the disc.

The study concludes that the star-disc collision model, in the regime where the star remains unperturbed, can reproduce the observed peak luminosities ($10^{41}-10^{43}$ erg s$^{-1}$), timescales (hours), and the alternating luminosity patterns of QPEs. The authors note limitations, including the use of a rigid star (neglecting mass stripping and deformation), the LTE assumption (which may break down in photon-starved regimes), and the neglect of global disc rotation and SMBH gravity. They suggest that future work incorporating non-LTE physics and realistic stellar structures is necessary to fully constrain the model and address discrepancies in spectral hardness (simulated $\sim 30$ eV vs. observed $\sim 100-200$ eV).