Oscillations of the Eddington Capture Sphere

We present a toy model of mildly super-Eddington, optically thin accretion onto a compact star in the Schwarzschild metric, which predicts periodic variations of luminosity when matter is supplied to the system at a constant accretion rate. These are related to the periodic appearance and disappearance of the Eddington Capture Sphere. In the model the frequency is found to vary inversely with the luminosity. If the input accretion rate varies (strictly) periodically, the luminosity variation is quasi-periodic, and the quality factor is inversely proportional to the relative amplitude of mass accretion fluctuations, with its largest value approximately Q= 1/(10 |delta Mdot/Mdot|) attained in oscillations at about 1 to 2 kHz frequencies for a 2 solar mass star.

💡 Research Summary

The paper introduces a highly simplified (“toy”) model to explore how a modestly super‑Eddington, optically thin inflow onto a compact star can generate periodic luminosity variations purely through the dynamics of the so‑called Eddington Capture Sphere (ECS). In the Schwarzschild metric, the ECS is defined as the spherical surface where outward radiation pressure exactly balances inward gravity; inside this surface matter can be held in quasi‑static equilibrium, while outside it is pushed away. The authors assume a constant mass supply rate (Ṁ₀) arriving from infinity. As the inflowing gas reaches the ECS it piles up because the radiation pressure prevents further infall. When the accumulated mass reaches a critical value, the radiation field intensifies, the ECS collapses, and the stored material free‑falls onto the stellar surface, producing a sharp luminosity spike. The star then cools, the radiation pressure drops, the ECS reforms at a larger radius, and the cycle repeats.

From the balance of forces the radius of the ECS scales linearly with the instantaneous luminosity L (r_ECS ∝ L/L_Edd). Consequently the time required for matter to travel from the ECS to the surface, and hence the oscillation period T, is inversely proportional to L. The model therefore predicts a frequency–luminosity relation ν ∝ L⁻¹, i.e., higher luminosities produce lower oscillation frequencies.

If the mass inflow is not perfectly steady but varies sinusoidally (Ṁ(t)=Ṁ₀