On the Eddington Capture Surface around Spherically Symmetric Compact Objects with Separable Luminosity Distributions

Radiation exerts pressure, and therefore it is possible for an intensely bright object to balance the gravitational force near a massive compact object. General relativity demonstrates that this balance occurs for super-Eddington luminosities at a finite distance from the center of the mass. These equilibrium positions are referred to as Eddington capture surfaces (ECSs). At the ECSs, particles can collect in a thin shell, balanced between the inward curvature of spacetime and the outward flow of radiation. We adopt spherical symmetry but otherwise leave the metric functions generalized. This approach allows us to study the ECSs under the effect of arbitrary spherically symmetric metrics. We adopt a separable luminosity function that depends on both the radial direction and the angular coordinates over the surface of the star. We demonstrate that the morphology of an ECS varies depending on the angular luminosity distribution and can even split into multiple, separate, disconnected equilibrium surfaces. The ECS phenomenon is closely related to type I photospheric radius expansion X-ray bursts.