Oscillations of the Eddington Capture Sphere

TL;DR

This paper models how the Eddington Capture Sphere causes periodic luminosity variations in accreting compact stars, with frequency inversely related to luminosity, providing insights into observed quasi-periodic oscillations.

Contribution

It introduces a toy model linking the Eddington Capture Sphere to luminosity oscillations and characterizes the frequency and quality factor dependencies on accretion parameters.

Findings

Luminosity oscillations are predicted to be periodic with frequency inversely proportional to luminosity.

The model shows quasi-periodic luminosity variations when accretion rate varies periodically.

Maximum quality factor of oscillations is approximately 10, occurring at 1-2 kHz for a 2 solar mass star.

Abstract

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.