  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.
