The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.