Shot noise cross-correlation functions and cross spectra - Implications for models of QPO X-ray sources

The cross-correlation functions (CCFs) and cross spectra expected for quasi-periodic oscillation (QPO) shot noise models are calculated under various assumptions, and the results are compared to observations. Effects due to possible coherence of the QPO oscillations are included. General formulas for the cross spectrum, the cross-phase spectrum, and the time-delay spectrum for QPO shot models are calculated and discussed. It is shown that the CCFs, cross spectra, and power spectra observed for Cyg X-e2 imply that the spectrum of the shots evolves with time, with important implications for the interpretation of these functions as well as of observed average energy spectra. The possible origins for the observed hard lags are discussed, and some physical difficulties for the Comptonization model are described. Classes of physical models for QPO sources are briefly addressed, and it is concluded that models involving shot formation at the surface of neutron stars are favored by observation.