Coupling between QPOs and broad-band noise components in GRS 1915+105

We explore the use of the bispectrum for understanding quasi-periodic oscillations. The bispectrum is a statistic which probes the relations between the relative phases of the Fourier spectrum at different frequencies. The use of the bispectrum allows us to break the degeneracies between different models for time series which produce identical power spectra. We look at data from several observations of GRS 1915+105 when the source shows strong quasi-periodic oscillations and strong broad-band noise components in its power spectrum. We show that, despite strong similarities in the power spectrum, the bispectra can differ strongly. In all cases, there are frequency ranges where the bicoherence, a measure of non-linearity, is strong for frequencies involving the frequency of the quasi-periodic oscillations, indicating that the quasi-periodic oscillations are coupled to the noise components, rather than being generated independently. We compare the bicoherences from the data to simple models, finding some qualitative similarities.