Probing the origin of quasi-periodic oscillations: the short-time-scale evolution of phase lags in GRS 1915+105

We present a model-independent analysis of the short-time-scale energy dependence of low-frequency quasi-periodic oscillations (QPOs) in the X-ray flux of GRS 1915+105. The QPO frequency in this source has previously been observed to depend on photon energy, with the frequency increasing with energy for observations with a high (≳2 Hz) QPO frequency, and decreasing with energy for observations with a low (≲2 Hz) QPO frequency. As this observed energy dependence is currently unexplained, we investigate if it is intrinsic to the QPO mechanism by tracking phase lags on (sub)second time-scales. We find that the phase lag between two broad energy bands systematically increases for 5–10 QPO cycles, after which the QPO becomes decoherent, the phase lag resets and the pattern repeats. This shows that the band with the higher QPO frequency is running away from the other band on short time-scales, providing strong evidence that the energy dependence of the QPO frequency is intrinsic. We also find that the faster the QPO decoheres, the faster the phase lag increases, suggesting that the intrinsic frequency difference contributes to the decoherence of the QPO. We interpret our results within a simple geometric QPO model, where different radii in the inner accretion flow experience Lense–Thirring precession at different frequencies, causing the decoherence of the oscillation. By varying the spectral shape of the inner accretion flow as a function of radius, we are able to qualitatively explain the energy-dependent behaviour of both QPO frequency and phase lag