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An imperfect double: probing the physical origin of the low-frequency QPO and its harmonic in black hole binaries

We extract the spectra of the strong low-frequency quasi-periodic oscillation (QPO) and its harmonic during the rising phase of an outburst in the black-hole binary XTE J1550-564. We compare these frequency resolved spectra to the time-averaged spectrum and the spectrum of the rapid (<0.1s) variability. The spectrum of the time averaged emission can be described by a disc, a Compton upscattered tail, and its reflection. The QPO spectrum contains no detectable disc, and the Compton spectrum is generally harder than in the time averaged emission, and shows less reflection, making it very similar to the spectrum of the rapid variability. The harmonic likewise contains no detectable disc component, but has a Compton spectrum which is systematically softer than the QPO, softer even than the Compton tail in the time averaged emission. We interpret these results in the context of the Lense-Thirring model for the QPO, where a precessing hot flow replaces the inner disc, and the harmonic is produced by the angular dependence of Compton scattering within the hot flow. We extend these models to include stratification of the hot flow, so that it is softer (lower optical depth) at larger radii closer to the truncated disc, and harder (higher optical depth) in the innermost parts of the flow where the rapid variability is produced. The different optical depth with radius gives rise to different angular dependence of the Comptonised emission, weighting the fundamental to the inner parts of the hot flow, and the harmonic to the outer. This is the first model which can explain both the spectrum of the QPO and its harmonic in a self consistent geometry.