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Inclination dependence of QPO phase lags in black hole X-ray binaries

Quasi-periodic oscillations (QPOs) with frequencies from $\sim0.05$-$30$ Hz are a common feature in the X-ray emission of accreting black hole binaries. As the QPOs originate from the innermost accretion flow, they provide the opportunity to probe the behaviour of matter in extreme gravity. In this paper, we present a systematic analysis of the inclination dependence of phase lags associated with both Type-B and Type-C QPOs in a sample of 15 Galactic black hole binaries. We find that the phase lag at the Type-C QPO frequency strongly depends on inclination, both in evolution with QPO frequency and sign. Although we find that the Type-B QPO soft lags are associated with high inclination sources, the source sample is too small to confirm this as a significant inclination dependence. These results are consistent with a geometrical origin of Type-C QPOs and a different origin for Type-B and Type-C QPOs. We discuss the possibility that the phase lags originate from a pivoting spectral power law during each QPO cycle, while the inclination dependence arises from differences in dominant relativistic effects. We also search for energy dependences in the Type-C QPO frequency. We confirm this effect in the three known sources (GRS 1915+105, H1743-322 and XTE J1550-564) and newly detect it in XTE J1859+226. Lastly, our results indicate that the unknown inclination sources XTE J1859+226 and MAXI J1543-564 are most consistent with a high inclination.