Investigation of the Quasi-periodic Oscillation Phase Lag of RE J1034+396

Abstract We conduct an in-depth study of the quasi-periodic oscillation (QPO) properties of RE J1034+396 by constructing QPO phase-folded light curves from 10 XMM-Newton observations during 2020–2021. Our analysis reveals that the QPO in the source exhibits two mutually convertible lag-energy modes: “hard lag” and “soft lag.” Despite different lag characteristics, the energy dependencies of the rms amplitude of the QPO under both modes are consistent, suggesting the two types of QPO originate from the same physical mechanism. By performing a spectral analysis, we further find a correlation between time-lag modes and spectral states: the soft lag mode typically corresponds to harder X-ray spectra and higher blackbody temperatures. Through comprehensive comparison of multiple theoretical models, we propose that the relativistic precession model of the corona provides a plausible qualitative explanation for the observed complex phenomena, including time-lag mode transitions, and variations of spectral hardness and QPO signal strength.