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

TL;DR

This study analyzes the phase lag properties of QPOs in RE J1034+396, revealing two lag modes and linking them to spectral states, with the relativistic precession model explaining the phenomena.

Contribution

It is the first detailed analysis connecting QPO lag modes, spectral states, and theoretical models in RE J1034+396.

Findings

Identification of two QPO lag-energy modes: hard and soft lag.

Correlation between lag modes and spectral states.

Relativistic precession model plausibly explains observed phenomena.

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 dependency of the root mean square (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 (RPM) 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.