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

TL;DR

This work analyzes a series of 10 XMM-Newton observations of RE J1034+396 to study the quasi-periodic oscillation (QPO) and its phase-lag behavior across energy bands. Using Hilbert-Huang Transform with Variational Mode Extraction, the authors extract phase-resolved QPOs and demonstrate two mutually convertible lag-energy modes: hard lag and soft lag, with consistent RMS-energy dependence. Spectral modeling reveals that soft-lag states correspond to harder spectra and higher blackbody temperatures, while hard-lag states are associated with softer spectra; no strong iron line is detected. A relativistic precession model (RPM) of a precessing corona emerges as a plausible qualitative explanation for the observed phase-lag transitions and their coupling to spectral hardness, offering a cohesive interpretation of the timing-spectral phenomenology in this AGN.

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.

Figures (7)

• Figure 1: (a),(b)Lomb-Scargle periodogram analysis of observation 1 and combined data from 10 observations (1--10 keV). Upper left: light curve; Upper right: power spectrum over 0.01-5 mHz; Lower left: detailed power spectrum in the QPO frequency band (0.1-1 mHz); Lower right: power distribution. The dashed line shows the statistical significance level.
• Figure 2: (a) Light curve of Observation 5 analyzed using Hilbert-Huang Transform. Blue line represents the original light curve (with 100-second time binning), red line represents the intrinsic QPO light curve, and orange line represents the instantaneous QPO phase obtained using HSA; (b) MCMC fitting results and residuals for two-period phase-folded light curves of observation 5 in the 0.2--0.7 keV (blue) and 2--10 keV (yellow, count rate multiplied by 10) energy bands. Points and short lines represent binned data points with errors, and long lines represent MCMC fitted curves (with width representing 1$\sigma$ confidence intervals). (c) Normalized fitting curves and their confidence intervals for Observation 5 across five energy bands: 0.2--0.7$\,\mathrm{keV}$, 0.7--1$\,\mathrm{keV}$, 1--1.3$\,\mathrm{keV}$, 1.3--2$\,\mathrm{keV}$, and 2--10$\,\mathrm{keV}$.
• Figure 3: (a) Fractional rms of QPO versus energy for $10$ observations; (b) Energy dependence of the phase lag for $10$ observations; (c) , (d) Fractional rms-energy and phase shift-energy relationship after combining soft and hard lag data. Both fractional rms and phase lags are from the best-fitting results of MCMC.
• Figure 4: Relationship between hardness ratio and phase lag for 10 observations, where hardness ratio $HR = H/S$, with $H$ being the count rate in the hard band ($1$--$10\,\mathrm{keV}$) and $S$ being the count rate in the soft band ($0.3$--$1\,\mathrm{keV}$). Phase lag is taken as the difference between phase shift values of the $1$--$10\,\mathrm{keV}$ and $0.3$--$1\,\mathrm{keV}$ energy bands.
• Figure 5: Upper panel: Joint fitting results of energy spectra (eeuf) for $9$ observations, with blue representing soft lag and red representing hard lag. Component 1 represents powerlaw and component 2 represents thcomp*bbody; Middle panel: Residual plots of energy spectra for the $9$ observations; Bottom panel: The variation of average flux ratio and its error between the soft lag group and hard lag group with energy, calculated from the total model.