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Characteristics of the High-frequency Humps in the Black hole X-ray Binary Swift J1727.8--1613

Ze-Xi Li, Liang Zhang, Lian Tao, Zi-Han Yang, Qing-Chang Zhao, Shu-Jie Zhao, Rui-Can Ma, Zi-Xu Yang, Pan-Ping Li, Xiang Ma, Yue Huang, Shu-Mei Jia, Shuang-Nan Zhang, Hua Feng, Jin-Lu Qu, Shu Zhang

Abstract

We present a detailed timing analysis of the two high-frequency humps observed in the power density spectrum of Swift J1727.8--1613 up to 100 keV, using data from the Hard X-ray Modulation Telescope (Insight-HXMT). Our analysis reveals that the characteristic frequencies of the humps increase with energy up to $\sim30$ keV, followed by a plateau at higher energies. The fractional rms amplitudes of the humps increase with energy, reaching approximately 15\% in the 50-100 keV band. The lag spectrum of the hump is characterized primarily by a soft lag that varies with energy. Our results suggest that the high-frequency humps originate from a corona close to the black hole. Additionally, by applying the relativistic precession model, we constrain the mass of Swift J1727.8--1613 to $2.84 < M / M_{\odot} < 120.01$ and the spin to $0.14 < a < 0.43$ from the full-energy band dataset, using triplets composed of a type-C quasi-periodic oscillation and two high-frequency humps. When considering only the high-energy bands with stable characteristic frequencies, we derive additional constraints of $2.84 < M/M_{\odot} < 13.98$ and $0.14 < a < 0.40$.

Characteristics of the High-frequency Humps in the Black hole X-ray Binary Swift J1727.8--1613

Abstract

We present a detailed timing analysis of the two high-frequency humps observed in the power density spectrum of Swift J1727.8--1613 up to 100 keV, using data from the Hard X-ray Modulation Telescope (Insight-HXMT). Our analysis reveals that the characteristic frequencies of the humps increase with energy up to keV, followed by a plateau at higher energies. The fractional rms amplitudes of the humps increase with energy, reaching approximately 15\% in the 50-100 keV band. The lag spectrum of the hump is characterized primarily by a soft lag that varies with energy. Our results suggest that the high-frequency humps originate from a corona close to the black hole. Additionally, by applying the relativistic precession model, we constrain the mass of Swift J1727.8--1613 to and the spin to from the full-energy band dataset, using triplets composed of a type-C quasi-periodic oscillation and two high-frequency humps. When considering only the high-energy bands with stable characteristic frequencies, we derive additional constraints of and .
Paper Structure (13 sections, 7 equations, 8 figures, 2 tables)

This paper contains 13 sections, 7 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Observation and Data Reduction
  3. Data Analysis and Results
  4. Power density spectrum and cross spectrum
  5. Energy-dependent properties of the QPO and high-frequency humps
  6. Measuring the mass and spin of the black hole with the Relativistic Precession Model
  7. Discussion
  8. Characteristics of the high-frequency humps
  9. The Mass and Spin of Swift J1727.8--1613
  10. Disk truncation
  11. Best-fitting parameters of the type-C QPO, $L_\mathrm{l}$ and $L_\mathrm{h}$ observed in the PDS of Swift J1727.8--1613. The errors presented in the table represent a $1\sigma$ confidence interval.
  12. The characteristic frequency and fractional rms of the type-C QPO, $L_\mathrm{l}$ and $L_\mathrm{h}$, together with the phase-lag of the type-C QPO and $L_\mathrm{l}$. The errors presented in the table represent a $1\sigma$ confidence interval.
  13. The best-fitting spectral parameters fitting to the NuSTAR spectrum (ObsID: 80902333004) of Swift J1727.8--1613 with the model Constant*Tbabs(diskbb+relxill+cutoffpl). Uncertainties are given at the 90 percent confidence level. The parameters $N_{\rm H}$, $a_*$ and emissivity indices ($\alpha_1$, $\alpha_2$) have been fixed during the fitting.

Figures (8)

  • Figure 1: $Insight$-HXMT LE 2-10 keV, ME 10-23 keV, and HE 23-100 keV light curves of Swift J1727.8--1613 during its 2023 outburst. Each data point corresponds to an exposure ID. The shaded regions mark the data groups selected for our timing analysis in this work.
  • Figure 2: $Insight$-HXMT hardness-intensity diagram (HID) of Swift J1727.8--1613 during its 2023 outburst. Each data point corresponds to an exposure ID. The different colored points represent the data groups selected for our timing analysis in this work.
  • Figure 3: Upper-left panel: PDS in the 4-10 keV energy band. Lower-left panel: phase lag versus Fourier frequency (phase-lag spectrum) together with the derived model obtained from the fits to the power and cross spectra. Upper-right and lower-right panels: Real and Imaginary parts of the cross spectrum calculated for the 4-10 keV band with respect to the 2-4 keV band. For the fitting and the plot, we rotated the cross-vector by $45\degree$. We modeled the PDS using 7 Lorentzian functions. Additionally, we fitted the Real and Imaginary parts of the cross spectrum by fixing the frequency and FWHM of each Lorentzian to the values derived from the best-fitting model of the PDS. Type-C QPO corresponds to the Lorentzian function used to fit the type-C QPO, while $L_{\rm l}$ and $L_{\rm h}$ represent the Lorentzian functions fitting the two high-frequency humps.
  • Figure 4: Energy dependence of the characteristic frequency and fractional rms of the type-C QPO and the two high-frequency humps ($L_{\rm l}$ and $L_\mathrm{h}$) for each data group. The color scheme for the 7 data groups follows that highlighted in Fig. \ref{['Fig2']}.
  • Figure 5: Energy dependence of the phase lag of the type-C QPOs and $L_{\rm l}$ for each data group. The color scheme for the 7 data groups follows that highlighted in Fig. \ref{['Fig2']}.
  • ...and 3 more figures