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Gaussian process analysis of type-B quasiperiodic oscillations in the black hole X-ray binary MAXI J1348-630

Yiran Wang, Ruican Ma, Haiyun Zhang, Dahai Yan

TL;DR

We address how type-B QPOs and associated stochastic variability arise in MAXI J1348-630 by applying a Gaussian process regression framework with additive SHO, DRW, and AWN kernels to Insight-HXMT light curves across LE, ME, and HE bands. The SHO captures a high-Q QPO at $\omega_0/(2\pi) \approx 4.9$ Hz, while the DRW and AWN components model energy-dependent red noise and fast fluctuations, respectively, revealing a timescale hierarchy $\tau_{\rm AWN} < \tau_{\rm SHO} < \tau_{\rm DRW,LE} < \tau_{\rm DRW,ME/HE}$ and a disk–corona coupling in a two-corona geometry. LE DRW is well constrained around $\sim16$ s, whereas ME/HE DRW are poorly constrained, indicating longer relaxation times at higher energies; AWN dominates ME/HE PSD with $\tau_{\rm DRW}$ effectively unresolved below $0.01$ s. The results imply MRI-driven fast fluctuations coupling the inner disk and corona and support a physically interpretable, time-domain decomposition that can be extended to other BHXBs and timing phenomena.

Abstract

We analyzed Insight-HXMT data of the black hole X-ray binary MAXI J1348-630 during the type-B QPO phase of its 2019 outburst. Using the Gaussian process method, we applied an additive composite kernel model consisting of an SHO, a DRW, and an additional white noise (AWN) to data from three energy bands: LE (1-10 keV), ME (10-30 keV), and HE (30-150 keV). We find that for the DRW component, correlations on the timescale of $τ_{\rm DRW}\sim10$ s are absent in the LE band, while they persist in the ME and HE bands over the full duration of the light curves. This energy-dependent behavior may reflect thermal instabilities, with the shorter correlation timescale in the disk compared to the corona. Alternatively, it may reflect variable Comptonizations of seed photons from different disk regions. Inner-disk photons are scattered by a small inner corona, producing soft X-rays. Outer-disk photons interact with an extended, jet-like corona, resulting in harder emission. The QPO is captured by an SHO component with a stable period of $\sim 0.2$ s and a high quality factor of $\sim 10$. The absence of significant evolution with energy or time of the SHO component suggests a connection between the accretion disk and the corona, which may be built by coherent oscillations of disk-corona driven by magnetorotational instability. The AWN components are present in all the three-band data and dominate over the DRW and SHO components. We interpret the AWN as another fast DRW with its $τ_{\rm DRW} < 0.01$ s. It may trace high-frequency fluctuations that occur in both the inner region of the accretion disk and the corona. Overall, our work reveals a timescale hierarchy in the coupled disk-corona scenario: fast DRW < SHO < disk DRW < corona DRW.

Gaussian process analysis of type-B quasiperiodic oscillations in the black hole X-ray binary MAXI J1348-630

TL;DR

We address how type-B QPOs and associated stochastic variability arise in MAXI J1348-630 by applying a Gaussian process regression framework with additive SHO, DRW, and AWN kernels to Insight-HXMT light curves across LE, ME, and HE bands. The SHO captures a high-Q QPO at Hz, while the DRW and AWN components model energy-dependent red noise and fast fluctuations, respectively, revealing a timescale hierarchy and a disk–corona coupling in a two-corona geometry. LE DRW is well constrained around s, whereas ME/HE DRW are poorly constrained, indicating longer relaxation times at higher energies; AWN dominates ME/HE PSD with effectively unresolved below s. The results imply MRI-driven fast fluctuations coupling the inner disk and corona and support a physically interpretable, time-domain decomposition that can be extended to other BHXBs and timing phenomena.

Abstract

We analyzed Insight-HXMT data of the black hole X-ray binary MAXI J1348-630 during the type-B QPO phase of its 2019 outburst. Using the Gaussian process method, we applied an additive composite kernel model consisting of an SHO, a DRW, and an additional white noise (AWN) to data from three energy bands: LE (1-10 keV), ME (10-30 keV), and HE (30-150 keV). We find that for the DRW component, correlations on the timescale of s are absent in the LE band, while they persist in the ME and HE bands over the full duration of the light curves. This energy-dependent behavior may reflect thermal instabilities, with the shorter correlation timescale in the disk compared to the corona. Alternatively, it may reflect variable Comptonizations of seed photons from different disk regions. Inner-disk photons are scattered by a small inner corona, producing soft X-rays. Outer-disk photons interact with an extended, jet-like corona, resulting in harder emission. The QPO is captured by an SHO component with a stable period of s and a high quality factor of . The absence of significant evolution with energy or time of the SHO component suggests a connection between the accretion disk and the corona, which may be built by coherent oscillations of disk-corona driven by magnetorotational instability. The AWN components are present in all the three-band data and dominate over the DRW and SHO components. We interpret the AWN as another fast DRW with its s. It may trace high-frequency fluctuations that occur in both the inner region of the accretion disk and the corona. Overall, our work reveals a timescale hierarchy in the coupled disk-corona scenario: fast DRW < SHO < disk DRW < corona DRW.

Paper Structure

This paper contains 10 sections, 15 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Observations and data reduction
  3. Data analysis
  4. Gaussian process method
  5. Fitting procedure
  6. Results
  7. General GP fitting results
  8. Statistical analysis of the GP results
  9. Key findings
  10. Discussion

Figures (8)

  • Figure 1: HID of MAXI J1348--630 during its 2019 outburst. The intensity is the count rate in the 2--10 keV band, while the hardness ratio is the ratio of the count rate in the 4--10 keV band to that in the 2--4 keV band. Each point corresponds to one ExpID. The ExpIDs used in our work are marked in red.
  • Figure 2: LE fitting results when $Q$ is free. Left column, from top to bottom: Light curve fitting results (including the mean prediction from the GP model and the 1$\sigma$ uncertainty range corresponding to the total kernel) and parameter corner plot. Right column, from top to bottom: Residual distribution, ACF, and PSD. In PSD plot the blue line in the background represents the LSP, and the darker blue line is the total PSD of SHO (green line) and DRW (red line). The AWN term is plotted with the dotted purple line.
  • Figure 3: Same as in Fig. \ref{['LE_Qfree']} but $Q$ is fixed at 30.
  • Figure 4: HE fitting results when $Q$ is free. Left column, from top to bottom: Light curve fitting results (including the mean prediction from the GP model and the 1$\sigma$ uncertainty range corresponding to the total kernel) and PSD. Right column: Parameter corner plot. The ME fitting results are similar to the HE results, which are not shown. For both HE and ME, $\tau_{\rm DRW}$ is not effectively constrained.
  • Figure 5: PSD obtained using the GP method (left panel) and the PSD computed with powspec (right panel) for the same ExpID in the LE energy band.
  • ...and 3 more figures