A NICER view of the corona through time-dependent Comptonization of the quasi-periodic oscillations in nine black-hole X-ray binaries

We present a systematic study of the evolution of the corona geometry in nine black hole X-ray binaries (BHXRBs) using archival data from NICER. We identify 171 observations exhibiting quasi-periodic oscillations (QPOs) across various spectral states and model the time-averaged energy spectra of the source, as well as the energy-dependent rms and phase-lag spectra of the QPO, with the time-dependent Comptonization model vKompthdk. This allows us to simultaneously constrain the corona size and feedback fraction during outbursts. By using the power color hue diagnostics, we identify different spectral states, and observe that the QPO frequency increases from $\sim$0.1 Hz to $\sim$10 Hz in the low-hard and hard-intermediate states (LHS and HIMS), and remains approximately constant at 4–5Hz in the soft-intermediate state (SIMS). The corona size shows significant evolution: the corona is large ($\sim10^4$–$10^5$ km) in the LHS, contracts rapidly to $\sim10^3$ km in the HIMS, and exhibits a flare-like expansion near the HIMS-to-SIMS transition. In the SIMS and high-soft state (HSS), the corona becomes compact and stable (4000–8000km). The feedback fraction of the corona photons increases during the periods in which the corona contracts and decreases during the periods in which the corona expands, indicating a change of the disk-corona coupling. Our results are consistent with previous QPO-based studies using vKompthdk on some individual sources. This work, however, provides the first view of the coronal evolution across outbursts for a diverse BHXRB sample, offering critical insights into coronal behavior as a function of the spectral state of the source.

💡 Research Summary

This paper presents a systematic NICER‑based investigation of coronal geometry evolution across spectral state transitions in nine black‑hole X‑ray binaries (BHXRBs). The authors first curated a sample of bright BHXRBs (peak flux > 100 mCrab) from the NICER archive, applying strict data‑quality cuts (removing noisy detectors, MPU1 timing anomalies, and post‑May‑2023 orbital‑night data to avoid optical leak). For each observation they generated power density spectra (PDS) in the full 0.3–12 keV band and six narrower sub‑bands, using 131 s segments (Nyquist = 250 Hz) and fitting the averaged PDS with a combination of Lorentzians representing the fundamental QPO, its harmonics, sub‑harmonic, and broadband noise components. Only observations with a well‑defined QPO (quality factor Q > 2) and robust rms and phase‑lag measurements across all energy bands were retained, yielding 171 QPO detections.

The authors employed the time‑dependent Comptonization model vKompthdk to jointly fit the time‑averaged energy spectrum, the QPO rms spectrum, and the QPO phase‑lag spectrum. vKompthdk explicitly models soft photons from the accretion disk being up‑scattered in a corona and a fraction of the resulting hard photons being reflected back onto the disk. Two key physical parameters are extracted: the coronal size L (in km) and the feedback fraction η (0–1), which quantifies the proportion of Comptonized photons that return to the disk. η≈1 indicates a corona extended primarily within the disk plane, while η≈0 suggests a vertically extended or outflowing corona.

Spectral states were identified using the power‑color hue diagnostic, which maps each observation onto a two‑dimensional color space defined by soft‑hard and broad‑narrow ratios. This classification separates the low‑hard state (LHS), hard‑intermediate state (HIMS), soft‑intermediate state (SIMS), and high‑soft state (HSS). The QPO frequency evolves smoothly from ~0.1 Hz in the LHS to ~10 Hz in the HIMS, then stabilises at 4–5 Hz throughout the SIMS, matching the canonical behaviour of type‑C and type‑B QPOs.

Coronal size shows a striking state‑dependent evolution. In the LHS the corona is large (L ≈ 10⁴–10⁵ km), consistent with a truncated disk that leaves ample space for an extended hot plasma. As the source moves into the HIMS, L contracts rapidly to ≈10³ km, indicating that the inner disk has moved inward toward the ISCO and the corona becomes more compact and likely more confined to the disk plane. Near the HIMS‑to‑SIMS transition a flare‑like expansion occurs, temporarily increasing L before it settles into a compact, stable configuration (L ≈ 4000–8000 km) in the SIMS and HSS. This “flare” may reflect a brief restructuring of the corona, possibly linked to jet ejection events.

The feedback fraction η tracks the opposite trend: η rises during periods of coronal contraction (reaching 0.6–0.8 in the HIMS) and falls when the corona expands (η ≈ 0.2–0.4 in the LHS and SIMS/HSS). This anti‑correlation suggests that a more compact corona intercepts a larger fraction of its own hard photons, enhancing disk‑corona coupling, whereas an expanded corona radiates more isotropically, reducing re‑illumination of the disk.

These findings corroborate earlier single‑source studies that applied vKompthdk (e.g., MAXI J1820+070, GX 339‑4) but extend the analysis to a diverse sample, providing the first statistical view of coronal evolution across full outbursts. The results challenge the simple lamppost geometry often inferred from reflection spectroscopy, instead supporting a scenario where the corona can be both disk‑plane‑extended and vertically dynamic, with its geometry tightly linked to the accretion state and possibly to jet activity.

In summary, by leveraging NICER’s high‑time‑resolution capabilities and the physically motivated vKompthdk model, the authors have directly measured how coronal size and disk‑corona feedback evolve from the low‑hard to the high‑soft state in multiple BHXRBs. This work offers a robust observational framework for testing theoretical models of accretion‑ejection coupling, corona formation, and QPO generation, and sets the stage for future multi‑wavelength campaigns that could further elucidate the interplay between the corona, the jet, and the accretion disk.