Abstract
The X-ray-emitting corona near a black hole (BH) is too small to be directly imaged, but the rapid variability is used to infer the geometry by measuring time lags caused by coronal X-rays reflecting off the disk, known as reverberation lags. Though reverberation lags have previously been detected for some supermassive BHs in active galactic nuclei (AGNs), detecting them from stellar-mass BHs poses much greater challenges due to their size being over a million times smaller. Previous measurements of reverberation lags for stellar-mass BHs were limited to energies below 10 keV. Here, we report the detection of the Compton hump reverberation, peaking at about 30 keV, from an X-ray binary. The accompanying detection of an iron line feature at about 6.4 keV confirms the X-ray reverberation scenario and provides strong evidence that accretion flows in AGNs and X-ray binaries are governed by an ubiquitous process.
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Data availability
All Insight-HXMT data used in this work (Proposal ID: P0114661) are publicly available and can be downloaded from the Insight-HXMT website (http://archive.hxmt.cn/proposal). The NICER datasets analyzed during this study are available at NASA’s High Energy Astrophysics Science Archive Research Center (https://heasarc.gsfc.nasa.gov/FTP/nicer/data/obs/). The data generated in this study are publicly available at: https://github.com/MAXIJ1820/generate_data. Source data are provided with this paper.
Code availability
The Insight-HXMT data reduction was performed using software available from the Insight-HXMT website (http://hxmten.ihep.ac.cn/). The time lag was performed with Stingray, a reliable Python library for X-ray timing analysis (see https://stingray.readthedocs.io/en/latest/index.html). The model PROPFLUC can be downloaded from the website: https://github.com/HEASARC/xspec_localmodels/tree/master/propfluc. The new model presented here, reltransCpF, can be downloaded from https://github.com/reltrans/Youetal2025.
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Acknowledgements
B.Y. is supported by NSFC grants 12322307, 12361131579, 12273026; the National Program on Key Research and Development Project 2021YFA0718500. Xiaomi Foundation/Xiaomi Young Talents Program. The data analysis in this paper has been done on the supercomputing system in the Supercomputing Center of Wuhan University. W.Y. acknowledges financial support from the Sino-German (CSC-DAAD) Postdoc Scholarship Program (No. 57718047) and the Alexander von Humboldt Foundation. A.I. acknowledges support from the Royal Society. B.D.M. acknowledges support via a Ramón y Cajal Fellowship (RYC2018-025950-I), the Spanish MINECO grants PID2023-148661NB-I00, PID2022-136828NB-C44, and the AGAUR/Generalitat de Catalunya grant SGR-386/2021. J.-L.Q. acknowledges support from the grant U2031205. Z.-H.Z. acknowledges support from the National Natural Science Foundation of China under Grants Nos. 12021003 and 12433001.
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B.Y. initiated the project, specifically proposing data analysis and model interpretation, and took the lead in manuscript writing. W. Y. led the timing analysis and contributed to the text writing. A.I. led the interpretation of the Frequency-dependent time lags and contributed to the writing of the text. B.D. contributed to the model discussion and the writing of the text. J.-L.Q., Z.-H.Z., A.S., and S.-E.X. contributed to the model discussion. All the authors joined in the modification of the text at all stages.
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You, B., Yu, W., Ingram, A. et al. Reverberation lags viewed in hard X-rays from an accreting stellar-mass black hole. Nat Commun (2026). https://doi.org/10.1038/s41467-026-69604-9
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DOI: https://doi.org/10.1038/s41467-026-69604-9
