Machine learning application to detect light echoes around black holes

Abstract

X-ray reverberation has become a powerful tool to probe the disc-corona geometry near black holes. Here, we develop Machine Learning (ML) models to extract the X-ray reverberation features imprinted in the Power Spectral Density (PSD) of AGN. The machine is trained using simulated PSDs in the form of a simple power-law encoded with the relativistic echo features. Dictionary Learning and sparse coding algorithms are used for the PSD reconstruction, by transforming the noisy PSD to a representative sparse version. Then, the Support Vector Machine is employed to extract the interpretable reverberation features from the reconstructed PSD that holds the information of the source height. The results show that the accuracy of predicting the source height, $h$, is genuinely high and the misclassification is only found when $h$ > 15$r_g$. When the test PSD has a bending power-law shape, which is completely new to the machine, the accuracy is still high. Therefore, the ML model does not require the intrinsic shape of the PSD to be determined in advance. By focusing on the PSD parameter space observed in real AGN data, classification for $h\le$ 10$r_g$ can be determined with 100% accuracy, even using a PSD in an energy band that contains a reflection flux as low as 10% of the total flux. For $h$ > 10$r_g$, the data, if misclassified, will have small uncertainties of $\Delta h$ ~ 2-4$r_g$. This work shows, as a proof of concept, that the ML technique could shape new methodological directions in the X-ray reverberation analysis.

arXiv comment12 pages, 13 figures, accepted for publication in MNRAS

References in corpus (30)

• X-ray reflected spectra from accretion disk models. III. A complete grid of ionized reflection calculations
• X-ray reverberation around accreting black holes
• X-ray reflected spectra from accretion disk models. I. Constant density atmospheres
• An extended scheme for fitting X-ray data with accretion disk spectra in the strong gravity regime
• A global look at X-ray time lags in Seyfert Galaxies
• X-ray variability of 104 active galactic nuclei. XMM-Newton power-spectrum density profiles
• Modelling the broad Fe Kα reverberation in the AGN NGC 4151
• General relativistic modelling of the negative reverberation X-ray time delays in AGN
• A public relativistic transfer function model for X-ray reverberation mapping of accreting black holes
• The origin of the lag spectra observed in AGN: Reverberation and the propagation of X-ray source fluctuations
• Towards modelling X-ray reverberation in AGN: Piecing together the extended corona
• A dynamic black hole corona in an active galaxy through X-ray reverberation mapping
• Reverberation Reveals the Truncated Disc in the Hard State of GX 339-4
• Relativistic X-ray reverberation modelling of the combined time-averaged and lag-energy spectra in AGN
• A search for X-ray reprocessing echoes in the power spectral density functions of AGN
• Investigating the X-ray time-lags in PG 1244+026 using an extended corona model
• Theoretical modelling of the AGN iron-line vs continuum time-lags in the lamp-post geometry
• Simultaneous spectral and reverberation modelling of relativistic reflection in Mrk 335
• A combined timing/spectral study of IRAS 13224-3809 using XMM-Newton data
• Testing the X-ray reverberation model KYNREFREV in a sample of Seyfert 1 Active Galactic Nuclei
• X-Ray Reverberation From Black Hole Accretion Disks with Realistic Geometric Thickness
• Multi-timescale reverberation mapping of Mrk 335
• Returning radiation in strong gravity around black holes: Reverberation from the accretion disc
• X-ray time lags in AGN: inverse-Compton scattering and spherical corona model
• Signatures of X-ray reverberation in the power spectra of AGN
• Interference as an origin of the peaked noise in accreting X-ray binaries
• Quasi-periodic oscillations under wavelet microscope: the application of Matching Pursuit algorithm
• Evolution of the truncated disc and inner hot-flow of GX 339-4
• Modelling the X-ray power spectra of AGN by using reprocessing echoes from an extended corona
• An Algorithm for the Visualization of Relevant Patterns in Astronomical Light Curves

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