Scaling Up: A Global Optical/X-ray Correlation For Reprocessing Across Black Hole Masses
Abstract
This study extends the optical/X-ray correlation from black hole low-mass X-ray binaries (XRBs) to active galactic nuclei (AGN), bridging scales from stellar-mass to supermassive black holes (SMBHs). In XRBs, optical emission predominantly originates from the thermal reprocessing of high-energy photons on the surface of the geometrically thin, optically thick accretion disk. The reprocessed optical luminosity follows a power-law relation of the form LV ∝ LXβ a, with β∼ 0.5, where LX is the X-ray luminosity and the orbital separation a serves as a proxy for the disk size. To test the universality of this relationship across all mass scales, we analyzed quasi-simultaneous X-ray and optical flux data from a sample of XRBs and AGN that have estimates of the radius of the optically emitting disk. To bridge the structural differences between these populations, we utilized the characteristic optical/X-ray time lag derived from reverberation mapping as a physical proxy for the reprocessing radius. Our analysis reveals a tight, global correlation across all black hole masses, described by log LV = 0.48log LX + 0.96log aR + 6.5 with a scatter of ∼ 0.20 dex, where aR is the reprocessing radius derived from the lag. Incorporating a geometric correction for the disk inclination angle (cos i) slightly reduces this scatter to $0.18$ dex. These results suggest that X-ray reprocessing is scale-invariant across accretion disks, from stellar-mass black holes to SMBHs. This scaling relation provides new constraints for models of X-ray emission regions in accreting black holes.
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BibTeX
@misc{cho2026scaling,
title = {{Scaling Up: A Global Optical/X-ray Correlation For Reprocessing Across Black Hole Masses}},
author = {Changhyun Cho and David M. Russell and Aaryan Sharma and Payaswini Saikia and Maria Cristina Baglio and Kevin Alabarta and Sandeep K. Rout and Yi-Jung Yang and Eleonora Caruso and Mokhine Motsoaledi and Meriana Allah and Ian M. McHardy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17248},
eprint = {2610.17248},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17248},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Scaling Up: A Global Optical/X-ray Correlation For Reprocessing Across Black Hole Masses
AU - Changhyun Cho
AU - David M. Russell
AU - Aaryan Sharma
AU - Payaswini Saikia
AU - Maria Cristina Baglio
AU - Kevin Alabarta
AU - Sandeep K. Rout
AU - Yi-Jung Yang
AU - Eleonora Caruso
AU - Mokhine Motsoaledi
AU - Meriana Allah
AU - Ian M. McHardy
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.17248
UR - https://arxiv.org/abs/2610.17248
AB - This study extends the optical/X-ray correlation from black hole low-mass X-ray binaries (XRBs) to active galactic nuclei (AGN), bridging scales from stellar-mass to supermassive black holes (SMBHs). In XRBs, optical emission predominantly originates from the thermal reprocessing of high-energy photons on the surface of the geometrically thin, optically thick accretion disk. The reprocessed optical luminosity follows a power-law relation of the form L_V ∝ L_X^β a, with β∼ 0.5, where L_X is the X-ray luminosity and the orbital separation a serves as a proxy for the disk size. To test the universality of this relationship across all mass scales, we analyzed quasi-simultaneous X-ray and optical flux data from a sample of XRBs and AGN that have estimates of the radius of the optically emitting disk. To bridge the structural differences between these populations, we utilized the characteristic optical/X-ray time lag derived from reverberation mapping as a physical proxy for the reprocessing radius. Our analysis reveals a tight, global correlation across all black hole masses, described by log L_V = 0.48log L_X + 0.96log a_R + 6.5 with a scatter of ∼ 0.20 dex, where a_R is the reprocessing radius derived from the lag. Incorporating a geometric correction for the disk inclination angle (cos i) slightly reduces this scatter to $0.18$ dex. These results suggest that X-ray reprocessing is scale-invariant across accretion disks, from stellar-mass black holes to SMBHs. This scaling relation provides new constraints for models of X-ray emission regions in accreting black holes.
ER -