Scaling Up: A Global Optical/X-ray Correlation For Reprocessing Across Black Hole Masses

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 proportional to L X β a, with β about 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 L V = 0.48 L X + 0.96 a R + 6.5 with a scatter of about 0.20 dex, where a R is the reprocessing radius derived from the lag. Incorporating a geometric correction for the disk inclination angle (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.