Exploring Quasar Variability with ZTF at 0 < z < 3: A Universal Relation with the Eddington Ratio

Quasars, powered by accretion onto supermassive black holes (SMBHs), exhibit significant variability, offering insights into the physics of accretion and the properties of the central engines. In this study, we analyze photometric variability and its correlation with key quasar properties, including black hole mass (MBH) and nuclear luminosities, using 915 quasars with 0 ≤ z < 3.0 from the All Quasar Multi-Epoch Spectroscopy sample monitored within the fifth-generation Sloan Digital Sky Survey (SDSS-V). Variability metrics were derived from approximately 6 yr light curves provided by the Zwicky Transient Facility (ZTF), while SMBH masses and luminosities were obtained from the SDSS DR16 quasar catalog of Q. Wu & Y. Shen. We identify a strong anticorrelation between variability amplitude and luminosity, which strengthens with redshift, and a redshift-dependent trend for MBH: a positive correlation at low redshifts, no significant correlation at intermediate redshifts, and an anticorrelation at the highest redshifts. Our main finding is a robust anticorrelation between photometric variability amplitude and Eddington ratio, consistent across different redshift bins. We present a general equation encapsulating this relationship, which appears to be almost free of redshift dependence, enabling predictions of quasar variability based on accretion parameters or vice versa. The derived relation with the Eddington ratio provides a unified framework for interpreting variability in active galactic nuclei and facilitates future studies of quasar variability using high-cadence surveys, such as the Vera C. Rubin Observatory’s Legacy Survey of Space and Time.