Feeding frenzy in the mighty black holes: what we could learn from them?

Abstract: Eddington ratio is a paramount parameter governing the accretion history and life cycles of Active Galactic Nuclei (AGNs). This short review presents a multi-faceted view of the importance of the Eddington ratio spanning varied AGN studies. We find that the Eddington ratio is crucial for standardizing the Radius-Luminosity (R-L) relation - a necessary step for employing quasars (QSOs) as standardizable cosmological probes to help clarify the standing of the Hubble tension. In this data-driven era, we consolidated disparate aspects by developing novel relations borne out of large datasets, such as the robust, nearly universal anti-correlation between fractional variability and Eddington ratio derived from Zwicky Transient Facility (ZTF) data, which is vital for interpreting forthcoming high-cadence surveys like Rubin Observatory's LSST. Addressing the conundrum where JWST results suggest an overabundance of massive high-redshift black holes, we demonstrate that local AGNs offer clarification: Changing-Look AGNs (CLAGNs), driven by rapid Eddington ratio shifts, cluster in the low-accretion regime, a rate independently confirmed by our integral field spectroscopy and photoionization modeling of a well-known Seyfert 2 galaxy, rich in high-ionization, forbidden, coronal lines. Conversely, for the high-redshift, high-luminosity population where traditional reverberation mapping (RM) is highly impractical, photometric reverberation mapping (PRM) offers a rapid alternative to constrain accretion disk sizes, enabling efficient estimates of black hole masses and Eddington ratios. Finally, we developed tailored semi-empirical spectral energy distributions (SEDs) for extremely high-accretion quasars, successfully validating their characteristic extreme physical conditions.