BAT AGN Spectroscopic Survey - XII. The relation between coronal properties of active galactic nuclei and the Eddington ratio

The bulk of the X-ray emission in active galactic nuclei (AGNs) is produced very close to the accreting supermassive black hole (SMBH), in a corona of hot electrons which up scatters optical and ultraviolet photons from the accretion flow. The cut-off energy (E_C) of the primary X-ray continuum emission carries important information on the physical characteristics of the X-ray emitting plasma, but little is currently known about its potential relation with the properties of accreting SMBHs. Using the largest broad-band (0.3-150 keV) X-ray spectroscopic study available to date, we investigate how the corona is related to the AGN luminosity, black hole mass and Eddington ratio (λ_Edd). Assuming a slab corona the median values of the temperature and optical depth of the Comptonizing plasma are kT_e = 105 ± 18 keV and τ = 0.25 ± 0.06, respectively. When we properly account for the large number of E_C lower limits, we find a statistically significant dependence of the cut-off energy on the Eddington ratio. In particular, objects with λ_Edd > 0.1 have a significantly lower median cut-off energy (E_C = 160 ± 41 keV) than those with λ_Edd ≤ 0.1 (E_C = 370 ± 51 keV). This is consistent with the idea that radiatively compact coronae are also cooler, because they tend to avoid the region in the temperature-compactness parameter space where runaway pair production would dominate. We show that this behaviour could also straightforwardly explain the suggested positive correlation between the photon index (Γ) and the Eddington ratio, being able to reproduce the observed slope of the Γ-λ_Edd trend.