A narrow Comptonization locus in Seyfert slab coronae: implications for dominant coronal dissipation and reduced feedback

Abstract

The thermal state of active galactic nucleus (AGN) coronae is commonly described by the electron temperature $kT_{\rm e}$, the Thomson optical depth $τ_{\rm T}$, and the geometry of the Comptonizing medium. We compile a literature sample of radio-quiet Seyfert galaxies with direct slab-geometry thermal Comptonization measurements of $kT_{\rm e}$ and $τ_{\rm T}$. For bottom-illuminated slab coronae, we adopt a geometry-motivated effective Comptonization parameter, $y=4θτ_{\rm T}\,{K_3(1/θ)} / {K_2(1/θ)}$, where $θ=kT_{\rm e}/m_{\rm e}c^2$ and $K_n$ is the modified Bessel function of the second kind. We find that the compiled slab-corona measurements are distributed along a narrow anti-correlated ridge in the $kT_{\rm e}-τ_{\rm T}$ plane. For the cleaned primary \texttt{compTT} sample, this ridge corresponds to $\langle y\rangle=0.770$ with a logarithmic dispersion of only 0.086 dex. We then compare the observed ridge with reduced-feedback slab-equilibrium calculations and find that the locus favours a corona-dominated local energy budget, $f\simeq1$, together with a feedback factor well below the full-covering value, $g\ll1$. We interpret the constant-$y$ locus as implications for dominant local coronal dissipation and reduced disc-corona radiative feedback, consistent with a patchy corona. Supplementary pair-balance calculations indicate that the low-temperature, high-optical-depth part of the sample is unlikely to be sustained by a purely thermal pair plasma alone, suggesting that the fitted optical depths are more plausibly dominated by electron--ion plasma.