Observed x-ray spectral indices support magnetic buoyancy sourced coronae in Seyfert active galactic nuclei

Standard radiation spectra modeling of active galactic nuclei like Seyfert galaxies typically involves tuning the relative contributions from an optically thick disc, optically thin corona, dust torus, and outflow by hand to match observations. The physics that quantifies this relative partitioning is not precisely understood. Here we make progress toward improving this understanding by testing the implications of a conceptual paradigm that the corona is supplied from below only by magnetic fields whose scales are large enough to escape turbulent shredding on their buoyant rise time. We use a generalized mean field accretion disc theory that includes both local radial angular momentum transport and angular momentum transport into a corona. We then use previous numerical simulations of magnetized turbulent accretion disc energy spectra to connect the fraction of disc magnetic energy that would escape to the fraction of coronal to total luminosity. Without explicitly calculating detailed particle acceleration and radiative processes, we assume that the disc radiation spectrum is thermal and the coronal radiation spectrum is a power law. We then show that the aforementioned paradigm for corona formation constrains the allowed x-ray power law index to a narrow range which agrees with observations. For the three AGNs studied here the predicted mean photon index is Γ=1.76, consistent with the mean observed value of Γ obs=1.73, bolstering confidence in the paradigm.