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Constraints on the Viscosity and Magnetic Field in Hot Accretion Flows around Black Holes

The magnitude of the viscosity and magnetic field parameters in hot accretion flows is investigated in low luminosity active galactic nuclei (LLAGNs). Theoretical studies show that a geometrically thin, optically thick disk is truncated at mass accretion rates less than a critical value by mass evaporated vertically from the disk to the corona, with the truncated region replaced by an advection dominated accretion flow (ADAF). The critical accretion rate for such a truncation is a function of the viscosity and magnetic field. Observations of X-ray photon indices and spectral fits of a number of LLAGNs published in the literature provide an estimate of the critical rate of mass accretion and the truncation radius respectively. By comparing the observational results with theoretical predictions, the viscosity and magnetic field parameters in the hot accretion flow region are estimated. Specifically, the mass accretion rates inferred in different sources constrain the viscosity parameter, whereas the truncation radii of the disk, as inferred from spectral fits, further constrain the magnetic field parameter. It is found that the value of the viscosity parameter in the corona/ADAF ranges from 0.17 to 0.5, with values clustered about 0.2-0.3. Magnetic pressure is required by the relatively small truncation radii for some LLAGNs and is found to be as high as its equipartition value with the gas pressure. The inferred values of the viscosity parameter are in agreement with those obtained from the observations of non-stationary accretion in stellar mass black hole X-ray transients. This consistency provides support for the paradigm that a geometrically thin disk is truncated by means of a mass evaporation process from the disk to the corona at low mass accretion rates.