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We study the observed relation between accretion rate (in terms of L/L_Edd)and shape of the hard X-ray spectral energy distribution (namely the photonindex Gamma_X) for a large sample of 228 hard X-ray selected, low-redshiftactive galactic nuclei (AGN), drawn from the Swift/BAT AGN Spectroscopic Survey(BASS). This includes 30 AGN for which black hole mass (and therefore L/L_Edd)is measured directly through masers, spatially resolved gas or stellardynamics, or reverberation mapping. The high quality and broad energy coverageof the data provided through BASS allow us to examine several alternativedeterminations of both Gamma_X and L/L_Edd. For the BASS sample as a whole, wefind a statistically significant, albeit very weak correlation between Gamma_Xand L/L_Edd. The best-fitting relations we find, Gamma_X=0.15log(L/L_Edd)+const., are considerably shallower than those reported in previousstudies. Moreover, we find no corresponding correlations among the subsets ofAGN with different M_BH determination methodology. In particular, we find norobust evidence for a correlation when considering only those AGN with director single-epoch M_BH estimates. This latter finding is in contrast to severalprevious studies which focused on z>0.5 broad-line AGN. We discuss this tensionand conclude that it can be partially accounted for if one adopts a simplified,power-law X-ray spectral model, combined with L/L_Edd estimates that are basedon the continuum emission and on single-epoch broad line spectroscopy in theoptical regime. We finally highlight the limitations on using Gamma_X as aprobe of supermassive black hole evolution in deep extragalactic X-ray surveys.

The Swift/BAT AGN Spectroscopic Survey (BASS) -- VI. The Gamma_X - L/L_Edd relation