We study the link between the X-ray emission in radio-quiet active galactic nuclei (AGN) and the accretion rate on the central supermassive black hole using a statistically well-defined and representative sample of 71 type 1 AGN extracted from the XMM–Newton Bright Serendipitous Survey. We search and quantify the statistical correlations between some fundamental parameters that characterize the X-ray emission, i.e. the X-ray spectral slope, Γ, and the X-ray ‘loudness’, and the accretion rate, both absolute (Ṁ) and normalized to the Eddington luminosity (Eddington ratio, λ). We parametrize the X-ray loudness using three different quantities: the bolometric correction Kbol, the two-point spectral index αOX and the disc/corona luminosity ratio. We find that the X-ray spectral index depends on the normalized accretion rate while the ‘X-ray loudness’ depends on both the normalized and the absolute accretion rate. The dependence on the Eddington ratio, in particular, is probably induced by the Γ – λ correlation. The two proxies usually adopted in the literature to quantify the X-ray loudness of an AGN, i.e. Kbol and αOX, behave differently, with Kbol being more sensitive to the Eddington ratio and αOX having a stronger dependence with the absolute accretion. The explanation of this result is likely related to the different sensitivity of the two parameters to the X-ray spectral index.
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Fanali et al. (2013) studied this question.