A statistical relation between the X-ray spectral index and Eddington ratio of active galactic nuclei in deep surveys. (arXiv:1305.3917v1 [astro-ph.HE]):
We present an investigation into how well the properties of the accretion
flow onto a supermassive black hole may be coupled to those of the overlying
hot corona. To do so, we specifically measure the characteristic spectral
index, Gamma, of a power-law energy distribution, over an energy range of 2 to
10 keV, for X-ray selected, broad-lined radio-quiet AGN up to z~2 in COSMOS and
E-CDF-S. We test the previously reported dependence between Gamma and black
hole mass, FWHM and Eddington ratio using a sample of AGN covering a broad
range in these parameters based on both the Mg ii and H-alpha emission lines
with the later afforded by recent near infrared spectroscopic observations
using Subaru/FMOS. We calculate the Eddington ratios, lambda_Edd, for sources
where a bolometric luminosity (L_Bol) has been presented in the literature,
based on SED fitting, or, for sources where these data do not exist, we
calculate L_Bol using a bolometric correction to the LX, derived from a
relationship between the bolometric correction, and LX/L3000. From a sample of
69 X-ray bright sources (>250 counts), where Gamma can be measured with
greatest precision, with an estimate of L_Bol, we find a statistically
significant correlation between Gamma and lambda_Edd, which is highly
significant with a chance probability of 6.59x10^-8. A statistically
significant correlation between Gamma and the FWHM of the optical lines is
confirmed, but at lower significance than with lambda_Edd indicating that
lambda_Edd is the key parameter driving conditions in the corona. Linear
regression analysis reveals that Gamma=(0.32+/-0.05)log10
lambda_Edd+(2.27+/-0.06) and
Gamma=(-0.69+/-0.11)log10(FWHM/km/s)+(4.44+/-0.42). Our results on
Gamma-lambda_Edd are in very good agreement with previous results. (ABRIDGED)
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