A statistical relation between the X-ray spectral index and Eddington ratio of active galactic nuclei in deep surveys

Abstract

We present an investigation into how well the properties of the accretion flow on to a supermassive black hole may be coupled to those of the overlying hot corona. To do so, we specifically measure the characteristic spectral index, Γ, of a power-law energy distribution, over an energy range of 2–10 keV, for X-ray selected, broad-lined radio-quiet active galactic nuclei (AGN) up to z ∼ 2 in Cosmic Evolution Survey (COSMOS) and Extended Chandra Deep Field South (E-CDF-S). We test the previously reported dependence between Γ and black hole mass, full width at half-maximum (FWHM) and Eddington ratio using a sample of AGN covering a broad range in these parameters based on both the Mg II and Hα emission lines with the later afforded by recent near-infrared spectroscopic observations using Subaru/Fibre Multi Object Spectrograph. We calculate the Eddington ratios, λ_(Edd), for sources where a bolometric luminosity (L_(Bol)) has been presented in the literature, based on spectral energy distribution fitting, or, for sources where these data do not exist, we calculate L_(Bol) using a bolometric correction to the X-ray luminosity, derived from a relationship between the bolometric correction and L_X/L_(3000). From a sample of 69 X-ray bright sources (>250 counts), where Γ can be measured with greatest precision, with an estimate of L_(Bol), we find a statistically significant correlation between Γ and λ_(Edd), which is highly significant with a chance probability of 6.59× 10^(−8). A statistically significant correlation between Γ and the FWHM of the optical lines is confirmed, but at lower significance than with λ_(Edd) indicating that λ_(Edd) is the key parameter driving conditions in the corona. Linear regression analysis reveals that Γ = (0.32 ± 0.05) log_(10)λ_(Edd) + (2.27 ± 0.06) and Γ = (−0.69 ± 0.11) log_(10)(FWHM/km s^(−1)) + (4.44 ± 0.42). Our results on Γ–λ_(Edd) are in very good agreement with previous results. While the Γ–λ_(Edd) relationship means that X-ray spectroscopy may be used to estimate black hole accretion rate, considerable dispersion in the correlation does not make this viable for single sources, however could be valuable for large X-ray spectral samples, such as those to be produced by eROSITA.

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