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 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, Γ, of a power-law energy distribution, over an energy range of 2 to 10 keV, for X-ray selected, broad-lined radio-quiet active galactic nuclei (AGN) up to z∼2 in COSMOS and E-CDF-S. We test the previously reported dependence between Γ 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 Hα emission lines with the later afforded by recent near infrared spectroscopic observations using Subaru/FMOS. We calculate the Eddington ratios, λ 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 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 however for large X-ray spectral samples, such as those to be produced by eROSITA.

Hard X-ray emission of the luminous infrared galaxy NGC 6240 as observed by NuSTAR

“…The relatively low accretion rate may be associated with the strong molecular outflow (Feruglio et al 2013b), which has depleted the nuclear regions of gas. We also note that in spite of the large uncertainties in the black hole mass and Eddington ratio, the photon index of the primary continuum is consistent with the low accretion rates of the two nuclei according to the relation found for a few AGN type 1 samples (Shemmer et al 2008;Risaliti et al 2009;Brightman et al 2013). …”

THE VARIABLE HARD X-RAY EMISSION OF NGC 4945 AS OBSERVED BYNUSTAR

“…Even if the slope of the relation and its normalization are close to that of a few AGN type 1 samples for which the accretion rate could be measured (Shemmer et al 2008;Risaliti et al 2009;Brightman et al 2013), we caution about the use of single-epoch X-ray data to derive λ Edd values for obscured AGN in the distant universe.…”

Was 49b: An Overmassive AGN in a Merging Dwarf Galaxy?

“…However, the hard X-ray spectral index of Γ=1.6 implies that the AGN is radiating at a small fraction of its Eddington limit (e.g., Brightman et al 2016 and references therein). For example, the relation between the Eddington ratio λ Edd and Γ from Brightman et al (2013) implies that the AGN in Was 49b is radiating at only ∼1% of its Eddington limit, and other relations between λ Edd and Γ from the literature consistently imply that the Eddington ratio is only a few percent. Given the bolometric luminosity calculated in Section 3.1, the Eddington ratio for a 1.3×10 8  M black hole is 0.08, meaning that our mass estimate is generally consistent with the X-ray spectral index.…”