tokens: specified by the photon index Γ of the underlying power law. Under the assumption of isotropic emission, this provides the bolometric luminosity, L bol . We express the luminosity as the Eddington ratio: the ratio of L bol to the Eddington limited luminosity, L Edd . The latter is determined as L Edd = (2.1 ± 0.5) × 10 45 erg s −1 using a black hole mass of (14 ± 4) × 10 6 M ⊙ (Peterson et al. 2004 , see also Grier et al. 2012a ) as well as a solar hydrogen abundance of X = 0.71. The Eddington ratio's uncertainty is dominated by systematics. The relation of Zhou Zhao ( 2010 ) introduces a substantial systematic uncertainty from the spread in the observations that they employed. Including this uncertainty and the uncertainty in the Eddington luminosity, the mean 1σ uncertainty in log L bol / L Edd is 0.77. Without these systematic uncertainties, and only including the uncertainties in Γ and the 2–10 keV luminosity, the mean error in log L bol / L Edd is 0.10. As the in-band flux is well measured, the uncertainty is mostly set by the error in Γ. We are interested in the correlation between parameters of a single source, so we omit the systematics from the uncertainty reported in each data point. The systematic error would only shift the observed trends with Eddington ratio. 3 SIMPLE POWER-LAW FIT Previous analyses of these observations required a complex spectral model that includes ionized absorption at energies ≲3 keV as well as photoionized reflection (e.g. Parker et al. 2014 ; Wilkins Gallo 2015 ). Before we apply a similar detailed spectral model in Section 4 , however, we first fit the data with a simple power law. The observed correlation of the photon index Γ and the X-ray flux (Sarma et al. 2015 ), suggests that we can gain some insight into the qualitative behaviour of the source with a simple spectral model. Following Parker et al. ( 2014 ), we fit a power law to the spectra in the energy intervals 3–4, 8.5–10, and 40–50 keV. This avoids absorption at low energies as well as the Fe Kα line and the Compton hump, which are prominent reflection features. These fits provide a relatively clean look at the underlying power law. We include absorption by the Galactic interstellar medium using the Tübingen–Boulder model (Wilms, Allen McCray 2000 ) with an equivalent hydrogen column of N H = 3.6 × 10 20 cm −2 (Kalberla et al. 2005 ), and we use solar abundances as reported by Grevesse Sauval ( 1998 ). A cosmological redshift is applied (Section 2.3 ). The spectral fits are performed using xspec v.12.8.2 (Arnaud 1996 ), and all presented errors in the fit parameters are at 1σ. For each spectrum, we determine Γ and the 3–10 keV power-law flux. We reproduce the logarithmic relation of Γ and the X-ray flux with a break at higher fluxes (Sarma et al. 2015 ), which has also been observed in other AGN (e.g. Perola et al. 1986 ; Done, Madejski Życki 2000 ; Shih, Iwasawa Fabian 2002 ), and we will quantify this relation with the detailed spectral
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