$\theta_{\mathrm{OA}}$, with a binning of $\Delta \theta_{\,\mathrm{i}}=3^{\circ}$. In XSPEC 12.7.1 [@Arnaud:1996kx] we simulated spectra for each of the three $\theta_{\mathrm{OA}}-L_{\mathrm{X}}$ relationships and for each bin of column density. For the continuum we used a power law with $\Gamma=1.9$ (e.g., [@Beckmann:2009fk]). Our choice of the photon index does not affect significantly the simulations, and adding a scatter of $\Delta \Gamma=0.3$ we found $EW-L_{\mathrm{X}}$ trends consistent with those obtained without scatter. The metallicity was set to the solar value in all our simulations, and the value of the normalization of the reflected component was fixed to that of the continuum.

We fitted the simulated spectra in the 0.3-10keV band using the same model adopted for the simulations, substituting the iron K$\alpha$ line component with a Gaussian line. We obtained a good fit for all the simulations, with a reduced chi-squared of $\chi^{2}_{\nu}\lesssim 1.1$. We report in Fig.\[fig:simulations\_line\] an example of a typical fit. The model used for the continuum fitting does not affect significantly the results, and using an alternative model like `pexrav` [@Magdziarz:1995pi] the equivalent width of the iron K$\alpha$ line differs on average of only $\sim4\%$. We evaluated the equivalent width of the iron K$\alpha$ line and studied its relationship 