Black hole spin measurements based on a thin disc model with finite thickness – I. An example study of MCG−06-30-15

We present a re-analysis of the XMM–Newton and NuSTAR observing campaigns for the well-studied, X-ray-bright AGN MCG−06-30-15. In particular, we consider a disc model with finite thickness. By fitting the disc reflection spectra in the data, we obtain a black hole spin of 0.87–0.99 (90 per cent confidence range) after taking the thickness of the disc into consideration. Spectral models with a grid of mass accretion rate from 0 to 30\, per\,cent\,ṀEdd are calculated for MCG−06-30-15. This result is obtained by considering a free disc reflection fraction parameter frefl and is consistent with previous measurements based on razor-thin disc models. Besides, an isotropic, point-like geometry, i.e. the ‘lamppost’ geometry, is assumed for the corona in our model. We find that such a geometry overestimates frefl in the data. Therefore, thin disc models with consistent ‘lamppost’ values of frefl provide a worse fit than ones with a free frefl parameter. We discuss possible reasons for the discrepancy between the observed and theoretical values of frefl at the end of the paper. Modifications for the over-simplified lamppost model might be needed when the thickness of the thin disc is considered in future work.