In a previous paper, we presented an extension of our reflection model RELXILL_NK to include the finite thickness of the accretion disk following the prescription in Taylor & Reynolds (2018). In this paper, we apply our model to fit the 2013 simultaneous observations by NuSTAR and XMM-Newton of the supermassive black hole in MCG-06-30-15 and the 2019 NuSTAR observation of the Galactic black hole in EXO 1846-031. The high-quality data of these spectra had previously led to precise black hole spin measurements and very stringent constraints on possible deviations from the Kerr metric. We find that the disk thickness does not change previous spin results found with a model employing an infinitesimally thin disk, which confirms the robustness of spin measurements in high radiative efficiency disks, where the impact of disk thickness is minimal. Similar analysis on lower accretion rate systems will be an important test for measuring the effect of disk thickness on black hole spin measurements.
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