tokens: structure is completely determined by the conservation of rest-mass, energy, and angular momentum of the accreting gas, the Polish donut model is less constrained. It requires the relation between the fluid angular velocity and the fluid angular momentum per unit energy, Ω = Ω ( l ), as well as the fluid angular momentum per unit energy at the inner edge of the disk, l in . The simplest Polish donut model is the configuration with l = constant, which turns out to be marginally stable with respect to axisymmetric perturbations (Font Daigne 2002 ). Accretion disks in the Kerr spacetime only exist for l ms l l mb , where l ms and l mb are, respectively, the angular momentum per unit energy of the marginally stable equatorial circular orbit (or ISCO) and of the marginally bound equatorial circular orbit (Abramowicz et al. 1978 ; Bardeen et al. 1972 ; Li Bambi 2013 ). Indeed, for l l ms , the fluid angular momentum is too low and there is no stable accretion disk (the fluid directly plunges onto the black hole), while, for l > l mb , the fluid angular momentum is too high and there is no accretion (there is just a fluid rotating around the black hole). In the presence of an accretion disk, when , the inner edge of the disk, R in , is between the marginally bound orbit and the ISCO, i.e., R mb R in R ISCO (Bardeen et al. 1972 ; Abramowicz et al. 1978 ; Li Bambi 2013 ); that is, for a given black hole spin, the inner edge of a Polish donut disk is always smaller than the inner edge of a Novikov–Thorne disk. Since the exact location of the inner edge of the disk is crucial in reflection spin measurements, we can already suspect that systematic uncertainties related to the use of an incorrect disk model to fit the data of a source can be important. 3. Simulations and Fits In order to estimate the impact of the disk structure on spin measurements with the iron line method, we use the code presented in Riaz et al. ( 2020 ) to calculate the theoretical reflection spectrum of a Polish donut disk. We use the xillver model (García Kallman 2010 ; García et al. 2013 ) to calculate the nonrelativistic reflection spectrum at the emission point in the rest-frame of the gas in the disk, and we use our ray-tracing code to convolve this nonrelativistic spectrum into a relativistic spectrum of a thick disk. At this point, we need to choose the properties of our source and of our instruments to simulate the observation of a black hole with a thick accretion disk. As X-ray mission, we consider NICER (Gendreau et al. 2016 ), which has a good energy resolution near the iron line and is thus suitable for X-ray reflection spectroscopy measurements. We assume that the source has a very simple spectrum, just a power-law component and a reflection component. In XSPEC language (Arnaud 1996 ):where TBABS takes the Galactic absorption into account (Wilms et al. 2000 ), powerlw is the power-law component generated by inverse Compton scattering of thermal photons from the disk off
ner_tags: O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model I-Model I-Model O O O B-Model I-Model B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Citation I-Citation O B-Model O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Model O O B-Model I-Model O O O O O O O O O O O O