Constraints on the spacetime geometry around 10 stellar-mass black hole candidates from the disk's thermal spectrum

In a previous paper, one of us has described a code to compute the thermal spectrum of geometrically thin and optically thick accretion disks around generic stationary and axisymmetric black holes, which are not necessarily of the Kerr type. As the structure of the accretion disk and the propagation of electromagnetic radiation from the disk to the distant observer depend on the background metric, the analysis of the thermal spectrum of thin disks can be used to test the actual nature of black hole candidates. In this paper, we consider the 10 stellar-mass black hole candidates for which the spin parameter has been already estimated from the analysis of the disk's thermal spectrum and under the assumption of the Kerr background, and we translate the measurements reported in the literature into constraints on the spin parameter--deformation parameter plane. The analysis of the disk's thermal spectrum can be used to estimate only one parameter of the geometry close to the compact object, and therefore it is not possible to get independent measurements of both the spin and the deformation parameters. The constraints obtained here will be used in combination with other measurements in future work, with the final goal to break the degeneracy between the spin and possible deviations from the Kerr solution and thus test the Kerr black hole hypothesis.