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In a previous paper, one of us has described a code to compute the thermalspectrum of geometrically thin and optically thick accretion disks aroundgeneric stationary and axisymmetric black holes, which are not necessarily ofthe Kerr type. As the structure of the accretion disk and the propagation ofelectromagnetic radiation from the disk to the distant observer depend on thebackground metric, the analysis of the thermal spectrum of thin disks can beused to test the actual nature of black hole candidates. In this paper, weconsider the 10 stellar-mass black hole candidates for which the spin parameterhas been already estimated from the analysis of the disk's thermal spectrum andunder the assumption of the Kerr background, and we translate the measurementsreported in the literature into constraints on the spin parameter--deformationparameter plane. The analysis of the disk's thermal spectrum can be used toestimate only one parameter of the geometry close to the compact object, andtherefore it is not possible to get independent measurements of both the spinand the deformation parameters. The constraints obtained here will be used incombination with other measurements in future work, with the final goal tobreak the degeneracy between the spin and possible deviations from the Kerrsolution and thus test the Kerr black hole hypothesis.

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