Determining the spin of two stellar-mass black holes from disc reflection signatures

We present measurements of the dimensionless spin parameters and inner-disc inclination of two stellar-mass black holes. The spin parameter of SWIFT J1753.5−0127 and GRO J1655−40 is estimated by modelling the strong reflection signatures present in their XMM–Newton observations. Using a newly developed, self-consistent reflection model which includes the blackbody radiation of the disc as well as the effect of Comptonization, blurred with a relativistic line function, we infer the spin parameter of SWIFT J1753.5−0127 to be  0.76^+0.11_−0.15  . The inclination of this system is estimated at  55°⁺²₋₇  . For GRO J1655−40, we find that the disc is significantly misaligned to the orbital plane, with an innermost inclination of  30°⁺⁵₋₁₀  . Allowing the inclination to be a free parameter, we find a lower limit for the spin of 0.90, this value increases to that of a maximal rotating black hole when the inclination is set to that of the orbital plane of J1655−40. Our technique is independent of the black hole mass and distance, uncertainties in which are among the main contributors to the spin uncertainty in previous works.