Black hole spin measurements through the relativistic precession model: XTE J1550-564

We present a systematic analysis of the complete set of observations of the black hole (BH) binary XTE J1550-564 obtained by the Rossi X-ray Timing Explorer. We study the fast time variability properties of the source and determine the spin of the BH through the relativistic precession model. Similarly to what is observed in the BH binary GRO J1655-40, the frequencies of the QPOs and broad-band noise components match the general relativistic frequencies of particle motion close to the compact object predicted by the relativistic precession model. The combination of two simultaneously observed quasi-periodic oscillation (QPO) frequencies together with the dynamical BH mass from optical/infrared observations yields a spin equal to a = 0.34 \plusmn 0.01, consistent with previous determinations from X-ray spectroscopy. Based on the derived BH parameters, the low-frequency QPO emission radii vary from \tilde30 gravitational radii (R$_g$) to the innermost stable orbit for this spin (\tilde5 R$_g$), where they sharply disappear as observed for the case of GRO J1655-40.