Dynamical Evidence for a Black Hole in the Microquasar XTE J1550–564^*

Optical spectroscopic observations of the companion star (type G8 IV to K4 III) in the microquasar system XTE J1550-564 reveal a radial velocity curve with a best-fitting spectroscopic period of P_sp = 1.552 ± 0.010 days and a semiamplitude of K₂ = 349 ± 12 km s^-1. The optical mass function is f(M) = 6.86 ± 0.71 M_☉ (1 σ). We tentatively measure the rotational velocity of the companion star to be V_rot sin i = 90 ± 10 km s^-1, which when taken at face value implies a mass ratio of Q ≡ M₁/M₂ = 6.6 (1 σ), using the above value of K₂. We derive constraints on the binary parameters from simultaneous modeling of the ellipsoidal light and radial velocity curves. We find 1 σ ranges for the photometric period (1.5430 days ≤ P_ph ≤ 1.5440 days), K-velocity (350.2 ≤ K₂ ≤ 368.6 km s^-1), inclination (670 ≤ i ≤ 774), mass ratio (Q ≥ 12.0), and orbital separation (11.55 R_☉ ≤ a ≤ 12.50 R_☉). Given these geometrical constraints, we find that the most likely value of the mass of the compact object is 9.41 M_☉ with a 1 σ range of 8.36 M_☉ ≤ M₁ ≤ 10.76 M_☉. If we apply our tentative value of V_rot sin i = 90 ± 10 km s^-1 as an additional constraint in the ellipsoidal modeling, we find 1 σ ranges of 1.5432 days ≤ P_ph ≤ 1.5441 days for the photometric period, 352.2 ≤ K₂ ≤ 370.1 km s^-1 for the K-velocity, 708 ≤ i ≤ 754 for the inclination, 6.7 ≤ Q ≤ 11.0 for the mass ratio, and 12.35 R_☉ ≤ a ≤ 13.22 R_☉ for the orbital separation. These geometrical constraints imply the most likely value of the mass of the compact object of 10.56 M_☉ with a 1 σ range of 9.68 M_☉ ≤ M₁ ≤ 11.58 M_☉. In either case the mass of the compact object is well above the maximum mass of a stable neutron star, and we therefore conclude that XTE J1550-564 contains a black hole.