  Optical spectroscopic observations of the companion star (type G8IV to K4III)
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 K_2 = 349 +/- 12 km/s. The optical mass function is f(M) =
6.86 +/- 0.71 solar masses (1 sigma). We tentatively measure the rotational
velocity of the companion star to be V_rot*sin(i) = 90 +/- 10 km/s, which when
taken at face value implies a mass ratio of Q = M_1/M_2 = 6.6 (+2.5 / -1.6) (1
sigma), using the above value of K_2. We derive constraints on the binary
parameters from simultaneous modelling of the ellipsoidal light and radial
velocity curves. We find the most likely value of the mass of the compact
object is 9.41 solar masses with a 1 sigma range of 8.36 < M_1 < 10.76 solar
masses. If we apply our tentative value of V_rot*sin(i) = 90 +/- 10 km/s as an
additional constraint in the ellipsoidal modelling, we find the most likely
value of the mass of the compact object is 10.56 solar masses with a 1 sigma
range of 9.68 < M_1 < 11.58 solar masses. In either case the mass of the
compact object is well above the maximum mass of a stable neutron star, and we
therefore conclude XTE J1550-564 contains a black hole.
