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 \pm 0.010 days and a semiamplitude of K _ { 2 } = 349 \pm 12 km s ^ { -1 } .
The optical mass function is f ( M ) = 6.86 \pm 0.71 M _ { \odot } ( 1 \sigma ) .
We tentatively measure the rotational velocity of the companion star to be V _ { rot } \sin i = 90 \pm 10 km s ^ { -1 } , which when taken at face value implies a mass ratio of Q \equiv 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 1 \sigma ranges for the photometric period ( 1.5430 { d } \leq P _ { ph } \leq 1.5440 { d } ) , K - velocity ( 350.2 \leq K _ { 2 } \leq 368.6 km s ^ { -1 } ) , inclination ( 67.0 ^ { \circ } \leq i \leq 77.4 ^ { \circ } ) , mass ratio ( Q \geq 12.0 ) , and orbital separation ( 11.55 R _ { \odot } \leq a \leq 12.50 R _ { \odot } ) .
Given these geometrical constraints we find the most likely value of the mass of the compact object is 9.41 M _ { \odot } with a 1 \sigma range of 8.36 M _ { \odot } \leq M _ { 1 } \leq 10.76 M _ { \odot } .
If we apply our tentative value of V _ { rot } \sin i = 90 \pm 10 km s ^ { -1 } as an additional constraint in the ellipsoidal modelling , we find 1 \sigma ranges of 1.5432 { d } \leq P _ { ph } \leq 1.5441 { d } for the photometric period , 352.2 \leq K _ { 2 } \leq 370.1 km s ^ { -1 } for the K - velocity , 70.8 ^ { \circ } \leq i \leq 75.4 ^ { \circ } for the inclination , 6.7 \leq Q \leq 11.0 for the mass ratio , and 12.35 R _ { \odot } \leq a \leq 13.22 R _ { \odot } for the orbital separation .
These geometrical constraints imply the most likely value of the mass of the compact object of 10.56 M _ { \odot } with a 1 \sigma range of 9.68 M _ { \odot } \leq M _ { 1 } \leq 11.58 M _ { \odot } .
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 .