2009ApJ...697..573O

We present a dynamical model of the high mass X-ray binary LMC X-1 based on high-resolution optical spectroscopy and extensive optical and near-infrared photometry. From our new optical data we find an orbital period of P = 3.90917 ±0.00005 days. We present a refined analysis of the All Sky Monitor data from RXTE and find an X-ray period of P = 3.9094±0.0008 days, which is consistent with the optical period. A simple model of Thomson scattering in the stellar wind can account for the modulation seen in the X-ray light curves. The V - K color of the star (1.17±0.05) implies A_V= 2.28±0.06, which is much larger than previously assumed. For the secondary star, we measure a radius of R₂= 17.0±0.8 R_☉ and a projected rotational velocity of V_rot sin i = 129.9±2.2 km/s. Using these measured properties to constrain the dynamical model, we find an inclination of i = 36°.38 ±1°.92, a secondary star mass of M₂= 31.79±3.48 M_☉, and a black hole mass of 10.91±1.41 M_☉. The present location of the secondary star in a temperature-luminosity diagram is consistent with that of a star with an initial mass of 35 M_☉ that is 5 Myr past the zero-age main sequence. The star nearly fills its Roche lobe (~90% or more), and owing to the rapid change in radius with time in its present evolutionary state, it will encounter its Roche lobe and begin rapid and possibly unstable mass transfer on a timescale of a few hundred thousand years.