A New Dynamical Model for the Black Hole Binary LMC X - 1 †

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 nearinfrared 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 AV = 2.28 ± 0.06, which is much larger than previously assumed. For the secondary star, we measure a radius of R2 = 17.0±0.8R⊙ and a projected rotational velocity of Vrot 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 ofM2 = 31.79±3.48M⊙, and a black hole mass of 10.91± 1.41M⊙. The present location of the secondary star in a temperature-luminosity diagram is consistent with that of a star with an initial mass of 35M⊙ 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.