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 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 R-2 = 17.0 +/- 0.8 R-circle dot and a projected rotational velocity of V-rot sin i = 129.9 +/- 2.2 km s(-1). Using these measured properties to constrain the dynamical model, we find an inclination of i = 36 degrees.38 +/- 1 degrees.92, a secondary star mass of M-2 = 31.79 +/- 3.48 M-circle dot, and a black hole mass of 10.91 +/- 1.41 M-circle dot. 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-circle dot that is 5 Myr past the zero-age main sequence. The star nearly fills its Roche lobe (approximate to 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.