MOA-2009-BLG-387Lb: a massive planet orbiting an M dwarf

Aims. We report the discovery of a planet with a high planet-to-star mass ratio in the microlensing event MOA-2009-BLG-387, which exhibited pronounced deviations over a 12-day interval, one of the longest for any planetary event. The host is an M dwarf, with a mass in the range 0.07 M-circle dot < M-host < 0.49 M-circle dot at 90% confidence. The planet-star mass ratio q = 0.0132 +/- 0.003 has been measured extremely well, so at the best-estimated host mass, the planet mass is m(p) = 2.6 Jupiter masses for the median host mass, M = 0.19 M-circle dot. Methods. The host mass is determined from two "higher order" microlensing parameters. One of these, the angular Einstein radius theta(E) = 0.31 +/- 0.03 mas has been accurately measured, but the other (the microlens parallax pi(E), which is due to the Earth's orbital motion) is highly degenerate with the orbital motion of the planet. We statistically resolve the degeneracy between Earth and planet orbital effects by imposing priors from a Galactic model that specifies the positions and velocities of lenses and sources and a Kepler model of orbits. Results. The 90% confidence intervals for the distance, semi-major axis, and period of the planet are 3.5 kpc < D-L < 7.9 kpc, 1.1 AU < a < 2.7 AU, and 3.8 yr < P < 7.6 yr, respectively.