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We report precise Doppler measurements of the nearby (d = 10.34 pc) M dwarf Gl 649 that reveal the presence of a planet with a minimum mass MP sin i = 0.328 MJup in an eccentric (e = 0.30), 598.3 day orbit. Our photometric monitoring reveals Gl 649 to be a new variable star with brightness changes on both rotational and decadal timescales. However, neither of these timescales are consistent with the 600 day Doppler signal and so provide strong support for planetary reflex motion as the best interpretation of the observed radial velocity variations. Gl 649b is only the seventh Doppler-detected giant planet around an M dwarf. The properties of the planet and host-star therefore contribute significant information to our knowledge of planet formation around low-mass stars. We revise and refine the occurrence rate of giant planets around M dwarfs based on the California Planet Survey sample of low-mass stars (M < 0.6 M). We find that of stars with M < 0.6 M harbor planets with MP sin i > 0.3 MJup and a < 2.5 AU. When we restrict our analysis to metal-rich stars with [Fe/H] > +0.2, we find that the occurrence rate is .