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A Keck HIRES Doppler Search for Planets Orbiting Metal-Poor Dwarfs. II. On the Frequency of Giant Planets in the Metal-Poor Regime

We present an analysis of three years of precision radial velocity measurements of 160 metal-poor stars observed with HIRES on the Keck 1 telescope. We report on variability and long-term velocity trends for each star in our sample. We identify several long-term, low-amplitude radial-velocity variables worthy of follow-up with direct imaging techniques. We place lower limits on the detectable companion mass as a function of orbital period. Our survey would have detected, with a 99.5% confidence level, over 95% of all companions on low-eccentricity orbits with velocity semi-amplitude K > 100 m/s, or M_p*sin(i) > 3.0 M_JUP*(P/yr)^(1/3), for orbital periods P< 3 yr. None of the stars in our sample exhibits radial-velocity variations compatible with the presence of Jovian planets with periods shorter than the survey duration. The resulting average frequency of gas giants orbiting metal-poor dwarfs with -2.0 < [Fe/H] < -0.6 is f_p<0.67% (at the 1-sigma confidence level). We examine the implications of this null result in the context of the observed correlation between the rate of occurrence of giant planets and the metallicity of their main-sequence solar-type stellar hosts. By combining our dataset with the Fischer & Valenti (2005) uniform sample, we confirm that the likelihood of a star to harbor a planet more massive than Jupiter within 2 AU is a steeply rising function of the host's metallicity. However, the data for stars with -1.0 < [Fe/H] < 0.0 are compatible, in a statistical sense, with a constant occurrence rate f_p~1%. Our results can usefully inform theoretical studies of the process of giant planet formation across two orders of magnitude in metallicity.