THE TRENDS HIGH-CONTRAST IMAGING SURVEY. IV. THE OCCURRENCE RATE OF GIANT PLANETS AROUND M DWARFS

Abstract

Doppler-based planet surveys have discovered numerous giant planets but are\nincomplete beyond several AU. At larger star-planet separations, direct planet\ndetection through high-contrast imaging has proven successful, but this\ntechnique is sensitive only to young planets and characterization relies upon\ntheoretical evolution models. Here we demonstrate that radial velocity\nmeasurements and high-contrast imaging can be combined to overcome these\nissues. The presence of widely separated companions can be deduced by\nidentifying an acceleration (long-term trend) in the radial velocity of a star.\nBy obtaining high spatial resolution follow-up imaging observations, we rule\nout scenarios in which such accelerations are caused by stellar binary\ncompanions with high statistical confidence. We report results from an analysis\nof Doppler measurements of a sample of 111 M-dwarf stars with a median of 29\nradial velocity observations over a median time baseline of 11.8 yr. By\ntargeting stars that exhibit a radial velocity acceleration ("trend") with\nadaptive optics imaging, we determine that 6.5% +/- 3.0% of M-dwarf stars host\none or more massive companions with 1 < m/M_Jupiter < 13 and 0 < a < 20 AU.\nThese results are lower than analyses of the planet occurrence rate around\nhigher-mass stars. We find the giant planet occurrence rate is described by a\ndouble power law in stellar mass M and metallicity F = [Fe/H] such that f(M,F)\n= 0.039(+0.056,-0.028) M^(0.8(+1.1,-0.9)) 10^((3.8 +/- 1.2)F). Our results are\nconsistent with gravitational microlensing measurements of the planet\noccurrence rate; this study represents the first model-independent comparison\nwith microlensing observations.\n