The statistics of accelerations seen in radial velocity searches for planets

Radial velocity searches for extrasolar planets have discovered stars undergoing slow accelerations. The accelerations are likely due to one or more gas giant planets or brown dwarfs orbiting with period longer than the total time span of observations. The stellar acceleration is proportional to the mass of the companion divided by the square of its radius from the star. In this paper we predict the distribution of accelerations using a Monte Carlo method and assuming a semi-major axis and mass distribution for the companions. Radial velocity surveys find that ∼ 20 and 10% of stars surveyed exhibit accelerations above ∼ 10 and 25 m s yr, respectively. We find that an extrapolation of the size and period distribution found by radial velocity surveys within ∼ 5 AU or companion imaging surveys predicts too few systems with detectable accelerations. The fractions of stars with accelerations above these values can be matched if every star hosts a gas giant planet or brown dwarf with semi-major axes between 4 and 20 AU or if a significant fraction (∼ 70%) of stars host 3 or more massive planets in this range. This suggests that there is a large undiscovered population of gas giant planets and brown dwarfs present with semi-major axes in the 5–30 AU range.