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Radial velocity searches for extrasolar planets have discovered starsundergoing slow accelerations. The accelerations are likely due to one or moregas giant planets or brown dwarfs orbiting with period longer than the totaltime span of observations. The stellar acceleration is proportional to the massof the companion divided by the square of its radius from the star. In thispaper we predict the distribution of accelerations using a Monte Carlo methodand assuming a semi-major axis and mass distribution for the companions. Radialvelocity surveys find that ~20 and 10% of stars surveyed exhibit accelerationsabove ~10 and 25 m s^-1 yr^-1, respectively. We find that an extrapolation ofthe size and period distribution found by radial velocity surveys within ~5 AUor companion imaging surveys predicts too few systems with detectableaccelerations. The fractions of stars with accelerations above these values canbe matched if every star hosts a gas giant planet or brown dwarf withsemi-major axes between 4 and 20 AU or if a significant fraction (~70%) ofstars host 3 or more massive planets in this range. If brown dwarfs are notdiscovered in imaging surveys then we would infer that there is a largepopulation of gas giant planets present with semi-major axes in the 5 to 30 AUrange.

The statistics of accelerations seen in radial velocity searches for planets