  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^-1 yr^-1, 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. If brown dwarfs are not
discovered in imaging surveys then we would infer that there is a large
population of gas giant planets present with semi-major axes in the 5 to 30 AU
range.
