  (Abridged) We present numerical simulations of the formation of the planetary
companions to 47 UMa, rho CrB, and 51 Peg. They are assumed to have formed in
situ according to the basic model that a core formed first by accretion of
solid particles, then later it captured substantial amounts of gas from the
protoplanetary disk. In most of the calculations we prescribe a constant
accretion rate for the solid core. The evolution of the gaseous envelope
assumes that: (1) it is in quasi-hydrostatic equilibrium, (2) the gas accretion
rate is determined by the requirement that the outer radius of the planet is
the place at which the thermal velocity of the gas allows it to reach the
boundary of the planet's Hill sphere, (3) the gas accretion rate is limited,
moreover, by the prescribed maximum rate at which the nebula can supply the
gas, and (4) the growth of the planet stops once it obtains approximately the
minimum mass determined from radial velocity measurements. Calculations are
carried out through an initial phase during which solid accretion dominates,
past the point of crossover when the masses of solid and gaseous material are
equal, through the phase of rapid gas accretion, and into the final phase of
contraction and cooling at constant mass. Alternative calculations are
presented for the case of 47 UMa in which the solid accretion rate is
calculated, not assumed, and the dissolution of planetesimals within the
gaseous envelope is considered. In all cases there is a short phase of high
luminosity (1e-3-1e-2 Lsun) associated with rapid gas accretion. The height and
duration of this peak depend on uncertain model parameters. The conclusion is
reached that in situ formation of all of these companions is possible under
some conditions. However, it is more likely that orbital migration was an
important component of the evolution, at least for the planets around rho CrB
and 51 Peg.
