  Pairs of extrasolar giant planets in a mean motion commensurability are
common with 2:1 resonance occurring most frequently. Disc-planet interaction
provides a mechanism for their origin. However, the time scale on which this
could operate in particular cases is unclear. We perform 2D and 3D numerical
simulations of pairs of giant planets in a protoplanetary disc as they form and
maintain a mean motion commensurability. We consider systems with current
parameters similar to those of HD 155358, 24 Sextantis and HD 60532, and disc
models of varying mass, decreasing mass corresponding to increasing age. For
the lowest mass discs, systems with planets in the Jovian mass range migrate
inwards maintaining a 2:1 commensurability. Systems with the inner planet
currently at around 1 au from the central star could have originated at a few
au and migrated inwards on a time scale comparable to protoplanetary disc
lifetimes. Systems of larger mass planets such as HD 60532 attain 3:1 resonance
as observed. For a given mass accretion rate, results are insensitive to the
disc model for the range of viscosity prescriptions adopted, there being good
agreement between 2D and 3D simulations. However, in a higher mass disc a pair
of Jovian mass planets passes through 2:1 resonance before attaining a
temporary phase lasting a few thousand orbits in an unstable 5:3 resonance
prior to undergoing a scattering. Thus finding systems in this commensurability
is unlikely.
