  We investigate orbital resonances expected to arise when a system of two
planets, with masses in the range 1-4 Earth masses, undergoes convergent
migration while embedded in a section of gaseous disc where the flow is
laminar. We consider surface densities corresponding to 0.5-4 times that
expected for a minimum mass solar nebula at 5.2 AU. Using hydrodynamic
simulations we find that when the configuration is such that convergent
migration occurs the planets can become locked in a first order
commensurability for which the period ratio is (p+1)/p with p being an integer
and migrate together maintaining it for many orbits. Relatively rapid
convergent migration as tends to occur for disparate masses, results in
commensurabilities with p larger than 2. However, in these cases the dynamics
is found to have a stochastic character. When the convergent migration is
slower, such as occurs in the equal mass case, lower p commensurabilities such
as 3:2 are attained which show much greater stability. In one already known
example of a system with nearly equal masses in the several Earth mass range
(planets around pulsar PSR B1257+12) the two largest planets are intriguingly
close to a 3:2 commensurability. A very similar behaviour is obtained when the
systems are modeled using an N body code with simple prescriptions for the disc
planet interaction. Using that, we found that an 8:7 resonance established in a
hydrodynamic simulation run for 10-100 thousand orbits could be maintained for
more than million orbits. Resonant capture leads to a rise in eccentricities
that can be predicted using a simple analytic model constructed in this paper.
We find that the system with the 8:7 commensurability is fully consistent with
this prediction.
