  Binary solar system objects are common and range from satellite systems with
very large mass ratios $M_1/M_2$ to mass ratios very close to unity. A
well-known example of a binary is the Pluto-Charon system. With Charon only
eight times less massive than Pluto the question arises as for many other
systems, why the mass-ratio is still close to unity. There is much evidence
that (binary) planet(esimal) formation happened early, when the protoplanetary
gas disk was still around. It is likely that (some of) these binaries grew up
together subject to pebble accretion. Here we focus on the question of how the
mass arriving in the gravitational influence zone of the binary during pebble
accretion, is distributed over the binary components. Does the accretion
through time lead to a converging mass ratio, or to a diverging mass ratio? We
numerically integrate pebble paths in the same well-known fashion as for a
single mass subject to pebble accretion and track what the efficiency of
accretion is for the two separate binary components, compared to a single body
with the same mass. These numerical simulations are done for a range of binary
mass-ratios, mutual separations, Stokes numbers and two orbital distances, 2.5
and 39 au. We find that in the limit where pebbles start to spiral around the
primary (this holds for relatively large pebbles), the pebble preferentially
collides with the secondary, causing the mass ratio to converge towards unity
on Myr timescales. In this regime the total sweep-up efficiency can lower to
half that of a pebble-accreting single body because pebbles that are thrown out
of the system, after close encounters with the system. The results show that
systems such as Pluto-Charon and other larger equal mass binaries could well
have co-accreted by means of pebble accretion in the disk phase without
producing binaries with highly diverging mass-ratios.
