  Content: For up to a few millions of years, pebbles must provide a
quasi-steady inflow of solids from the outer parts of protoplanetary disks to
their inner regions. Aims: We wish to understand how a significant fraction of
the pebbles grows into planetesimals instead of being lost to the host star.
Methods:We examined analytically how the inward flow of pebbles is affected by
the snow line and under which conditions dust-rich (rocky) planetesimals form.
When calculating the inward drift of solids that is due to gas drag, we
included the back-reaction of the gas to the motion of the solids. Results: We
show that in low-viscosity protoplanetary disks (with a monotonous surface
density similar to that of the minimum-mass solar nebula), the flow of pebbles
does not usually reach the required surface density to form planetesimals by
streaming instability. We show, however, that if the pebble-to-gas-mass flux
exceeds a critical value, no steady solution can be found for the solid-to-gas
ratio. This is particularly important for low-viscosity disks (alpha < 10^(-3))
where we show that inside of the snow line, silicate-dust grains ejected from
sublimating pebbles can accumulate, eventually leading to the formation of
dust-rich planetesimals directly by gravitational instability. Conclusions:
This formation of dust-rich planetesimals may occur for extended periods of
time, while the snow line sweeps from several au to inside of 1 au. The
rock-to-ice ratio may thus be globally significantly higher in planetesimals
and planets than in the central star.
