  We study the conditions for collisions between planetesimals to be
accretional or disruptive in turbulent disks, through analytical arguments
based on fluid dynamical simulations and orbital integrations. In turbulent
disks, the velocity dispersion of planetesimals is pumped up by random
gravitational perturbations from density fluctuations of the disk gas. When the
velocity dispersion is larger than the planetesimals' surface escape velocity,
collisions between planetesimals do not result in accretion, and may even lead
to their destruction. In disks with a surface density equal to that of the
``minimum mass solar nebula'' and with nominal MRI turbulence, we find that
accretion proceeds only for planetesimals with sizes above $\sim 300$ km at 1AU
and $\sim 1000$ km at 5AU. We find that accretion is facilitated in disks with
smaller masses. However, at 5AU and for nominal turbulence strength, km-sized
planetesimals are in a highly erosive regime even for a disk mass as small as a
fraction of the mass of Jupiter. The existence of giant planets implies that
either turbulence was weaker than calculated by standard MRI models or some
mechanism was capable of producing Ceres-mass planetesimals in very short
timescales. In any case, our results show that in the presence of turbulence
planetesimal accretion is most difficult in massive disks and at large orbital
distances.
