The Validity of the Super-Particle Approximation during Planetesimal
  Formation
  The formation mechanism of planetesimals in protoplanetary discs is hotly
debated. Currently, the favoured model involves the accumulation of meter-sized
objects within a turbulent disc, followed by a phase of gravitational
instability. At best one can simulate a few million particles numerically as
opposed to the several trillion meter-sized particles expected in a real
protoplanetary disc. Therefore, single particles are often used as
super-particles to represent a distribution of many smaller particles. It is
assumed that small scale phenomena do not play a role and particle collisions
are not modeled. The super-particle approximation can only be valid in a
collisionless or strongly collisional system, however, in many recent numerical
simulations this is not the case.
  In this work we present new results from numerical simulations of
planetesimal formation via gravitational instability. A scaled system is
studied that does not require the use of super-particles. We find that the
scaled particles can be used to model the initial phases of clumping if the
properties of the scaled particles are chosen such that all important
timescales in the system are equivalent to what is expected in a real
protoplanetary disc. Constraints are given for the number of particles needed
in order to achieve numerical convergence.
  We compare this new method to the standard super-particle approach. We find
that the super-particle approach produces unreliable results that depend on
artifacts such as the gravitational softening in both the requirement for
gravitational collapse and the resulting clump statistics. Our results show
that short range interactions (collisions) have to be modelled properly.
