Accretion in protoplanetary discs is thought to be driven by magnetohydrodynamic ( MHD ) turbulence via the magnetorotational instability ( MRI ) .
Recent work has shown that a planetesimal swarm embedded in a fully turbulent disc is subject to strong excitation of the velocity dispersion , leading to collisional destruction of bodies with radii R _ { p } < 100 km .
Significant diffusion of planetesimal semimajor axes also arises , leading to large-scale spreading of the planetesimal population throughout the inner regions of the protoplanetary disc , in apparent contradiction of constraints provided by the distribution of asteroids within the asteroid belt .
In this paper , we examine the dynamics of planetesimals embedded in vertically stratified turbulent discs , with and without dead zones .
Our main aims are to examine the turbulent excitation of the velocity dispersion , and the radial diffusion , of planetesimals in these discs .
We employ three dimensional MHD simulations using the shearing box approximation , along with an equilibrium chemistry model that is used to calculate the ionisation fraction of the disc gas as a function of time and position .
Ionisation is assumed to arise because of stellar X-rays , galactic cosmic rays and radioactive nuclei .
In agreement with our previous study , we find that planetesimals in fully turbulent discs develop large random velocities that will lead to collisional destruction/erosion for bodies with sizes below 100 km , and undergo radial diffusion on a scale \sim 2.5 au over a 5 Myr disc life time .
But planetesimals in a dead zone experience a much reduced excitation of their random velocities , and equilibrium velocity dispersions lie between the disruption thresholds for weak and strong aggregates for sizes R _ { p } \leq 100 km .
We also find that radial diffusion occurs over a much reduced length scale \sim 0.25 au over the disc life time , this being consistent with solar system constraints .
We conclude that planetesimal growth via mutual collisions between smaller bodies can not occur in a fully turbulent disc .
By contrast , a dead zone may provide a safe haven in which km-sized planetesimals can avoid mutual destruction through collisions .