  Context. Observations of flux emergence indicate that rotational velocities
may develop within sunspots. However, the dependence of this rotation on
sub-photospheric field strength and twist remains largely unknown.
  Aims. We investigate the effects of varying the initial field strength and
twist of an emerging sub-photospheric magnetic flux tube on the rotation of the
sunspots at the photosphere.
  Methods. We consider a simple model of a stratified domain with a
sub-photospheric interior layer and three overlying atmospheric layers. A
twisted arched flux tube is inserted in the interior and is allowed to rise
into the atmosphere. To achieve this, the MHD equations are solved using the
Lagrangian-remap code, Lare3d. We perform a parameter study by independently
varying the sub-photospheric magnetic field strength and twist.
  Results. Altering the initial field strength and twist significantly affects
the tube's evolution and the rotational motions that develop at the
photosphere. The rotation angle, vorticity, and current show a direct
dependence on the initial field strength. We find that an increase in field
strength increases the angle through which the fieldlines rotate, the length of
fieldlines extending into the atmosphere, and the magnetic energy transported
to the atmosphere. This also affects the amount of residual twist in the
interior. The length of the fieldlines is crucial as we predict the twist per
unit length equilibrates to a lower value on longer fieldlines. No such direct
dependence is found when we modify the twist owing to the complex effect this
has on the tension force acting on the tube. However, there is still a clear
ordering in quantities such as the rotation angle, helicity, and free energy
with higher initial twist cases being related to sunspots that rotate more
rapidly, transporting more helicity and magnetic energy to the atmosphere.
