We have applied axisymmetric magnetohydrodynamic ( MHD ) simulations in order to investigate the impact of the accretion disk magnetic flux profile on the collimation of jets .
Using the ZEUS-3D code modified for magnetic diffusivity , our simulations evolve from an initial state in hydrostatic equilibrium and a force-free magnetic field configuration .
Considering a power law for the disk poloidal magnetic field profile B _ { P } \sim r ^ { - \mu } and for the density profile of the disk wind \rho \sim r ^ { - \mu _ { \rho } } , we have performed a systematic parameter study over a wide range of parameters \mu and \mu _ { \rho } .
We apply a toy parameterization for the magnetic diffusivity derived from the internal turbulent Alfvénic pressure .
We find that the degree of collimation ( quantified by the ratio of mass flow rates in axial and lateral direction ) decreases for a steeper disk magnetic field profile ( increasing \mu ) .
Varying the total magnetic flux does not change the degree of jet collimation substantially , it only affects the time scale of outflow evolution and the terminal jet speed .
As our major result we find a general relation between the collimation degree with the disk wind magnetization power law exponent .
Outflows with high degree of collimation resulting from a flat disk magnetic field profile tend to be unsteady , producing axially propagating knots as discussed earlier in the literature .
Depending slightly on the inflow density profile this unsteady behavior sets in for \mu < 0.4 .
We also performed simulations of jet formation with artificially enhanced decay of the toroidal magnetic field component in order to investigate the idea of a purely ” poloidal collimation ” previously discussed in the literature .
These outflows remain only weakly collimated and propagate with lower velocity .
Thanks to our large numerical grid size ( about 7 \times 14 AU for protostars ) , we may apply our results to recently observed hints of jet rotation ( DG Tau ) indicating a relatively flat disk magnetic field profile , \mu \simeq 0.5 .
In general , our results are applicable to both stellar and extragalactic sources of MHD jets .