Collimation of astrophysical jets - the role of the accretion disk magnetic field distribution

We have applied axisymmetric MHD simulations to investigate the impact of the accretion disk magnetic flux profile on the jet collimation. Using the ZEUS-3D code modified for magnetic diffusivity, our simulations evolve from an initial hydrostatic equilibrium state in a force-free magnetic field. Considering a power law for the disk poloidal magnetic field profile Bp ~ r^{-mu} and for the disk wind density profile rho ~ r^{-mu_rho} we performed a systematic study over a wide parameter range mu and mu_rho. We find a degree of collimation (ratio of mass flow rates in axial and lateral direction) decreasing for steeper disk magnetic field profiles (increasing mu). Varying the total magnetic flux doesn't 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 collimation degree resulting from a flat disk magnetic field profile tend to be unsteady, producing axially propagating knots as discussed earlier. 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 in order to investigate the idea of a purely "poloidal collimation" discussed in the literature. These outflows remain weakly collimated and propagate with lower velocity. Thanks to our large numerical grid size (7x14 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 ~ 0.5. In general, our results are applicable to both stellar and extragalactic sources of MHD jets.