  Cold steady-state disk wind theory from near Keplerian accretion disks
requires a large scale magnetic field at near equipartition strength. However
the minimum magnetization has never been tested. We investigate the time
evolution of an accretion disk threaded by a weak vertical magnetic field. The
strength of the field is such that the disk magnetization falls off rapidly
with radius. Four 2.5D numerical simulations of viscous resistive accretion
disk are performed using the magnetohydrodynamic code PLUTO. In these
simulations, a mean field approach is used and turbulence is assumed to give
rise to anomalous transport coefficients (alpha prescription). The large scale
magnetic field introduces only a small perturbation to the disk structure, with
accretion driven by the dominant viscous torque. A super fast magnetosonic jet
is observed to be launched from the innermost regions and remains stationary
over more than 953 Keplerian orbits. The self-confined jet is launched from a
finite radial zone in the disk which remains constant over time. Ejection is
made possible because the magnetization reaches unity at the disk surface, due
to the steep density decrease. However, no ejection is reported when the
midplane magnetization becomes too small. The asymptotic jet velocity remains
nevertheless too low to explain observed jets due to the negligible power
carried away by the jet. Astrophysical disks with superheated surface layers
could drive analogous outflows even if their midplane magnetization is low.
Sufficient angular momentum would be extracted by the turbulent viscosity to
allow the accretion process to continue. The magnetized outflows would be no
more than byproducts, rather than a fundamental driver of accretion. However,
if the midplane magnetization increases towards the center, a natural
transition to an inner jet dominated disk could be achieved.
