  The diffusion of astrophysical magnetic fields in conducting fluids in the
presence of turbulence depends on whether magnetic fields can change their
topology via reconnection in highly conducting media. Recent progress in
understanding fast magnetic reconnection in the presence of turbulence is
reassuring that the magnetic field behavior in computer simulations and
turbulent astrophysical environments is similar, as far as magnetic
reconnection is concerned. Our studies of magnetic field diffusion in turbulent
medium reveal interesting new phenomena. In the presence of gravity and
turbulence, our 3D simulations show the decrease of the magnetic flux-to-mass
ratio as the gaseous density at the center of the gravitational potential
increases. We observe this effect both in the situations when we start with
equilibrium distributions of gas and magnetic field and when we follow the
evolution of collapsing dynamically unstable configurations. Thus the process
of turbulent magnetic field removal should be applicable both to quasi-static
subcritical molecular clouds and cores and violently collapsing supercritical
entities. The increase of the gravitational potential as well as the
magnetization of the gas increases the segregation of the mass and magnetic
flux in the saturated final state of the simulations, supporting the notion
that the reconnection-enabled diffusivity relaxes the magnetic field + gas
system in the gravitational field to its minimal energy state. This effect is
expected to play an important role in star formation, from its initial stages
of concentrating interstellar gas to the final stages of the accretion to the
forming protostar.
