Moving mesh simulations of star forming cores in
  magneto-gravo-turbulence
  Star formation in our Galaxy occurs in molecular clouds that are
self-gravitating, highly turbulent, and magnetized. We study the conditions
under which cloud cores inherit large-scale magnetic field morphologies and how
the field is governed by cloud turbulence. We present four moving-mesh
simulations of supersonic, turbulent, isothermal, self-gravitating gas with a
range of magnetic mean-field strengths characterized by the Alfv\'enic Mach
number $\mathcal{M}_{{\rm A}, 0}$, resolving pre-stellar core formation from
parsec to a few AU scales. In our simulations with the turbulent kinetic energy
density dominating over magnetic pressure ($\mathcal{M}_{{\rm A}, 0}>1$), we
find that the collapse is approximately isotropic with $B\propto\rho^{2/3}$,
core properties are similar regardless of initial mean-field strength, and the
field direction on $100$ AU scales is uncorrelated with the mean field.
However, in the case of a dominant large-scale magnetic field
($\mathcal{M}_{{\rm A}, 0}=0.35$), the collapse is anisotropic with
$B\propto\rho^{1/2}$. This transition at $\mathcal{M}_{{\rm A}, 0}\sim1$ is not
expected to be sharp, but clearly signifies two different paths for magnetic
field evolution in star formation. Based on observations of different star
forming regions, we conclude that star formation in the interstellar medium may
occur in both regimes. Magnetic field correlation with the mean-field extends
to smaller scales as $\mathcal{M}_{{\rm A}, 0}$ decreases, making future ALMA
observations useful for constraining $\mathcal{M}_{{\rm A}, 0}$ of the
interstellar medium.
