  Are the kG-strength magnetic fields observed in young stars a fossil field
left over from their formation or are they generated by a dynamo? We use
radiation non-ideal magnetohydrodynamics simulations of the gravitational
collapse of a rotating, magnetized molecular cloud core over 17 orders of
magnitude in density, past the first hydrostatic core to the formation of the
second, stellar core, to examine the fossil field hypothesis. Whereas in
previous work we found that magnetic fields in excess of 10 kG can be implanted
in stars at birth, this assumed ideal magnetohydrodynamics (MHD), i.e. that the
gas is coupled to the magnetic field. Here we present non-ideal MHD
calculations which include Ohmic resistivity, ambipolar diffusion and the Hall
effect. For realistic cosmic ray ionization rates, we find that magnetic field
strengths of $\lesssim$ kG are implanted in the stellar core at birth, ruling
out a strong fossil field. While these results remain sensitive to resolution,
they cautiously provide evidence against a fossil field origin for stellar
magnetic fields, suggesting instead that magnetic fields in stars originate in
a dynamo process.
