  Recent observational results for magnetic fields in molecular clouds reviewed
by Crutcher (2012) seem to be inconsistent with the predictions of the
ambipolar diffusion theory of star formation. These include the measured
decrease in mass to flux ratio between envelopes and cores, the failure to
detect any self-gravitating magnetically subcritical clouds, the determination
of the flat PDF of the total magnetic field strengths implying that there are
many clouds with very weak magnetic fields, and the observed scaling $B \propto
\rho^{2/3}$ that implies gravitational contraction with weak magnetic fields.
We consider the problem of magnetic field evolution in turbulent molecular
clouds and discuss the process of magnetic field diffusion mediated by magnetic
reconnection. For this process that we termed "reconnection diffusion" we
provide a simple physical model and explain that this process is inevitable in
view of the present day understanding of MHD turbulence. We address the issue
of the expected magnetization of cores and envelopes in the process of star
formation and show that reconnection diffusion provides an efficient removal of
magnetic flux that depends only on the properties of MHD turbulence in the core
and the envelope. As a result, the magnetic flux trapped during the collapse in
the envelope is being released faster than the flux trapped in the core,
resulting in much weaker fields in envelopes than in cores, as observed. We
provide simple semi-analytical model calculations which support this conclusion
and qualitatively agree with the observational results. We argue that magnetic
reconnection provides a solution to the magnetic flux problem of star formation
that agrees better with observations than the long-standing ambipolar diffusion
paradigm.
