Star Formation and the Hall Effect

The breakdown of flux-freezing in molecular clouds and protostellar discs is usually approximated by ambipolar diffusion at low densities or by resistive diffusion at high densities. Here I discuss an intermediate regime in which the Hall term in the conductivity tensor is significant, and the vector evolution of the magnetic field -- and therefore the evolution of the system under consideration -- is dramatically altered. Calculations of charged particle abundances in dense gas in molecular clouds and protostellar discs demonstrate that Hall diffusion is important over a surprisingly broad range of conditions.