{Influence of Primordial Magnetic Fields on 21 cm Emission}

We explore the effects of magnetic energy dissipation on the formation of the first stars. For this purpose, we follow the evolution of primordial chemistry in the presence of magnetic fields in the post-recombination universe until the formation of the first virialized halos. From the point of virialization, we follow the protostellar collapse up to densities of ~1012 cm-3 in a one-zone model. In the intergalactic medium (IGM), comoving field strengths of gsim0.1 nG lead to Jeans masses of 108 M sun or more and thus delay gravitational collapse in the first halos until they are sufficiently massive. During protostellar collapse, we find that the temperature minimum at densities of ~103 cm-3 does not change significantly, such that the characteristic mass scale for fragmentation is not affected. However, we find a significant temperature increase at higher densities for comoving field strengths of gsim 0.1 nG. This may delay gravitational collapse, in particular at densities of ~109 cm-3, where the proton abundance drops rapidly and the main contribution to the ambipolar diffusion resistivity is due to collisions with Li+. We further explore how the thermal evolution depends on the scaling relation of magnetic field strength with density. While the effects are already significant for our fiducial model with B vprop ρ0.5-0.57, the temperature may increase even further for steeper relations and lead to the complete dissociation of H2 at densities of ~1011 cm-3 for a scaling with B vprop ρ0.6. The correct modeling of this relation is therefore very important, as the increase in temperature enhances the subsequent accretion rate onto the protostar. Our model confirms that initial weak magnetic fields may be amplified considerably during gravitational collapse and become dynamically relevant. For instance, a comoving field strength above 10-5 nG will be amplified above the critical value for the onset of jets which can magnetize the IGM.