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We explore the effects of magnetic energy dissipation on the formation of thefirst stars. For this purpose, we follow the evolution of primordial chemistryin the presence of magnetic fields in the post-recombination universe until theformation of the first virialized halos. From the point of virialization, wefollow the protostellar collapse up to densities of $\sim10^{12}$ cm$^{-3}$ ina one-zone model. In the intergalactic medium (IGM), comoving field strengthsof $\gtrsim0.1$ nG lead to Jeans masses of $10^8 M_\odot$ or more and thusdelay gravitational collapse in the first halos until they are sufficientlymassive. During protostellar collapse, we find that the temperature minimum atdensities of $\sim10^3$ cm$^{-3}$ does not change significantly, such that thecharacteristic mass scale for fragmentation is not affected. However, we find asignificant temperature increase at higher densities for comoving fieldstrengths of $\gtrsim0.1$ nG. This may delay gravitational collapse, inparticular at densities of $\sim10^9$ cm$^{-3}$, where the proton abundancedrops rapidly and the main contribution to the ambipolar diffusion resistivityis due to collisions with Li$^+$. After the formation of the protostar, theincreased gas temperatures may enhance the protostellar accretion rate. Ourmodel confirms that initial weak magnetic fields may be amplified considerablyduring gravitational collapse and become dynamically relevant. For instance, acomoving field strength above $10^{-5}$ nG will be amplified above the criticalvalue for the onset of jets which can magnetize the IGM.

The influence of magnetic fields on the thermodynamics of primordial star formation