The Influence of Magnetic Fields on the Thermodynamics of Primordial Star Formation

Abstract

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 ∼ 10 12 cm −3 in a one-zone model. In the intergalactic medium (IGM), comoving field strengths of 0.1 nG lead to Jeans masses of 10 8 M ⊙ 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 ∼ 10 3 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 0.1 nG. This may delay gravitational collapse, in particular at densities of ∼ 10 9 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 ∝ ρ 0.5−0.57 , the temperature may increase even further for steeper relations and lead to the complete dissociation of H 2 at densities of ∼ 10 11 cm −3 for a scaling with B ∝ ρ 0.6 . 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.

The role of magnetic fields during primordial star formation

“…A spectral analysis shows that turbulence is injected at the Jeans scale [14], and confirms the expected Kazantsev slope [15]. Using models for ambipolar diffusion and Ohmic dissipation in primordial gas [16], we checked that the resistive scales are always smaller than the Jeans scale during gravitational collapse (see Fig. 1).…”

Formation and evolution of primordial protostellar systems

“…Another complication is given by magnetic fields, which are thought to be important in minihaloes (e.g. Machida et al 2008;Xu et al 2008;Schleicher et al 2009Schleicher et al , 2010Sur et al 2010;Federrath et al 2011;Schober et al 2012;Turk et al 2012). Next-generation simulations should therefore include additional physics, as well as continue the simulations to later times.…”

Reionization constraints on primordial magnetic fields

“…The matter power spectrum is shown in the Figure 1 for different values of B0 and nB along with the power spectrum for the usual ΛCDM case. As shown in the Figure, we adopt a sharp cut-off of the matter power spectrum at the magnetic Jeans' scale k = kJ (Peebles 1980;Sethi & Subramanian 2005;Tashiro & Sugiyama 2006a;Tashiro & Sugiyama 2006b;Schleicher et al 2009;Tashiro & Sugiyama 2011;Schleicher & Miniati 2011;Tashiro, Takahashi, & Ichiki 2012;Pandey & Sethi 2012). We note that the mass dispersion σ 2 ∝ k 3 P (k) and the number of haloes for a given mass is very sensitive to σ.…”