Generation of Primordial Magnetic Fields on Linear Overdensity Scales

Magnetic fields appear to be present in all galaxies and galaxy clusters. Recent measurements indicate that a weak magnetic field may be present even in the smooth low density intergalactic medium. One explanation for these observations is that a seed magnetic field was generated by some unknown mechanism early in the life of the Universe, and was later amplified by various dynamos in nonlinear objects like galaxies and clusters. We show that a primordial magnetic field is expected to be generated in the early Universe on purely linear scales through vorticity induced by scale-dependent temperature fluctuations, or equivalently, a spatially varying speed of sound of the gas. Residual free electrons left over after recombination tap into this vorticity to generate magnetic field via the Biermann battery process. Although the battery operates even in the absence of any relative velocity between dark matter and gas at the time of recombination, the presence of such a relative velocity modifies the predicted spatial power spectrum of the magnetic field. At redshifts of order a few tens, we estimate a root mean square field strength of order ${10}^{-25}–{10}^{-24}\mathrm{G}$ on comoving scales $\sim 10\mathrm{kpc}$. This field, which is generated purely from linear perturbations, is expected to be amplified significantly after reionization, and to be further boosted by dynamo processes during nonlinear structure formation.

Figure 1

Perturbation ratios ${\delta }_T/{\delta }_b$ (top panel) and ${\delta }_T/{\delta }_e$ (bottom panel) as a function of wave number $k$. We consider two cases: no stream velocity, $v_{\mathrm{bc}}=0$ (solid lines), and a typical stream velocity, $v_{\mathrm{bc}}=1{\sigma }_{\mathrm{vbc}}$ (dashed lines). Results are shown for two redshifts, $z=100$ (blue lines) and $z=30$ (red lines).

Figure 2

Root mean square magnetic field generated by the Biermann battery as a function of wave number. Two cases are shown: no stream velocity, $v_{\mathrm{bc}}=0$ (solid lines), and a typical stream velocity, $v_{\mathrm{bc}}=1{\sigma }_{\mathrm{vbc}}$ (dashed lines). Three redshifts are considered: $z=100$ (blue lines), $z=30$ (red lines), $z=10$ (black lines).