A precise numerical estimation of the magnetic field generated around recombination

Understand

We investigate the generation of magnetic fields from non-linear effects around recombination.

• As tight-coupling is gradually lost when approaching $z\simeq 1100$, the velocity difference between photons and baryons starts to increase, leading to an increasing Compton drag of the photons on the electrons.
• The protons are then forced to follow the electrons due to the electric field created by the charge displacement; the same field, following Maxwell's laws, eventually induces a magnetic field on cosmological scales.
• Since scalar perturbations do not generate any magnetic field as they are curl-free, one has to resort to second-order perturbation theory to compute the magnetic field generated by this effect.