Can galactic magnetic fields diffuse into the voids?

Cosmic voids are magnetized at the level of at least 10-17 G on Mpc scales, as implied by blazar observations. We show that an electrically conducting plasma is present in the voids, and that, because of the plasma, diffusion into the voids of galactic fields generated by a mean-field dynamo is far too slow to explain the present-day void magnetization. Indeed, we show that even in the presence of turbulence in the voids, dynamo-generated galactic fields diffuse out to a galactocentric radius of only 200-400 kpc. Therefore, it is challenging to meet the required volume filling-factor of the void magnetic field. We conclude that a primordial origin remains the most natural explanation to the space-filling weak fields in voids.