Gravitational to Coulomb force ratio and the origin of the Cosmic magnetic field

The origin of the seeds of galactic magnetic fields is a subject that remains under debate. Here we will explore a simple source based on tiny charge asymmetries in slowly rotating protogalaxies. We use current knowledge of galaxy formation and evolution to estimate that a charge imbalance of $1$ every $\sim 10^{38\pm 5}$ charge carriers in slowly rotating protogalaxies can provide adequate seeds for the galactic dynamos. Interestingly, this is of the same order than the ratio of gravitational to Coulomb forces between the elementary plasma constituents. Motivated by this fact, we study different mechanisms for generating such charge imbalances from a direct interplay of gravitational and Coulomb forces, namely the possibility that these are of primordial origin, that stellar or primordial black holes redistribute charge in protogalaxies, or that the imbalance is sourced by gravity as the galaxy forms in quasi-hydrostatic equilibrium. Our results show that primordial asymmetries drop to small values by the onset of galaxy formation, with an amplitude that is similar to the possible charge asymmetries that could be produced by black holes. Although these charge asymmetries can have values within the range of interest, they are much smaller than the gravitationally induced one in hydrostatic equilibrium conditions. The latter lies in the upper range of the required charge imbalance.