Primordial magnetic field generation via primordial black hole disks

Large scale primordial magnetic fields (PMFs) threading the intergalactic medium are observed ubiquitously in the Universe playing a key role in the cosmic evolution. Their origin is still debated constituting a very active field of research. In the present article, we propose a novel natural ab initio mechanism for the origin of such PMFs through the portal of supermassive primordial black holes (PBHs) forming between the Big Bang Nucleosynthesis and the recombination era. In particular, by considering PBHs furnished with a locally isothermal disk we study the generation of a Biermann battery induced seed magnetic field (MF) due to the vortexlike motion of the primordial plasma around the black hole. Finally, by considering monochromatic PBH mass distributions and deriving the relevant MF power spectrum we make a conservative estimate for the seed PMF in intergalactic scales and at redshift $z=30$, when typical galaxies are considered to form, which reads as $B\simeq 10^{-30}\mathrm{G}\left(\frac{\ell_\mathrm{R}}{10^6}\right)^2\left(\frac{M_\mathrm{PBH}}{10^{14}M_\odot}\right)^{5/2}$, where $M_\mathrm{PBH}$ is the PBH mass and $\ell_\mathrm{R}\equiv R_\mathrm{d}/R_\mathrm{ISCO}$, is the ratio of the radius of the disk, $R_\mathrm{d}$ over the radius of the innermost stable circular orbit, $R_\mathrm{ISCO}$. Interestingly enough, by requiring to seed a PMF of the order of $10^{-30}\mathrm{G}$ necessary to give rise to a present day $10^{-18}\mathrm{G}$ in intergalactic scales, we find a lower bound on the PBH mass within the range $[10^{10}- 10^{16}]M_\odot$ depending on the radius of the PBH disk.