Primordial black holes as seeds of magnetic fields in the universe

Abstract: Although it is assumed that magnetic fields in accretion disks are dragged from the interstellar medium, the idea is likely not applicable to primordial black holes (PBHs) formed in the early universe. Here we show that magnetic fields can be generated in initially unmagnetized accretion disks around PBHs through the Biermann battery mechanism, and therefore provide the small scale seeds of magnetic field in the universe. The radial temperature and vertical density profiles of these disks provide the necessary conditions for the battery to operate naturally. The generated seed fields have a toroidal structure with opposite sign in the upper and lower half of the disk. In the case of a thin accretion disk around a rotating PBH, the field generation rate increases with increasing PBH spin. At a fixed $r/r_{\rm isco}$, where $r$ is the radial distance from the PBH and $r_{\rm isco}$ is the radius of the innermost stable circular orbit, the battery scales as $M^{-9/4}$, where $M$ is the PBH's mass. The very weak dependency of the battery on accretion rate, makes this mechanism a viable candidate to provide seed fields in an initially unmagnetized accretion disk, following which the magnetorotational instability could take over.