Primordial black holes as seeds of magnetic fields in the universe

Abstract

Although it is assumed that magnetic fields in accretion discs 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 discs 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 discs 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 disc. In the case of a thin accretion disc around a rotating PBH, the field generation rate increases with increasing PBH spin. At a fixed r/risco, where r is the radial distance from the PBH and risco 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 dependence of the battery on accretion rate makes this mechanism a viable candidate to provide seed fields in an initially unmagnetized accretion disc, following which the magnetorotational instability could take over.