Magnetic field generation from primordial black hole distributions

Abstract

We introduce a general statistical method for estimating first-order magnetic field fluctuations generated from primordial black hole (PBH) populations. To that end, we consider monochromatic and extended Press-Schechter PBH mass functions for different formation scenarios, such that each constituent is capable of producing its own magnetic field due to some given physical mechanism. Assuming the simplest linear correlation between magnetic field fluctuations and matter over-densities, our estimates depend on the mass function, on the physical field generation mechanism by each PBH constituent, and on a certain PBH characteristic distance which is also introduced in this work. After studying the statistics of magnetic field fluctuations by defining the corresponding magnetic power spectrum, we apply our general formalism to study the plausibility that two particular field generation mechanisms could have given rise to the expected seed fields according to current observational constraints. The first example is the Biermann battery as a prominent primordial seed field generation candidate, and the second one is due to the accretion of magnetic monopoles at PBH formation, constituting magnetic PBHs. Our results show that, for monochromatic distributions, it does not seem to be possible to generate sufficiently intense seed fields in any of the two field generation mechanisms explored here. For extended distributions, it is also not possible to generate the required seed field by only assuming a Biermann battery mechanism. In fact, we report an average seed field by this mechanism of about 10 −47 G, at z = 20. For the case of magnetic monopoles we instead assume that the seed values from the literature are achieved and calculate the necessary number density of monopoles. In this case we obtain values that are below the upper limits from current constraints.