Exploring Faraday rotation signatures and population bounds for primordial magnetic black holes

Abstract: Primordial black holes bearing magnetic charges may bypass the constraints imposed by Hawking radiation, thereby enabling reasonable present-day populations, even for masses below $10^{15}\, \mathrm{g} $--a range previously considered improbable. They could, therefore, conceivably contribute to a component of dark matter. We investigate novel Faraday rotation signatures exhibited by primordial magnetic black holes while also establishing new Parker-type bounds on their populations. For the latter, we bound the dark matter fraction from intergalactic magnetic fields in cosmic voids $\left(f_{\text{ DM}} \lesssim 10^{-8}\right)$ and cosmic web filaments $\left(f_{\text{ DM}} \lesssim 10^{-4}\right)$, notably eclipsing previous bounds. Exploring Faraday rotation effects, we discern a pronounced rotation of the polarization angle and the rotation measure values for extremal primordial magnetic black holes with masses $M^{\text{ex.}}_{\text{ BH}} \gtrsim 10^{-6}~ \text{M}_\odot$. This makes them potentially detectable in current observations. A comparative investigation finds that the effects are notably greater than for a neutron star, like a Magnetar, with a similar magnetic field at the surface. Moreover, the polarization angle maps for primordial magnetic black holes exhibit unique features, notably absent in other astrophysical magnetic configurations. In this context, we also introduce a simple integral measure, offering a quantitative measure for their discrimination in many scenarios. These traits potentially suggest a robust avenue for their observational detection and differentiation.