Constraints on Primordial Black Holes from Galactic Diffuse Synchrotron Emissions

We investigate the possibility of constraining primordial black holes (PBHs) with masses $M_\mathrm{PBH}\gtrsim 10^{15}\,\mathrm{g}$ through Galactic diffuse synchrotron emissions. Due to Hawking radiation, these types of PBHs are expected to be stable sources of cosmic-ray (CR) electrons and positrons with energies below $\mathcal{O}(10\,\mathrm{MeV})$. In many CR propagation models with diffusive re-acceleration characterized by a significant Alfv\'{e}n velocity $V_a\sim \mathcal{O}(10)\,\mathrm{km/s}$, the energies of the evaporated electrons/positrons can be further enhanced to $\mathcal{O}(100)\,\mathrm{MeV}$ through their scattering with the Galactic random magnetic fields. Consequently, the observation of Galactic synchrotron emissions at frequencies above $\sim 20\,\mathrm{MHz}$ can provide useful constraints on the abundance of PBHs. Using the AMS-02 and Voyager-1 data on the boron-to-carbon nuclei flux ratio, we confirm that a significant Alfv\'{e}n velocity $V_a \sim 20\,\mathrm{km/s}$ is favored in several benchmark diffusive re-acceleration models. We show that, in this scenario, the observed low-frequency synchrotron emissions (from 22 MHz to 1.4 GHz) can provide stringent constraints on PBH abundance. The obtained conservative constraints are stronger than those derived from the Voyager-1 all-electron (electron plus positron) data by more than one order of magnitude for $M_\mathrm{PBH}\gtrsim 1\times 10^{16}\,\mathrm{g}$, and also stronger than our previous constraints derived from the AMS-02 positron data for $M_\mathrm{PBH}\gtrsim 2\times 10^{16}\,\mathrm{g}$.