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 Alfvén 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 Alfvén 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 $M_\mathrm{PBH}\gtrsim 2\times 10^{16},\mathrm{g}$.

💡 Research Summary

This paper investigates how primordial black holes (PBHs) with masses above the evaporation limit ($M_{\rm PBH}\gtrsim10^{15}$ g) can be constrained by the diffuse Galactic synchrotron emission they generate through Hawking‑radiated electrons and positrons. The authors first compute the primary and secondary electron/positron spectra emitted by PBHs using the BlackHawk code, considering both monochromatic and log‑normal mass functions. They then model the propagation of these particles in the Milky Way with the GALPROP framework, solving the full diffusion–convection–reacceleration equation.

A key ingredient is diffusive re‑acceleration, parameterized by the Alfvén speed $V_a$. By fitting the boron‑to‑carbon (B/C) ratio measured by AMS‑02 and Voyager‑1, the authors find that several benchmark propagation models (with halo heights $z_h=4$–10 kpc) favor a sizable $V_a\sim20$ km s⁻¹. In such models, low‑energy ($\sim10$ MeV) electrons/positrons from PBH evaporation are boosted to $\sim100$ MeV during their Galactic journey. This energy corresponds to synchrotron frequencies above $\sim20$ MHz for typical Galactic magnetic fields, making low‑frequency radio observations a sensitive probe of the PBH‑induced electron population.

The synchrotron intensity is calculated for a set of Galactic magnetic field models and compared with existing all‑sky radio surveys at 22 MHz, 45 MHz, 150 MHz, 408 MHz, and 1.4 GHz. By requiring that the PBH‑induced synchrotron component does not exceed the observed sky brightness, the authors derive upper limits on the PBH dark‑matter fraction $f_{\rm PBH}$. For masses $M_{\rm PBH}\gtrsim10^{16}$ g, the constraints reach $f_{\rm PBH}\lesssim10^{-3}$ (or lower depending on the exact mass), which are more than an order of magnitude stronger than those obtained from Voyager‑1 all‑electron data and also surpass previous limits based on AMS‑02 positron measurements for $M_{\rm PBH}\gtrsim2\times10^{16}$ g.

The analysis includes robustness checks: varying $V_a$ from 13 km s⁻¹ to 40 km s⁻¹ shows the constraints tighten dramatically with larger re‑acceleration; changing the magnetic field strength or geometry has a modest impact; and exploring different widths of the log‑normal mass distribution confirms that the limits are relatively insensitive to the exact shape of the PBH mass function as long as the characteristic mass lies in the $10^{16}$–$10^{17}$ g range.

Overall, the work demonstrates that Galactic diffuse synchrotron emission, when interpreted with well‑constrained cosmic‑ray propagation parameters, provides a powerful and complementary avenue to probe PBHs in the $10^{15}$–$10^{18}$ g mass window. The method leverages independent B/C measurements to fix the re‑acceleration strength, reducing model dependence, and exploits low‑frequency radio data that are already available. Future improvements in low‑frequency radio surveys (e.g., SKA‑Low, upgraded LOFAR) and tighter CR propagation constraints could push the limits on $f_{\rm PBH}$ down to $10^{-4}$ or below, further testing the hypothesis that PBHs constitute a significant fraction of dark matter.