Constraining memory-burdened primordial black holes with graviton-photon conversion and binary mergers

The memory-burden effect stabilizes the evaporating Primordial Black Holes (PBHs) before its complete decay. This also suppresses the evaporation flux via the entropy factor to the $k$-th power and circumvents severely astrophysical and cosmological constraints, such that it opens a new mass window for PBH Dark Matter lighter than $10^{15}$ g which has entered the memory-burden phase in the present epoch. In this study, we propose two scenarios to probe PBHs in the earlier semiclassical phase that evaporate at unsuppressed rates. The first scenario considers gravitons, emitted semiclassically from PBHs, propagating across the recombination epoch, then the magnetic field in the cosmological filaments converts them into photons via the Gertsenshtein effect. The second scenario relies on the PBHs mergers today, reproducing young semiclassical black holes with unsuppressed evaporation, but it is highly model dependent and has no sufficient theory support. For phenomenology studies, we perform computations of the extragalactic photon spectrum from PBHs emission according to these scenarios. The upper limits on the fractional abundance of PBH are obtained by comparing with the sensitivities of gamma-ray observations. The graviton-photon conversion scenario excludes the mass window $7.5\times 10^5\,{\rm g} \leq M_{\rm PBH}\leq 4.4\times 10^7\,{\rm g}$ with $f_{\rm PBH}|_{T_\phi}\geq 1$ and $k=1$, assuming the optimistic magnetic field $B_0=100$ nG. Meanwhile, the merging scenario, which is insensitive on $k$, restricts PBH Dark Matter lighter than $2.2\times 10^{11}$ g.