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

TL;DR

The memory-burden effect prolongs the lifetime of low-mass primordial black holes (PBHs) by suppressing Hawking evaporation with a factor $S(M_{ m PBH})^k$, creating a distinct semiclassical-burden evolution that opens a light-mass dark matter window. The authors propose two probes of PBHs in the early semiclassical phase: (i) gravitons emitted from PBHs can convert to photons in cosmological filaments via the Gertsenshtein effect, and (ii) present-day PBH mergers produce young semiclassical black holes with unsuppressed evaporation, leading to observable gamma-ray spectra. They compute the resulting extragalactic photon flux for both scenarios and derive upper bounds on the PBH abundance $f_{ m PBH}$ by comparing with gamma-ray observations, finding that graviton-photon conversion excludes a mass window $7.5\times10^{5}\,\mathrm{g} \le M_{ m PBH}|_{T_\phi} \le 4.4\times10^{7}\,\mathrm{g}$ for $f_{\rm PBH}|_{T_\phi} \ge 1$ and $k=1$, while mergers constrain dark matter lighter than $2.2\times10^{11}\,\mathrm{g}$ (independent of $k$). These results provide complementary, pre-CMB probes of memory-burden PBHs and demonstrate how high-energy gamma-ray data constrain the early evaporation history of the smallest PBHs through distinct channels.

Abstract

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. 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 $f_{\rm PBH}\geq 1$ and $k=1$. Meanwhile, the merging scenario, which is insensitive on $k$, restricts PBH Dark Matter lighter than $2.2\times 10^{11}$ g.

Figures (4)

• Figure 1: The graviton spectra, observed at present, from evaporation of PBH with $M_{\rm PBH}|_{T_\phi}=10^8\,{\rm g}$, $f_{\rm PBH}|_{T_\phi}=10^{-5}$, and various values of $k$. The first peak around $\mathcal{O}(10^{-5})$ GeV is emitted from PBH in semiclassical phase, while the second peak at higher energy is induced by PBH in burden phase.
• Figure 2: The constraints on $f_{\rm PBH}\vert_{T_\phi}$ for burden parameter $k=0$ and 1. The $f_{\rm PBH}\vert_{T_\phi}$ values above the solid curves are excluded, based on the graviton-photon conversion in the cosmological filaments and sensitivities of extragalactic gamma-ray observations. For $k=1$, it is divided into four regions by the phase of PBH evaporation and first/second peak dominates the gamma-ray observations. Here, we define the PBH mass into Region-I to -IV for $k=1$.
• Figure 3: Left panel: The comparison of $f_{\rm PBH}|_{T_\phi}$ constraints via photon flux from graviton-photon conversion (blue curve), PBH merger (black curve), and combination of the two (green curve). Compared with other analysis, the cyan-shaded region is the merger neutrino constraint derived from IceCube Collaboration Zantedeschi:2024ram, and the orange-shaded region is the combined gamma-ray constraint (galactic and extragalactic) from Dondarini:2025ktz. The dashed part of the "Merger exg-$\gamma$" indicates the evaporated mass before present epoch for $k=1$, and the "$\star$" label the benchmark points ( BP$^\prime$s) with corresponding values in Table \ref{['table_mer']}. Right panel: The corresponding photon spectra of BP$^\prime$s from left panel, and their values are listed in Table \ref{['table_mer']}
• Figure 4: Left panel: The solid curves are constraints on $f_{\rm PBH}|_{T_\phi}$ from graviton-photon conversion for $k=0\,,0.5\,,1.0\,,2.0$. The BPs, labeled by "$\star$", are selected along the $k=1.0$ sensitivity curve. Their parameters $(M_{\rm PBH}\vert_{T_\phi},f_{\rm PBH}\vert_{t_\phi})$ are shown in Table \ref{['table1']}. Compared with other analysis, the red-, blue-, and green-shaded regions are respectively excluded for $k=2.0$, $k=1.0$Chaudhuri:2025asm, and $k=0.5$Thoss:2024hsr; the gray-shaded region is excluded for PBH in semiclassical phase which is applicable for all $k$ value. Right panel: The photon spectra of the corresponding BPs in left panel, and their values are listed in Table \ref{['table1']}.