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

This paper proposes two scenarios—graviton-to-photon conversion via the Gertsenshtein effect and binary PBH mergers—to constrain the abundance of memory-burdened primordial black holes, thereby excluding specific mass windows for sub-$10^{15}$ g PBH dark matter that would otherwise evade standard evaporation limits.

The Gist

The Big Picture: Tiny Black Holes That Won't Die

Imagine the universe is filled with tiny, invisible "ghosts" called Primordial Black Holes (PBHs). These aren't the massive black holes at the center of galaxies; they are microscopic, some weighing less than a mountain.

For decades, scientists thought these tiny ghosts would evaporate and vanish completely, like a snowball melting in the sun. If they vanished, they would have exploded into a burst of energy (light and particles) that we should be able to see today. Since we don't see these explosions, we thought these tiny black holes couldn't exist as "Dark Matter" (the invisible stuff holding galaxies together).

The Twist: A new theory called the "Memory Burden" suggests these black holes have a "memory." As they lose mass, they start remembering all the information they've swallowed. This memory acts like a heavy backpack, slowing them down. Instead of melting away quickly, they get stuck in a "slow-motion" phase where they barely evaporate at all. This means they could still be around today, hiding in plain sight.

The Problem: How Do We Catch Them?

If these black holes are "burdened" and moving slowly, they aren't shooting out enough light to be seen by our telescopes. It's like trying to spot a firefly that has decided to turn off its light.

However, the paper proposes two clever ways to catch them:

Scenario 1: The "Graviton-to-Photon" Magic Trick

1. The Emission: Even when these black holes are "burdened," they still emit a tiny bit of something called gravitons (particles of gravity) during their early, fast-moving days.
2. The Journey: These gravitons travel through the universe. They are ghosts within ghosts; they pass through everything without hitting anything.
3. The Conversion: The universe is filled with invisible "highways" called cosmic filaments (huge strands of matter). These filaments have magnetic fields. The paper suggests that when a graviton flies through these magnetic fields, it can magically transform into a photon (a particle of light).
   • Analogy: Imagine a silent, invisible ghost (graviton) walking through a forest of giant magnets (filaments). As it passes, the magnets zap it, turning it into a glowing firefly (photon) that we can finally see.
4. The Detection: We look for this specific "glow" using gamma-ray telescopes. If we see too much glow, it means there are too many of these tiny black holes. If we don't see it, we know how many can exist.

The Result: Using this method, the authors found that if these black holes exist, they cannot be too heavy or too light in a specific range. They ruled out a "mass window" between roughly the weight of a large asteroid and a small moon. If they were in that range, we would have seen the light from the conversion by now.

Scenario 2: The "Reboot" via Collision

1. The Idea: Imagine two of these "burdened" black holes crash into each other and merge.
2. The Reboot: When they merge, they create a new, slightly larger black hole. Because this new black hole is fresh, it forgets the "memory burden" of its parents. It resets to its "fast mode" (semiclassical phase) and starts evaporating rapidly again, shooting out a lot of light.
   • Analogy: It's like two tired, slow-moving runners (burdened black holes) high-fiving and merging into one super-runner who suddenly has a burst of energy and sprints away.
3. The Catch: This scenario is very theoretical. We aren't 100% sure if the physics of the merger actually works this way. It's a "what if" scenario.

The Result: Even though this idea is shaky on theory, the math shows that if these collisions happen often enough, they would create a detectable signal. This puts a limit on how many of these black holes can exist: they can't be lighter than a certain weight, or we would have seen the light from their collisions.

The Conclusion: A New Map for the Invisible

The paper essentially draws a new map for where these tiny black holes might hide.

• The "Memory Burden" saves them from dying too fast, allowing them to be Dark Matter candidates.
• The "Graviton Trick" (Scenario 1) is the strongest tool. It tells us that if these black holes are lighter than a specific limit, they would have converted enough gravitons into light for us to see. Since we don't see that light, we know they aren't there in that specific mass range.
• The "Collision" (Scenario 2) is a backup plan. It suggests that even if the first method doesn't catch them, the act of them crashing together might reveal them.

In short: The authors used the idea of "heavy memories" and "magnetic magic tricks" to prove that if these tiny black holes exist as Dark Matter, they must be heavier than a certain weight, or they would have lit up the universe in a way we haven't seen yet.

Technical Summary

1. Problem Statement

Primordial Black Holes (PBHs) are a leading candidate for Dark Matter (DM). However, standard Hawking evaporation theory predicts that PBHs with masses $M_{PBH} \lesssim 10^{15}$ g would have completely evaporated by the present epoch, emitting high-energy particles that are severely constrained by gamma-ray and neutrino observations. This excludes light PBHs as viable DM candidates.

Recent theoretical developments (Refs. [10, 11]) suggest that the Memory Burden Effect significantly alters this picture. When a black hole loses approximately half its initial mass, the backreaction of emitted information on the quantum state of the black hole suppresses the evaporation rate by a factor of $S^{-k}$ (where $S$ is the black hole entropy and $k$ is a suppression parameter). This "burden phase" extends the lifetime of low-mass PBHs, potentially allowing them to survive to the present day and constitute DM.

The Challenge: While the burden effect suppresses the emission of Standard Model (SM) particles (photons, neutrinos) in the late universe, it does not necessarily suppress the emission of gravitons during the earlier semiclassical phase (before the mass drops below the threshold). Since gravitons interact weakly with SM particles, they can free-stream from the early universe. However, direct detection of these high-frequency gravitons is beyond current interferometer capabilities. The paper aims to probe these "memory-burdened" PBHs by converting their early-universe graviton flux into detectable photons and by analyzing the photon flux from PBH mergers.

2. Methodology

The authors propose and analyze two distinct scenarios to constrain the fractional abundance of PBHs ($f_{PBH}$):

A. Graviton-Photon Conversion (Gertsenshtein Effect)

1. Source: PBHs emit gravitons during their semiclassical phase (before entering the memory burden phase).
2. Mechanism: These gravitons propagate through the universe and encounter magnetic fields in cosmological filaments. Through the Gertsenshtein effect, gravitons convert into photons.
3. Modeling:
   • Magnetic Fields: The authors model the magnetic field in filaments as $B(z) = B_0(1+z)^2$, using an optimistic value of $B_0 = 100$ nG.
   • Conversion Probability: Calculated using the oscillation length and amplitude, approximated for the coherence length of filaments ($1-10$ Mpc).
   • Spectrum Calculation: The graviton spectrum is computed using the BlackHawk v2.3 package, modified to include the memory burden suppression factor ($S^{-k}$) for $t > t_q$ (where $t_q$ is the time when mass drops to $q M_{initial}$, with $q=0.5$).
   • Flux Integration: The total extragalactic photon flux is obtained by convolving the graviton emission rate with the conversion probability over redshift.

B. PBH Binary Mergers

1. Scenario: Two memory-burdened PBHs merge to form a new, larger PBH.
2. Physics: The new PBH has a horizon area four times larger than the sum of the initial areas, effectively resetting the "memory" storage capacity. Consequently, the new PBH re-enters a semiclassical phase with unsuppressed evaporation rates.
3. Rate Calculation: The merger rate is calculated using a standard formula for monochromatic binary PBHs, adjusted for the specific mass range and suppression factors.
4. Flux: The resulting Hawking radiation (photons) from these "young" semiclassical black holes is calculated and compared to observational limits.

C. Observational Constraints

The calculated photon fluxes (from both scenarios) are compared against:

• Current Limits: JEM-X, IBIS-ISGRI, and Fermi-LAT extragalactic gamma-ray upper limits.
• Future Sensitivities: e-ASTROGAM, CTA South, LHAASO, and HiSCORE.

3. Key Contributions

1. New Detection Channel: The paper introduces graviton-photon conversion in cosmological filaments as a viable method to probe the early semiclassical phase of memory-burdened PBHs. This bypasses the entropy suppression that hides the late-stage emission of light PBHs.
2. Double-Peak Spectrum Characterization: The authors demonstrate that the resulting photon spectrum exhibits a unique double-peak structure:
   • First Peak (Low Energy): Originates from the semiclassical phase (early universe). It is highly redshifted but not suppressed by the entropy factor.
   • Second Peak (High Energy): Originates from the burden phase (late universe). It is less redshifted but heavily suppressed by the $S^{-k}$ factor.
3. Refined Constraints on Light PBHs: By combining the conversion scenario and the merger scenario, the authors derive rigorous upper bounds on the PBH abundance fraction ($f_{PBH}$) for masses lighter than $10^{15}$ g.
4. Model Dependence Analysis: The study explicitly contrasts the robustness of the graviton-conversion scenario (less model-dependent) against the merger scenario (highly model-dependent, relying on specific merger rates and the assumption that merging resets the memory burden).

4. Results

Constraints on Graviton-Photon Conversion

• Mass Window Exclusion: For an optimistic magnetic field ($B_0 = 100$ nG) and suppression parameter $k=1$, the scenario excludes the mass window:
  $$7.5 \times 10^5 \text{ g} \leq M_{PBH} \leq 4.4 \times 10^7 \text{ g}$$
  for $f_{PBH} \geq 1$.
• Four Mass Regions: The constraints on $f_{PBH}$ vary across four distinct mass regions based on which spectral peak dominates and the PBH's evolutionary state:
  • Region I ($<10^7$ g): PBHs evaporate completely today; constraints driven by final burst.
  • Region II ($10^7 - 10^9$ g): PBHs are currently in the burden phase; second peak dominates.
  • Region III ($10^9 - 4 \times 10^{14}$ g): First peak dominates; constraints driven by low-energy gamma-ray sensitivity.
  • Region IV ($>4 \times 10^{14}$ g): PBHs remain in the semiclassical phase; single-peak spectrum.
• Comparison: While the converted photon constraints are 7–8 orders of magnitude weaker than direct photon constraints from the burden phase, they provide a complementary probe for the semiclassical phase, which was previously unconstrained by direct photon observations.

Constraints on PBH Mergers

• Mass Limit: The merger scenario restricts PBH Dark Matter lighter than $2.2 \times 10^{11}$ g (assuming $f_{PBH} \leq 1$).
• Sensitivity: This constraint is largely insensitive to the parameter $k$ (provided $k$ is large enough for survival) but depends on the merger rate and the parameter $q$.
• Caveat: The authors note this scenario is highly model-dependent and lacks rigorous theoretical confirmation regarding the "resetting" of the memory burden upon merger.

Combined Constraints

• The combination of both scenarios (merger + conversion) yields a constraint that is generally weaker than the individual limits due to the double suppression of the merger rate and conversion probability, except in a tiny mass range ($7.6 \times 10^8 - 3.2 \times 10^9$ g).

5. Significance

• Opening a New Mass Window: This work demonstrates that the "memory burden" effect creates a viable window for PBHs to be Dark Matter in the mass range $10^5 - 10^{11}$ g, a region previously thought to be excluded by evaporation limits.
• Probing the Early Universe: By utilizing the Gertsenshtein effect, the study offers a unique method to observe the semiclassical phase of black hole evaporation, which occurs before the cosmic microwave background (CMB) recombination. This is a regime inaccessible to traditional gamma-ray astronomy.
• Theoretical Implications: The results highlight the importance of non-SM particle interactions (gravitons) in constraining black hole physics and suggest that future gamma-ray telescopes (like CTA and LHAASO) could test the existence of memory-burdened PBHs.
• Future Directions: The paper suggests that investigating non-universal suppression (e.g., in Large Extra Dimension models where graviton emission rates differ from SM particles) is a crucial next step for refining these constraints.

In conclusion, Tseng and Yeh provide a robust phenomenological framework that leverages graviton-photon conversion and binary mergers to significantly tighten the constraints on light Primordial Black Holes, effectively ruling out specific mass ranges as the sole constituent of Dark Matter under the memory burden hypothesis.