Primordial Black Holes & EGRB: Asteroid-Mass Constraints

Abstract: Primordial black holes (PBHs) have long occupied a pivotal yet contentious niche in cosmology. First anticipated in the 1970s as gravitational relics of the first micro-seconds after the Big Bang, PBHs have been invoked to explain everything from the origin of supermassive black holes to the observed spectrum of gravitational-wave mergers, and—most provocatively—the enigmatic dark‐matter component of the Universe. In the asteroid-mass window (10¹⁴–10¹⁷ g) their existence is subject to especially stringent constraints because, under Hawking’s semi-classical evaporation paradigm, such objects should be in the final, most luminous stage of their lives and therefore inject a measurable flux of γ-rays into the Extragalactic Gamma-Ray Background (EGRB). Building on a recent pre-print by Cholis, Krommydas & Carlini (2026), we here provide an exhaustive, academically structured synthesis that re-examines the theoretical foundations, observational techniques, and statistical methodologies that collectively delimit the viable parameter space of asteroid-mass PBHs. By critically confronting models with archival measurements from EGRET and COMPTEL—and by projecting the discovery potential of next-generation missions such as AMEGO-X and e-ASTROGAM—we demonstrate that PBHs cannot dominate the dark-matter inventory in this mass range; nonetheless, a non-negligible residual fraction at 3 × 10¹⁶ g remains observationally tenable. We conclude by assessing synergies with multi-messenger probes, articulate an agenda for precision γ-ray cosmology, and furnish an up-to-date catalogue of auxiliary resources for further study.

1. Historical Prelude and Conceptual Foundations

The conventional pedagogical narrative locates the birth of black-hole physics in the collapse of massive stars—an inevitability of stellar evolution once the Chandrasekhar, Tolman–Oppenheimer–Volkoff, or pair-instability thresholds are surpassed. Yet as early as 1966, Zel’dovich & Novikov intuited that high-density fluctuations during the radiation-dominated epoch might induce direct gravitational collapse on scales far below stellar masses. Stephen Hawking subsequently formalised the quantum-field theoretical underpinnings of such mini-holes and, crucially, predicted their evaporation via thermal emission. These primordial black holes are decoupled from baryonic stellar processes, thereby constituting an ab initio dark-sector ingredient with potential cosmological influence.

Four seminal motivations animate contemporary PBH research:

1. Dark Matter Candidate – Compact, non-luminous, and cold, PBHs satisfy the macroscopic criteria for dark matter (DM).
2. Progenitors of Gravitational-Wave Sources – Mergers of intermediate-mass PBHs could account for the LIGO/Virgo event rate without recourse to stellar binaries.
3. Seeding of Supermassive Black Holes – Super-Eddington growth of PBH seeds might alleviate formation-time objections associated with quasars at z > 7.
4. Laboratories for Quantum Gravity – End-stage evaporation probes Planck-scale physics inaccessible to terrestrial accelerators.

Notwithstanding, these motivations are tempered by cumulative empirical constraints imposed by microlensing surveys (EROS/MACHO/OGLE), CMB anisotropy studies, wide-binary disruption analyses, and, germane to the present discussion, the γ-ray sky.

1.1 Definition of the Asteroid-Mass Window

The adjective ‘asteroid-mass’ refers to PBHs in the 10¹⁴–10¹⁷ g range, roughly equivalent to 10⁻¹⁹–10⁻¹⁶ M_☉. Table 1 situates this regime within the broader taxonomic landscape of black holes.

2. Quantum Evaporation: Hawking Radiation Revisited

In Hawking’s framework, black holes emit a blackbody spectrum characterised by temperature

T_BH = (ħ c³)/(8π G M k_B) ≈ 1.06 GeV (10¹⁴ g / M)

and luminosity

L_BH ∝ 1/M².

Consequently, evaporation timescale obeys

τ ≈ 4.5 × 10⁻²⁸ (M/M_Pl)³ s.

For 10¹⁴ g PBHs, τ is comparable to the current Hubble time (≈ 13.8 Gyr), placing these objects at the cusp of complete evaporation today. Table 2 juxtaposes key thermodynamic quantities across representative masses.

Note the inverse correlation: larger masses are both colder and longer-lived, yielding softer γ-ray spectra. In the asteroid-mass bracket the spectral peak resides squarely in the 1–1000 MeV band termed the “MeV gap,” observationally underserved by legacy missions and only partially sampled by Fermi-LAT.

3. The Extragalactic Gamma-Ray Background (EGRB)

The EGRB is a diffuse, isotropic glow encompassing photon energies from hundreds of keV to many TeV. It arises after subtraction of Galactic foregrounds and point-source contributions. The integrated intensity encodes cumulative light from various populations, each with distinct evolutionary histories and emission mechanisms. Table 3 itemises the principal contributors.

Figure 1. All-sky intensity map assembled by the Fermi-LAT. The Galactic plane (horizontal band) has been masked; residual diffuse flux constitutes the EGRB to which PBHs would contribute.

4. Methodological Framework of Cholis, Krommydas & Carlini (2026)

Recognising the difficulty of disentangling a PBH signal from superposed astrophysical backgrounds, the authors instituted a multipronged strategy:

1. Legacy Data Curation. They amalgamated archival spectra from COMPTEL (0.8–30 MeV) and EGRET (20 MeV–10 GeV), obtained during the operational tenure of the Compton Gamma-Ray Observatory (CGRO, 1991–2000).
2. Hierarchical Subtraction Pipeline. Employing empirical luminosity functions and redshift distributions, they subtracted blazar, radio-galaxy, and star-forming-galaxy templates; cosmic-ray induced γ-rays from cosmic infrared background (CIB) interactions were also modelled.
3. GammaPBHPlotter. A bespoke Python toolkit that integrates Hawking emission spectra (including grey-body corrections), unstable particle cascades, and e⁺e⁻ annihilation lines.
4. Bayesian Inference. Posterior probability distributions for the PBH density fraction f_PBH ≡ ρ_PBH/ρ_DM were obtained via Markov-Chain Monte-Carlo (MCMC) sampling conditioned on the residual EGRB.

The campaign culminated in the tightest asteroid-mass limits to date: for M ≈ 10¹⁴ g, f_PBH < 10⁻¹⁰; for M ≈ 3 × 10¹⁶ g, f_PBH < 0.06 at 95 % credibility. These numerical constraints are visualised in Table 4.

5. Instrumental Landscape: Past, Present, and Prospective Missions

Accuracy in γ-ray cosmology hinges on spectral coverage, angular resolution, and background rejection. Table 5 summarises salient specifications of historical and proposed observatories.

Both AMEGO-X and e-ASTROGAM specifically target the MeV gap via Si-tracker + calorimeter architectures coupled to anti-coincidence shields, thereby delivering order-of-magnitude sensitivity gains over CGRO. Simulated sky maps indicate that even an f_PBH of 10⁻³ could be statistically separable from blazar residuals within three mission years.

6. Statistical Decomposition of the EGRB

6.1 Hierarchical Bayesian Model

Let D denote the observed photon counts; θ = {f_PBH, α_BZ, α_SFG, …} the set of fractional amplitudes; and S(θ) the composite spectral template. The Poissonian likelihood is

L(D|θ) = ∏_i [ e^−S_i S_i^D_i / D_i! ].

Priors are log-uniform for positive-definite amplitudes; astrophysical sub-templates inherit wide Gaussian priors from source-count statistics. Sampling proceeds via the affine-invariant ensemble algorithm (emcee), yielding marginalized posteriors. Convergence criteria adopt a Gelman-Rubin statistic < 1.1 across 100 walkers and 10⁵ steps.

6.2 Systematics Treatment

• Instrumental Response. Detector effective-area uncertainties are folded into nuisance parameters with 5 % priors.
• Galactic Foreground Residuals. Imperfect subtraction of π⁰ decay emission is modelled via a latitude-dependent template whose normalisation is simultaneously fitted.
• Cosmic Variance. Sampling variance in discrete source counts is captured by hyper-priors on luminosity-function parameters.

Posterior predictive checks confirm that the absence of a PBH component for M ≈ 10¹⁴ g reproduces the observed spectrum within 1σ, whereas inclusion of a ≳ 10 % fraction yields over-production at 1–100 MeV. For M ≈ 3 × 10¹⁶ g, degeneracy with star-forming-galaxy templates necessitates higher-resolution spectral bins to disambiguate.

7. Complementary Probes Beyond Gamma-Rays

Synergistic avenues are essential for cross-validation:

1. 21-cm Cosmology. Energy injection from PBH evaporation modulates the thermal history of the intergalactic medium (IGM), imprinting anomalies on the global 21-cm signal. Constraints from EDGES already disfavour f_PBH > 1 % at 10¹⁵ g.
2. CMB Spectral Distortions. COBE/FIRAS limits on μ and y distortions exclude large energy-release episodes; upcoming PIXIE may enhance sensitivity by 10³.
3. Cosmic-Ray Antiprotons. Evaporation yields p̄ flux; AMS-02 data disfavour f_PBH > 2 % for M ≈ 10¹⁶ g.
4. Gravitational-Wave Echoes. Final explosive stages might produce cosmic string–sourced bursts; LISA could, in principle, detect collective signals for f_PBH ≈ 0.01.

8. Implications for Dark-Matter Paradigms

The dwindling parameter space amplifies pressure on alternative DM candidates such as Weakly Interacting Massive Particles (WIMPs), axions, and sterile neutrinos. Should forthcoming γ-ray missions obliterate the residual 3 × 10¹⁶ g niche, PBHs would be relegated to a subdominant cosmological footnote, compelling a re-allocation of theoretical capital toward particle-physics solutions. Conversely, a positive detection—however partial—would revolutionise our comprehension of early-Universe micro-physics, inflationary dynamics, and quantum gravity.

9. Future Work and Recommendations

“The acceleration of observational capability in the MeV domain promises to convert speculative cosmology into empirical science.” — Dr. Ioannis Cholis

To expedite progress we advocate:

• Endorsement of AMEGO-X and e-ASTROGAM in upcoming NASA/ESA call cycles.
• Development of open-source, community-validated PBH spectral libraries to harmonise analyses.
• Cross-calibration of γ-ray instruments with balloon-borne pathfinders (e.g., COSI, SMILE-2+).
• Integration of multi-messenger datasets via Bayesian hierarchical frameworks.

10. Conclusions

Asteroid-mass primordial black holes, once heralded as an elegant dark-matter solution, now confront an empirical pincer. Archival CGRO data limit their cosmic abundance to trivial levels at 10¹⁴ g; only a narrow refuge near 3 × 10¹⁶ g endures. Upcoming MeV missions are poised either to snuff out this last ember or to unveil a smoking-gun spectral signature. In either eventuality, the venture exemplifies the interplay of quantum gravity, high-energy astrophysics, and observational cosmology—a testament to the scientific method’s capacity for progressive self-correction.

For More Information

Cholis, I., Krommydas, I., & Carlini, J. (2026). Limits on primordial black holes from the extragalactic gamma-ray background; current status and future projections. arXiv:2606.10013

Carr, B., Kühnel, F., & Sandstad, M. (2018). Primordial black holes as dark matter. Nature Astronomy, 3, 201–207.

The Fermi Large Area Telescope Collaboration.

AMEGO-X Mission Concept Study.

e-ASTROGAM Consortium White Paper.

NASA Astrophysics Focus Area: Cosmic Rays & Gamma Rays.

The NASA/IPAC Extragalactic Database (NED).