Constraints on primordial black holes from Galactic gamma-ray background

TL;DR

This paper recalibrates constraints on primordial black holes evaporating today by analyzing the Galactic gamma-ray background, highlighting that the dominant Galactic signal arises from PBHs with current mass near $M_*$ formed slightly above $M_*$. It develops a refined emission framework including primary and secondary channels, and demonstrates that the low-mass tail of the current PBH mass function—and not the edge-at-$M_*$ population—drives the Galactic background, with secondary emission crucial near the QCD scale. It then explores a range of mass-function scenarios (nearly monochromatic, extended, and critical-collapse) and computes line-of-sight fluxes against Fermi-LAT diffuse emission to derive bounds on the formation fraction $\\beta(M)$; in many cases extended or critical-collapse spectra push PBHs to substantially larger masses while remaining consistent with gamma-ray limits, though often requiring fine-tuning. The extragalactic gamma-ray background remains a complementary constraint, but the Galactic background can be more restrictive for certain mass ranges and functions, underscoring the importance of the mass-function shape around $M_*$. Overall, the work clarifies how PBH formation physics, Hawking evaporation (including hadronic secondaries), and halo-geometry interplay to restrict PBH dark matter scenarios and informs future gamma-ray searches for PBH signatures.

Abstract

The fraction of the Universe going into primordial black holes (PBHs) with initial mass M_* \approx 5 \times 10^{14} g, such that they are evaporating at the present epoch, is strongly constrained by observations of both the extragalactic and Galactic gamma-ray backgrounds. However, while the dominant contribution to the extragalactic background comes from the time-integrated emission of PBHs with initial mass M_*, the Galactic background is dominated by the instantaneous emission of those with initial mass slightly larger than M_* and current mass below M_*. Also, the instantaneous emission of PBHs smaller than 0.4 M_* mostly comprises secondary particles produced by the decay of directly emitted quark and gluon jets. These points were missed in the earlier analysis by Lehoucq et al. using EGRET data. For a monochromatic PBH mass function, with initial mass (1+μ) M_* and μ<< 1, the current mass is (3μ)^{1/3} M_* and the Galactic background constrains the fraction of the Universe going into PBHs as a function of μ. However, the initial mass function cannot be precisely monochromatic and even a tiny spread of mass around M_* would generate a current low-mass tail of PBHs below M_*. This tail would be the main contributor to the Galactic background, so we consider its form and the associated constraints for a variety of scenarios with both extended and nearly-monochromatic initial mass functions. In particular, we consider a scenario in which the PBHs form from critical collapse and have a mass function which peaks well above M_*. In this case, the largest PBHs could provide the dark matter without the M_* ones exceeding the gamma-ray background limits.

Figures (16)

• Figure 1: Dependence of $f(M)$ on $M$ . Dotted red line shows step-function approximation at mass thresholds for quarks (up, down, strange, charm, bottom, top), gluons, $W$/$Z$ bosons and the Higgs particle. Solid red curve shows MacGibbon's approximation formula MacGibbon:1991tj, updated to include $W$/$Z$ boson, top quark and Higgs. The most notable feature is the increase by factor $\alpha = 4$ at $2 \times10^{14}\,\mathrm g$ .
• Figure 2: (a): $m$ versus $M$ . (b): Comparison of exact $m(\mu)$ relation (red line) with various approximations.
• Figure 3: (a) Instantaneous emission rates for black holes of various temperatures, with primary component at bottom. The $50\,\mathrm{MeV}$ emission rate (solid red) corresponds to $T_\mathrm{BH} \approx M_\mathrm q^{-1}$ . (b) Ratios of secondary to primary peak energies (dashed green) and fluxes (solid red) for the instantaneous emission. The right figure confirms the secondary peak is proportional to the temperature for $m < M_\mathrm q$ (as the primary peak is always constant). In (a) it is noted that the widths of secondary emission are roughly proportional to the temperature.
• Figure 4: (a) Time-integrated spectra for different values of $M_\mathrm i$ . (b) Ratios of secondary to primary peak energies (solid red) and fluxes (dashed green) for the time-integrated emission as a function of $M_\mathrm i$ .
• Figure 5: This shows the relationship between the PBH mass functions at formation (dotted) and currently (solid) for extended mass functions with a fine-tuned upper (a) or lower (b) cut-off.