Primordial Black Hole Abundance from Reionization

TL;DR

The paper constrains the initial abundance of evaporating primordial black holes (PBHs) in the mass range $3.2\times10^{13}$ g to $5\times10^{14}$ g by tracking their Hawking radiation and the resulting electromagnetic cascades in the intergalactic medium. A fully time-dependent emission history is computed with BlackHawk, while energy deposition into ionization, excitation, and heating is propagated with DarkHistory and fed into a Gaussian Process reconstruction of the reionization history from Planck low-$\ell$ polarization to derive high-redshift optical-depth constraints. By decomposing the optical depth into high- and low-redshift contributions and using the GP-derived bound on $\tau_{\rm highz}$, the authors obtain robust, conservative upper limits on the PBH abundance parameter $\beta$ across the mass window, highlighting the power of reionization observables to probe late-time energy injection. The framework, which couples time-dependent evaporation with non-parametric reionization modeling, offers a broadly applicable tool for testing exotic energy injection scenarios with cosmological data and motivates future multi-messenger probes.

Abstract

We derive robust constraints on the initial abundance of evaporating primordial black holes (PBHs) using the reionization history of the Universe as a cosmological probe. We focus on PBHs that inject electromagnetic (EM) energy into the intergalactic medium (IGM) after recombination, in the mass range $3.2\times 10^{13}\,\mathrm{g} \lesssim M_{\rm PBH} \lesssim 5\times 10^{14}\,\mathrm{g}$. For each PBH mass, we compute the redshift-dependent energy injection from Hawking evaporation using \texttt{BlackHawk}, fully accounting for the time evolution of the PBH mass and the complete spectrum of emitted Standard Model particles and gravitons. The resulting photons and electrons are propagated through the primordial plasma using \texttt{DarkHistory}, which self-consistently models EM cascades and determines the fraction of injected energy deposited into ionization, excitation, and heating of the IGM. These modifications to the ionization and thermal histories are incorporated into a Gaussian Process reconstruction of the free-electron fraction based on low-$\ell$ CMB polarization data from the \textit{Planck} mission. This non-parametric approach allows for a statistically well-defined separation between exotic high-redshift energy injection and late-time astrophysical reionization, allowing PBH evaporation to be constrained through its contribution to the high-redshift optical depth. Requiring consistency with current CMB measurements, we obtain upper limits on the initial PBH abundance that are robust against reionization modeling uncertainties and systematically more conservative than existing bounds, reflecting the fully numerical and time-dependent treatment of Hawking evaporation and energy deposition. Our results demonstrate the power of reionization observables as a precision probe of PBH evaporation and other scenarios involving late-time energy injection.

Figures (5)

• Figure 1: Upper bounds at 95% C.L. on the initial PBH mass fraction at formation, $\beta$, as a function of the PBH mass for non-spinning black holes. The mass range shown corresponds to PBHs whose EM energy injection occurs predominantly at redshifts $z < z_{\rm max}$. The constraints are derived from the impact of Hawking evaporation on the thermal and ionization history of the IGM, as inferred from the high-redshift optical depth.
• Figure 2: Time evolution of the effective EM branching ratio into photons (red) and electrons/positrons (blue) for PBH evaporation with mass $M_{\rm PBH} = 3.2\times 10^{13}\,\mathrm{g}$ and initial abundance $\beta = 1.6\times10^{-27}$. The EM branching ratio is defined as the fraction of the total Hawking luminosity that ultimately appears in electromagnetically interacting particles after hadronization, decays, and secondary EM cascades.
• Figure 3: Hydrogen ionization fraction $X_e(z)$ as a function of redshift for two representative PBH populations evaluated near their respective upper limits on the initial PBH mass fraction $\beta$: $M_{\rm PBH}=3.2\times10^{13}\,\mathrm{g}$ (red) and $M_{\rm PBH}=1.12\times10^{14}\,\mathrm{g}$ (blue). The black solid line shows the baseline $\Lambda$CDM ionization history.
• Figure 4: High-redshift CMB optical depth $\tau_{\rm highz}$ induced by PBH evaporation as a function of the initial PBH mass fraction $\beta$. The red solid line corresponds to PBHs with mass $M_{\rm PBH}=3.2\times10^{13}\,\mathrm{g}$, while the blue solid line corresponds to $M_{\rm PBH}=1.12\times10^{14}\,\mathrm{g}$. For each mass, $\tau_{\rm highz}$ is obtained by integrating the modified ionization history resulting from the full time-dependent Hawking evaporation and EM energy deposition into the IGM at redshifts above $z_c$. The black dashed line denotes the $\Lambda$CDM baseline contribution in the absence of PBHs. The horizontal gray dashed line indicates the 95% C.L. upper limit on $\tau_{\rm highz}$ inferred from the GP reconstruction of the reionization history in Ref. Cheng:2025cmb. The intersection of this bound with each colored curve determines the corresponding upper limit on $\beta$.
• Figure 5: Ratio of the baryon temperature $T_b$ to the CMB photon temperature $T_\gamma$ as a function of redshift. The black line shows the standard $\Lambda$CDM prediction. Colored lines include the effect of PBH evaporation for populations with masses $M_{\rm PBH} = 3.2\times10^{13}\,\mathrm{g}$ (red) and $1.12\times10^{14}\,\mathrm{g}$ (blue), and corresponding initial abundances $\beta = 1.6\times10^{-27}$ and $1.4\times10^{-26}$.