Primordial black hole abundance from reionization

We derive robust constraints on the initial abundance of evaporating primordial black holes (PBHs) using the reionization history of the Universe. We consider PBHs with initial masses 3.2 × 10 13 , g ≲ M PBH ≲ 5 × 10 14 , g, whose Hawking emission injects electromagnetic (EM) energy into the intergalactic medium (IGM) after recombination. Using BlackHawk , we compute the redshift-dependent emission spectra, accounting for PBH mass evolution and the full spectrum of Standard Model particles and gravitons. The photon and electron spectra are folded with channel-specific DarkHistory deposition efficiencies, which encode EM cascade cooling and delayed deposition into hydrogen ionization and excitation and IGM heating. The modified ionization histories determine the high-redshift Thomson optical depth, which we constrain using the posterior obtained from a Gaussian-process reconstruction of the free-electron fraction based on low-ℓ Planck CMB polarization data. This nonparametric reconstruction provides an operational separation between high-redshift energy injection and late-time astrophysical reionization without imposing a fixed ionization template. Requiring consistency with this posterior, we obtain upper limits on the initial PBH abundance that are less sensitive to late-time reionization assumptions. Compared with earlier analytic CMB estimates, our bounds are generally more conservative, reflecting the restriction to low-ℓ polarization data and the time-dependent treatment of PBH mass evolution and Hawking emission combined with channel- and redshift-dependent deposition efficiencies. Our results demonstrate the power of reionization observables as a precision probe of PBH evaporation.