The effect of primordial black holes on 21 cm fluctuations

The 21 cm signal produced by non-evaporating primordial black holes (PBHs) is investigated. X-ray photons emitted by accretion of matter onto a PBH ionize and heat the intergalactic medium (IGM) gas near the PBH. Using a simple analytic model, we show that this X-ray heating can produce an observable differential 21 cm brightness temperature. The region of the observable 21 cm brightness temperature can extend to 1-10 Mpc comoving distance from a PBH depending on the PBH mass. The angular power spectrum of 21 cm fluctuations due to PBHs is also calculated. The peak position of the angular spectrum depends on PBH mass, while the amplitude is independent of PBH mass. Comparing this angular power spectrum with the angular power spectrum caused by primordial density fluctuations, it is found that both of them become comparable if $\Omega_{{\rm PBH}} = 10^{-11} (M/10^{3} M_\odot)^{-0.2}$ at $z=30$ and $10^{-12} (M/10^{3} M_\odot)^{-0.2}$ at $z=20$ for the PBH mass from $10 M_\odot $ to $10^8 M_\odot $. Finally we find that the Square Kilometer Array can detect the signal due to PBHs up to $\Omega_{\rm PBH}=10^{-5} (M/10^{3} M_\odot)^{-0.2}$ at $z=30$ and $10^{-7} (M/10^{3} M_\odot)^{-0.2}$ at $z=20$ for PBHs with mass from $10^2 M_\odot $ to $10^8 M_\odot $.