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 resulting from PBHs is also calculated. The peak position of the angular spectrum depends on the PBH mass, while the amplitude is independent of mass. On comparing this power spectrum with the angular power spectrum caused by primordial density fluctuations, it is found that the two spectra are comparable if the density parameter of PBHs is Ω_PBH = 10^-11(M/10³ M_⊙)^-0.2 at z = 30 and if Ω_PBH = 10^-12(M/10³ M_⊙)^-0.2 at z = 20 for a PBH mass from 10 M_⊙ to 10⁸ M_⊙. Finally, we find that the Square Kilometre Array can detect the signal caused by PBHs up to Ω_PBH = 10^-5(M/10³ M_⊙)^-0.2 at z = 30 and up to Ω_PBH = 10^-7(M/10³ M_⊙)^-0.2 at z = 20 for PBHs with mass in the range from 10² M_⊙ to 10⁸ M_⊙.