Astrophysical luminous objects such as the first stars have not yet formed in the dark ages. However, primordial black holes (PBHs) have always existed throughout cosmic history since the inflation epoch. During the dark ages, PBHs may accrete the ambient gas and release radiation like astrophysical luminous objects, and change the cosmic radiation field, the thermal status of the intergalactic medium (IGM), and the hydrogen spin temperature. The accretion rate is modulated by the relic supersonic relative streaming velocities between dark matter (DM) and baryons, imprinting velocity acoustic oscillation (VAO) features in the 21-cm power spectrum. Such VAO features could be a promising probe for detecting the PBHs in the dark ages. We find that even if PBHs comprise only a small fraction of DM, they can generate VAO wiggles with a relative amplitude up to $\sim 30\%$ in dark ages. For example, for PBHs with mass $M_{\mathrm{PBH},\mathrm{rec}}=200M_{\odot }$ and mass fraction in the total DM $f_{\mathrm{PBH},\mathrm{rec}}\sim {10}^{-13}$ at the recombination era, VAO features appear at $z\sim 20$; if $f_{\mathrm{PBH},\mathrm{rec}}\sim 3\times {10}^{-10}$, then VAO features could appear as early as $z\sim 40$. Moreover, the redshift evolution of the VAO features exhibits clearly separated stages dominated by inhomogeneous $\mathrm{Ly}\alpha$ scattering, and inhomogeneous x-ray heating, respectively. It reflects the characteristics of PBHs (mass and fraction in total DM) and their interactions with the IGM. We also estimate that, the VAO wiggles at $z\sim 20$ are detectable for the upcoming SKA-low AA*, while wiggles at $z\sim 40$ are detectable for an hypothetic lunar surface-based interferometer array in the future.

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• Dark matter
• Evolution of the Universe
• Large scale structure of the Universe
• Radio, microwave, & sub-mm astronomy
• Intergalactic medium
• Primordial black holes