Velocity acoustic oscillations on Cosmic Dawn 21 cm power spectrum as a probe of small-scale density fluctuations

We investigate the feasibility of using the velocity acoustic oscillations (VAO) features on the Cosmic Dawn 21 cm power spectrum to probe small-scale density fluctuations. In the standard cold dark matter (CDM) model, Pop III stars form in minihalos and affect the 21 cm signal through Ly$\alpha$ and X-ray radiation. Such a process is modulated by the relative motion between dark matter and baryons, generating the VAO wiggles on the 21 cm power spectrum. In the fuzzy or warm dark matter models for which the number of minihalos is reduced, the VAO wiggles are weaker or even fully invisible. We investigate the wiggle features in the CDM with different astrophysical models and in different dark matter models. We find: 1) In the CDM model the relative streaming velocities can generate the VAO wiggles for broad ranges of parameters $f_*$, $\zeta_X$ and $f_{\rm esc,LW}\zeta_{\rm LW}$, though for different parameters the wiggles would appear at different redshifts and have different amplitudes. 2) For the axion model with $m_{\rm a} \lesssim10^{-19}$ eV, the VAO wiggles are negligible. In the mixed model, the VAO signal is sensitive to the axion fraction. For example, the wiggles almost disappear when $f_{\rm a} \gtrsim 10\%$ for $m_{\rm a}=10^{-21}$ eV. Therefore, the VAO signal can be an effective indicator for small-scale density fluctuations and a useful probe of the nature of dark matter. The SKA-low with $\sim$2000 hour observation time has the ability to detect the VAO signal and constraint dark matter models.