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Impact of the turnover in the high-z galaxy luminosity function on the 21-cm signal during Cosmic Dawn and Epoch of Reionization

The shape of the faint-end of the high-z galaxy luminosity function (LF) informs early star formation and reionization physics during the Cosmic Dawn and Epoch of Reionization. Until recently, based on the strong gravitational lensing cluster deep surveys, the Hubble Frontier Fields (HFF) has found a potential turnover in the ultraviolet (UV) LF at z$\sim$6. In this paper, we analyze the contribution of extremely faint galaxies with the magnitude larger than the turnover magnitude in LF to cosmic reionization. We apply the measurement from HFF to our suppressed star formation efficiency model, including three free parameters: halo mass threshold $M_t$, curvature parameter $β$ and a UV conversion factor $l_{\rm UV}$. According to our fit of 68\% confidence level, the high-redshift star formation in haloes smaller than $ M_t=1.82^{+2.86}_{-1.08}\times10^{10} \rm M_{\odot}$ is found to be dampened. The turnover magnitude $\rm \gtrsim -13.99-2.45$, correspondingly the halo mass $\lesssim(4.57+20.03)\times10^{9} \rm M_{\odot}$. We find that the absorption trough in the global 21-cm signal is sensitive to our SFE model parameters. Together with ($β$, $l_{\rm UV}$) = ($2.17^{+2.42}_{-1.72}$, $9.33^{+0.43}_{-0.42} \rm ~erg~yr ~s^{-1}M_{\odot}^{-1})$, the trough locates at $\sim$ $134^{+10}_{-17}$ $\rm MHz$ with an amplitude of $\sim$ $-237^{-6}_{+7}$ $\rm mK$, compared to (106\rm MHz, -212\rm mK) in the absence of turnover. Besides, we find that the star formation of faint galaxies has also an impact on the 21-cm power spectra. The best fitting peak power decreases by $\sim4\%$ and shifts towards smaller scales from $0.88 h \rm Mpc^{-1}$ to $0.91 h \rm Mpc^{-1}$. According to our calculation, such impact is distinguishable with the forthcoming Square Kilometre Array.