Probing Population III Initial Mass Functions with He II/H$\alpha$ Intensity Mapping

We demonstrate the potential of line-intensity mapping to place constraints on the initial mass function (IMF) of Population III stars via measurements of the mean He II 1640A/H$\alpha$ line-intensity ratio. We extend the 21cmFAST code with modern high-redshift galaxy-formation and photoionization models, and estimate the line emission from Population II and Population III galaxies at redshifts $5 \le z \le 20$. In our models, mean ratio values of He II/H$\alpha \gtrsim 0.1$ indicate top-heavy Population III IMFs with stars of several hundred solar masses, reached at $z \gtrsim 10$ when Population III stars dominate star formation. A next-generation space mission with capabilities moderately superior to those of CDIM will be able to probe this scenario by measuring the He II and H$\alpha$ fluctuation power spectrum signals and their cross-correlation at high significance up to $z\sim 20$. Moreover, regardless of the IMF, a ratio value of He II/H$\alpha \lesssim 0.01$ indicates low Population III star formation and, therefore, it signals the end of the period dominated by this stellar population. However, a detection of the corresponding He II power spectrum may be only possible for top-heavy Population III IMFs or through cross-correlation with the stronger H$\alpha$ signal. Finally, ratio values of $0.01 \lesssim$ He II/H$\alpha$ $\lesssim 0.1$ are complex to interpret because they can be driven by several competing effects. We discuss how various measurements at different redshifts and the combination of the line-intensity ratio with other probes can assist in constraining the Population III IMF in this case.