Probing Population III IMFs 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 (Pop III) stars via measurements of the mean He II 1640A/H$\alpha$ emission line ratio. We extend the 21cmFAST code with modern high-redshift galaxy formation and photoionization models, and estimate the line emission from Pop II and Pop 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 Pop III IMFs with stars of several hundred solar masses, reached at $z \gtrsim 10$ when Pop 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 Pop 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 Pop 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 ratio with other probes can assist in constraining the Pop III IMF in this case.