A hide-and-seek game: Looking for Population III stars during the Epoch of Reionization through the HeII$\lambda$1640 line

The gas surrounding first-generation (Pop III) stars is expected to emit a distinct signature in the form of the HeII recombination line at 1640 \r{A} (HeII$\lambda$1640). Here we explore the challenges and opportunities in identifying this elusive stellar population via the HeII$\lambda$1640 in $M_\star > 10^{7.5} ~ \mathrm{M_\odot}$ galaxies during the Epoch of Reionization (EoR, $z \simeq 6 - 10$), using JWST/NIRSpec. With this aim in mind, we combine cosmological dustyGadget simulations with analytical modeling of the intrinsic HeII emission. While tentative candidates with bright HeII emission like GN-z11 have been proposed in the literature, the prevalence of such bright systems remains unclear due to significant uncertainties involved in the prediction of the HeII luminosity. In fact, similar Pop III clumps might be almost two orders of magnitude fainter, primarily depending on the assumed Pop III-formation efficiency and initial mass function in star-forming clouds, while the effect of stellar mass loss is responsible for a factor of order unity. Moreover, up to $\sim 90 \%$ of these clumps might be missed with NIRSpec/MOS due to the limited FoV, while this problem appears to be less severe with NIRSpec/IFU. We investigate the potential of deep spectroscopy targeting peripheral Pop III clumps around bright, massive galaxies to achieve a clear detection of the first stars.