Observable and ionizing properties of star-forming galaxies with very massive stars and different IMFs

The presence of very massive stars (VMS, masses $>100$ M$_{\odot}$) is now firmly established in the local group, nearby galaxies, and out to cosmological distances. If present, these stars could boost the UV luminosity and ionizing photon production of galaxies, helping thus to alleviate the overabundance of UV-bright galaxies found with the JWST at high-redshift. Combing consistent stellar evolution and atmosphere models tailored to VMS we compute spectral energy distributions (SEDs) for a large set of models. We find that VMS contribute significantly to the UV luminosity and Lyman continuum of young stellar populations, and they are characterized by strong stellar HeII1640 emission, with EW(HeII) up to 4-8 Ang at young ages or $\sim 2.5-4$ Ang for constant SFR. For IMFs with a Salpeter slope, the boost of the UV luminosity is relatively modest. However, small changes in the IMF slope (e.g.~from $\alpha_2=-2.35$ to $-2$) lead to large increases in $L_{UV}$ and the ionizing photon production $Q$. Emission line strengths and the ionizing photon efficiency $\xi_{\rm ion}$ are also increased with VMS. Interestingly, SEDs including VMS show smaller Lyman breaks, and the shape of the ionizing spectra remain unaltered up to $\sim 35$ eV, but becomes softer at higher energies. We derive and discuss the maximum values quantities such as $L_{UV}$ per stellar mass or unit SFR, and $\xi_{\rm ion}$, $Q$ can reach when VMS are included, and we show that these values become essentially independent of the IMF. We propose observational methods to test for VMS and constrain the IMF. Finally, using JWST observations, we examine if high-redshift galaxies show some evidence of the presence of VMS and signs of non-standard IMFs. Very top-heavy IMFs can be excluded on average, but the IMF could well extend into the regime of VMS and be flatter than Salpeter in the bulk of high-$z$ galaxies. (abridged)