Theoretically modelling the 21-cm signals caused by Population III stars (Pop III stars) is the key to extracting fruitful information on Pop III stars from current and forthcoming 21-cm observations. In this work we develop a new module of Pop III stars in which the escape fractions of ionizing photons and Lyman-Werner (LW) photons, photo-heating by UV radiation, and LW feedback are consistently incorporated. By implementing the module into a public 21-cm semi-numerical simulation code, 21CMFAST, we demonstrate 21-cm signal calculations and investigate the importance of Pop III star modelling. What we find is that the contribution from Pop III stars to cosmic reionization significantly depends on the treatment of the escape fraction. With our escape fraction model, Pop III stars hardly contribute to reionization because less massive halos, whose escape fraction are high, cannot host Pop III stars due to LW feedback. On the other hand, Pop III stars well contribute to reionization with the conventional constant escape fraction. We also find that UV photo-heating has non-negligible impact on the 21-cm global signal and the 21-cm power spectrum if the ionization fraction of the Universe is higher than roughly 1 percent. In this case, the strength of the 21-cm global signal depends on the photo-heating efficiency and thus on the Pop III star mass. We conclude that detailed modelling of Pop III stars is imperative to predict 21-cm observables accurately for future observations.
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