Impact of the Primordial Stellar Initial Mass Function on the 21-cm
  Signal
  Properties of the first generation of stars (Pop III), such as their initial
mass function (IMF), are poorly constrained by observations and have yet to
converge between simulations. The cosmological 21-cm signal of neutral hydrogen
is predicted to be sensitive to Lyman band photons produced by these stars,
thus providing a unique way to probe the first stellar population. In this
paper, we investigate the impacts of the Pop III IMF on the cosmic dawn 21-cm
signal via the Wouthysen-Field effect, Lyman-Werner feedback, Ly-alpha heating,
and CMB heating. We calculate the emission spectra of star-forming halos for
different IMFs by integrating over individual metal-free stellar spectra,
computed from a set of stellar evolution histories and stellar atmospheres, and
taking into account variability of the spectra with stellar age. Through this
study, we therefore relax two common assumptions: that the zero-age main
sequence emission rate of a Pop III star is representative of its lifetime mean
emission rate, and that Pop III emission can be treated as instantaneous.
Exploring a bottom-heavy, a top-heavy, and intermediate IMFs, we show that
variations in the 21-cm signal are driven by stars lighter than 20 solar
masses. For the explored models we find maximum relative differences of 68% in
the cosmic dawn global 21-cm signal, and 137% between power spectra. Although
this impact is modest, precise modelling of the first stars and their evolution
is necessary for accurate prediction and interpretation of the 21-cm signal.
