  The first generation of galaxies is expected to form in minihalos, accreting
gas through ${\rm H}_2$ cooling, and possessing unique properties. Although
unlikely to be directly detected in UV/infrared surveys, the radiation from
these molecular-cooling galaxies (MCGs) could leave an imprint in the 21-cm
signal from the Cosmic Dawn. Here we quantify their detectability with upcoming
radio interferometers. We generate mock 21-cm power spectra using a model for
both MCGs as well as more massive, atomic-cooling galaxies (AGCs), allowing
both populations to have different properties and scaling relations. The galaxy
parameters are chosen so as to be consistent with: (i) high-redshift UV
luminosity functions; (ii) the upper limit on the neutral fraction from QSO
spectra; (iii) the Thomson scattering optical depth to the CMB; and (iv) the
timing of the recent putative EDGES detection. The latter implies a significant
contribution of MCGs to the Cosmic Dawn, if confirmed to be cosmological. We
then perform Bayesian inference on two models including and ignoring MCG
contributions. Comparing their Bayesian evidences, we find a strong preference
for the model including MCGs, despite the fact that it has more free
parameters. This suggests that if MCGs indeed play a significant role in the
Cosmic Dawn, it should be possible to infer their properties from upcoming
21-cm power spectra. Our study illustrates how these observations can
discriminate among uncertain galaxy formation models with varying complexities,
by maximizing the Bayesian evidence.
