  The properties of the first galaxies, expected to drive the Cosmic Dawn (CD)
and the Epoch of Reionization (EoR), are encoded in the 3D structure of the
cosmic 21-cm signal. Parameter inference from upcoming 21-cm observations
promises to revolutionize our understanding of these unseen galaxies. However,
prior inference was done using models with several simplifying assumptions.
Here we introduce a flexible, physically-motivated parametrization for high-$z$
galaxy properties, implementing it in the public code 21cmFAST. In particular,
we allow their star formation rates and ionizing escape fraction to scale with
the masses of their host dark matter halos, and directly compute inhomogeneous,
sub-grid recombinations in the intergalactic medium. Combining current Hubble
observations of the rest-frame UV luminosity function (UV LFs) at high-$z$ with
a mock 1000h 21-cm observation using the Hydrogen Epoch of Reionization Arrays
(HERA), we constrain the parameters of our model using a Monte Carlo Markov
Chain sampler of 3D simulations, 21CMMC. We show that the amplitude and scaling
of the stellar mass with halo mass is strongly constrained by LF observations,
while the remaining galaxy properties are constrained mainly by 21-cm
observations. The two data sets compliment each other quite well, mitigating
degeneracies intrinsic to each observation. All eight of our astrophysical
parameters are able to be constrained at the level of $\sim 10\%$ or better.
The updated versions of 21cmFAST and 21CMMC used in this work are publicly
available.
