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The 21-cm signal from neutral hydrogen in the early universe will provideunprecedented information about the first stars and galaxies. Extracting thisinformation, however, requires accounting for many unknown astrophysicalprocesses. Semi-numerical simulations are key for exploring the vast parameterspace of said processes. These simulations use approximate techniques such asexcursion-set and perturbation theory to model the 3D evolution of theintergalactic medium, at a fraction of the computational cost of hydrodynamicand/or radiative transfer simulations. However, exploring the enormousparameter space of the first galaxies can still be computationally expensive.Here we introduce 21cmfish, a Fisher-matrix wrapper for the semi-numericalsimulation 21cmFAST. 21cmfish facilitates efficient parameter forecasts,scaling to significantly higher dimensionalities than MCMC approaches, assuminga multi-variate Gaussian posterior. Our method produces comparable parameteruncertainty forecasts to previous MCMC analyses but requires ~10$^4$x fewersimulations. This enables a rapid way to prototype analyses adding new physicsand/or additional parameters. We carry out a forecast for HERA using thelargest astrophysical parameter space to-date, with 10 free parameters,spanning both population II and III star formation. We find X-ray parametersfor the first galaxies could be measured to sub-percent precision, and, thoughthey are highly degenerate, the stellar-to-halo mass relation and ionizingphoton escape fraction for population II and III galaxies can be constrained to~10% precision (logarithmic quantities). Using a principal component analysiswe find HERA is most sensitive to the product of the ionizing escape fractionand the stellar-to-halo mass fraction for population II galaxies.

21cmfish: Fisher-matrix framework for fast parameter forecasts from the cosmic 21-cm signal