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

The 21-cm signal from neutral hydrogen in the early universe will provide unprecedented information about the first stars and galaxies. Extracting this information, however, requires accounting for many unknown astrophysical processes. Seminumerical simulations are key for exploring the vast parameter space of said processes. These simulations use approximate techniques such as excursion-set and perturbation theory to model the 3D evolution of the intergalactic medium, at a fraction of the computational cost of hydrodynamic and/or radiative transfer simulations. However, exploring the enormous parameter space of the first galaxies can still be computationally expensive. Here, we introduce 21cmfish, a Fisher-matrix wrapper for the seminumerical simulation 21cmfast. 21cmfish facilitates efficient parameter forecasts, scaling to significantly higher dimensionalities than MCMC approaches, assuming a multivariate Gaussian posterior. Our method produces comparable parameter uncertainty forecasts to previous MCMC analyses but requires ∼104 × fewer simulations. This enables a rapid way to prototype analyses adding new physics and/or additional parameters. We carry out a forecast for HERA using the largest astrophysical parameter space to date, with 10 free parameters, spanning both population II and III star formation. We find X-ray parameters for the first galaxies could be measured to sub-per cent precision, and, though they are highly degenerate, the stellar-To-halo mass relation and ionizing photon escape fraction for population II and III galaxies can be constrained to precision (logarithmic quantities). Using a principal component analysis, we find HERA is most sensitive to the product of the ionizing escape fraction and the stellar-To-halo mass fraction for population II galaxies.