Fitting and Comparing Galactic Foreground Models for Unbiased 21-cm Cosmology

Accurate detection of the cosmological 21-cm global signal requires galactic foreground models that can fit spectra down to a level of ~ 20 mK or less, representing a removal of power over nearly six orders of magnitude. Rarely, however, are such models tested to this level, let alone their dependence upon model inputs like sky temperature maps. If not removed entirely, residual foreground power will bias extracted global signals. In this work, we test the ability of seven commonly employed foreground models — including a nonlinear forward-model, a linear forward-model, polynomials, and maximally-smooth polynomials — to fit highly realistic simulated mock spectra, as well as their dependence upon model inputs. The mock spectra are built from intrinsic foregrounds with realistic spatial and spectral structure, chromatic beams, horizon profiles, and discrete time-sampling. For a spectrum consisting of a single LST bin, we find that the nonlinear-forward model with 4 parameters is preferred above all other models, using a KS-test of the normalized residuals. The linear forward-model fits the mock spectra well with 6-7 parameters. The polynomial and maximally-smooth polynomial models, like those employed by the EDGES and SARAS3 global signal experiments, however, are unable to provide good fits to the mock spectra with 5 parameters, as commonly used, and instead need 11 or more parameters to produce χ_red² which are one σ from the expected value. When fitting multiple local sidereal time (LST) bins simultaneously, which applies only to the first two models, and is desirable as it decreases overlap with global signal models and thus significantly improves signal extraction, we find that the linear forward-model far outperforms the nonlinear for cases with 2, 5 and 10 LST bins. In addition, the nonlinear forward-model fails to produce any good fits to spectra with 10 LST bins, in contrast to the linear. Importantly, we also find that the KS-test consistently identifies best-fit and preferred models as opposed to the χ²_red and Bayesian evidence, especially in cases involving nonlinear forward-models.