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 remove power over 10⁶. Although foreground and global signal models unavoidably exhibit overlap in their vector spaces inducing bias error in the extracted signal, a second source of bias and error arises from inadequate foreground models, i.e., models that cannot fit spectra down to the noise level of the signal. We therefore test the level to which seven commonly employed foreground models—including nonlinear and linear forward models, polynomials, and maximally smooth polynomials—fit realistic simulated mock foreground spectra, as well as their dependence upon model inputs. The mock spectra are synthesized for an EDGES-like experiment and we compare all models' goodness of fit and preference using a Kolmogorov–Smirnov (K-S) test of the noise-normalized residuals in order to compare models with differing, and sometimes indeterminable, degrees of freedom. For a single local sidereal time (LST) bin spectrum and p-value threshold of p = 0.05, the nonlinear forward model with four parameters is preferred (p = 0.99), while the linear forward model fits well with six to seven parameters (p = 0.94, 0.97, respectively). The polynomials and maximally smooth polynomials, like those employed by the EDGES and SARAS3 experiments, cannot produce good fits with five parameters for the experimental simulations in this work (p < 10⁻⁶). However, we find that polynomials with six parameters pass the K-S test (p = 0.4), although a nine-parameter fit produces the highest p-value (p ∼ 0.67). When fitting multiple LST bins simultaneously, we find that the linear forward model outperforms (a higher p-value) the nonlinear model for 2, 5, and 10 LST bins. Importantly, the K-S test consistently identifies best-fit and preferred models.